Two-mirror Schwarzschild aplanats. Basic relations

OpenAIRE

Terebizh, V. Yu.

2005-01-01

It is shown that the theory of aplanatic two-mirror telescopes developed by Karl Schwarzschild in 1905 leads to the unified description both the prefocal and the postfocal systems. The class of surfaces in the ZEMAX optical program has been properly extended to ascertain the image quality in exact Schwarzschild aplanats. A comparison of Schwarzschild aplanats with approximate Ritchey-Chretien and Gregory-Maksutov aplanatic telescopes reveals a noticeable advantage of the former at fast focal ...

Two-Mirror Schwarzschild Aplanats: Basic Relations

Science.gov (United States)

Terebizh, V. Yu.

2005-02-01

The theory of aplanatic two-mirror telescopes developed by Karl Schwarzschild in 1905 is shown to lead to a unified description of both prefocal and postfocal systems. The class of surfaces in the ZEMAX optical program has been properly extended to ascertain the image quality in exact Schwarzschild aplanats. A comparison of Schwarzschild aplanats with approximate Ritchey-Chrétien and Gregory-Maksutov aplanatic telescopes reveals a noticeable advantage of the former at the system’s fast focal ratio.

A Classical Based Derivation of Time Dilation Providing First Order Accuracy to Schwarzschild's Solution of Einstein's Field Equations

Science.gov (United States)

Austin, Rickey W.

provides a minimum first order accuracy to Schwarzschild's solution to Einstein's field equations.

A comment on the null geodesic equations in Schwarzschild geometry

International Nuclear Information System (INIS)

Rosa, M.A.F.; Rodrigues Junior, W.A.

1986-01-01

An integration of the null geodesic equations in the Schwarzschild geometry, which is valid to first order in GM/Rc 2 is presented. The solution is compared with others published in the literature and their range of validity is analysed. Some misunderstandings are also clarified. (Author) [pt

Interactive visualization of a thin disc around a Schwarzschild black hole

International Nuclear Information System (INIS)

Müller, Thomas; Frauendiener, Jörg

2012-01-01

In a first course in general relativity, the Schwarzschild spacetime is the most discussed analytic solution to Einstein's field equations. Unfortunately, there is rarely enough time to study the optical consequences of the bending of light for some advanced examples. In this paper, we present how the visual appearance of a thin disc around a Schwarzschild black hole can be determined interactively by means of an analytic solution to the geodesic equation processed on current high-performance graphical processing units. This approach can, in principle, be customized for any other thin disc in a spacetime with geodesics given in closed form. The interactive visualization discussed here can be used either in a first course in general relativity for demonstration purposes only or as a thesis for an enthusiastic student in an advanced course with some basic knowledge of OpenGL and a programming language. (paper)

Features and stability analysis of non-Schwarzschild black hole in quadratic gravity

International Nuclear Information System (INIS)

Cai, Yi-Fu; Zhang, Hezi; Liu, Junyu; Cheng, Gong; Wang, Min

2016-01-01

Black holes are found to exist in gravitational theories with the presence of quadratic curvature terms and behave differently from the Schwarzschild solution. We present an exhaustive analysis for determining the quasinormal modes of a test scalar field propagating in a new class of black hole backgrounds in the case of pure Einstein-Weyl gravity. Our result shows that the field decay of quasinormal modes in such a non-Schwarzschild black hole behaves similarly to the Schwarzschild one, but the decay slope becomes much smoother due to the appearance of the Weyl tensor square in the background theory. We also analyze the frequencies of the quasinormal modes in order to characterize the properties of new back holes, and thus, if these modes can be the source of gravitational waves, the underlying theories may be testable in future gravitational wave experiments. We briefly comment on the issue of quantum (in)stability in this theory at linear order.

Distortion of Schwarzschild-anti-de Sitter black holes to black strings

International Nuclear Information System (INIS)

Tomimatsu, Akira

2005-01-01

Motivated by the existence of black holes with various topologies in four-dimensional spacetimes with a negative cosmological constant, we study axisymmetric static solutions describing any large distortions of Schwarzschild-anti-de Sitter black holes parametrized by the mass m. Under the approximation such that m is much larger than the anti-de Sitter radius, it is found that a cylindrically symmetric black string is obtained as a special limit of distorted spherical black holes. Such a prolonged distortion of the event horizon connecting a Schwarzschild-anti-de Sitter black hole to a black string is allowed without violating both the usual black hole thermodynamics and the hoop conjecture for the horizon circumference

Relativistic positioning in Schwarzschild space-time

International Nuclear Information System (INIS)

Puchades, Neus; Sáez, Diego

2015-01-01

In the Schwarzschild space-time created by an idealized static spherically symmetric Earth, two approaches -based on relativistic positioning- may be used to estimate the user position from the proper times broadcast by four satellites. In the first approach, satellites move in the Schwarzschild space-time and the photons emitted by the satellites follow null geodesics of the Minkowski space-time asymptotic to the Schwarzschild geometry. This assumption leads to positioning errors since the photon world lines are not geodesics of any Minkowski geometry. In the second approach -the most coherent one- satellites and photons move in the Schwarzschild space-time. This approach is a first order one in the dimensionless parameter GM/R (with the speed of light c=1). The two approaches give different inertial coordinates for a given user. The differences are estimated and appropriately represented for users located inside a great region surrounding Earth. The resulting values (errors) are small enough to justify the use of the first approach, which is the simplest and the most manageable one. The satellite evolution mimics that of the GALILEO global navigation satellite system. (paper)

First integrals of geodesics in the Einstein-Schwarzschild space

International Nuclear Information System (INIS)

Meshkov, A.G.; Dordzhiev, P.B.

1984-01-01

Linear and quadratic velocity integrals of geodesics in the Einstein-Schwarzschild space are calculated. The Schwarzschild geodesics equations have only four independent linear integrals. Quadratic integrals are polynomials from linear ones with constant coefficients. Total separation of variables in the Hamilton-Jacobi equation with Schwarzschild metric is possible only in two coordinate systems: ''spherical'' and ''conic'' systems

Initial data sets for the Schwarzschild spacetime

International Nuclear Information System (INIS)

Gomez-Lobo, Alfonso Garcia-Parrado; Kroon, Juan A. Valiente

2007-01-01

A characterization of initial data sets for the Schwarzschild spacetime is provided. This characterization is obtained by performing a 3+1 decomposition of a certain invariant characterization of the Schwarzschild spacetime given in terms of concomitants of the Weyl tensor. This procedure renders a set of necessary conditions--which can be written in terms of the electric and magnetic parts of the Weyl tensor and their concomitants--for an initial data set to be a Schwarzschild initial data set. Our approach also provides a formula for a static Killing initial data set candidate--a KID candidate. Sufficient conditions for an initial data set to be a Schwarzschild initial data set are obtained by supplementing the necessary conditions with the requirement that the initial data set possesses a stationary Killing initial data set of the form given by our KID candidate. Thus, we obtain an algorithmic procedure of checking whether a given initial data set is Schwarzschildean or not

Interactive Visualization of a Thin Disc around a Schwarzschild Black Hole

Science.gov (United States)

Muller, Thomas; Frauendiener, Jorg

2012-01-01

In a first course in general relativity, the Schwarzschild spacetime is the most discussed analytic solution to Einstein's field equations. Unfortunately, there is rarely enough time to study the optical consequences of the bending of light for some advanced examples. In this paper, we present how the visual appearance of a thin disc around a…

The scalar wave equation in a Schwarzschild space-time

International Nuclear Information System (INIS)

Schmidt, B.G.; Stewart, J.M.

1979-01-01

This paper studies the asymptotic behaviour of solutions of the zero rest mass scalar wave equation in the Schwarzschild space-time in a neighbourhood of spatial infinity which includes parts of future and pass null infinity. The behaviour of such fields is essentially different from that which occurs in a flat space-time. In particular fields which have a Bondi-type expansion in powers of 'r(-1)' near past null infinity do not have such an expansion near future null infinity. Further solutions which have physically reasonable Cauchy data probably fail to have Bondi-type expansions near null infinity. (author)

Quadratic curvature terms and deformed Schwarzschild–de Sitter black hole analogues in the laboratory

Directory of Open Access Journals (Sweden)

R. da Rocha

2017-12-01

Full Text Available Sound waves on a fluid stream, in a de Laval nozzle, are shown to correspond to quasinormal modes emitted by black holes that are physical solutions in a quadratic curvature gravity with cosmological constant. Sound waves patterns in transsonic regimes at a laboratory are employed here to provide experimental data regarding generalized theories of gravity, comprised by the exact de Sitter-like solution and a perturbative solution around the Schwarzschild–de Sitter standard solution as well. Using the classical tests of General Relativity to bound free parameters in these solutions, acoustic perturbations on fluid flows in nozzles are then regarded, to study quasinormal modes of these black holes solutions, providing deviations of the de Laval nozzle cross-sectional area, when compared to the Schwarzschild solution. The fluid sonic point in the nozzle, for sound waves in the fluid, is shown to implement the acoustic event horizon corresponding to quasinormal modes. Keywords: Black holes, Fluid branes, Fluid dynamics, Quadratic curvature gravity, de Laval nozzle

Nonexistence theorems for Yang-Mills fields and harmonic maps in the Schwarzschild spacetime

International Nuclear Information System (INIS)

Hu Hesheng

1987-01-01

The nonexistence of static solutions to pure Yang-Mills equations and nonconstant harmonic maps defined on the Schwarzschild spacetime outside the black hole (r>2M) is considered. Nonexistence theorems for pure Yang-Mills equations and harmonic maps in the region r≥5M and r≥3M are obtained, respectively. (orig.)

Exact optics - III. Schwarzschild's spectrograph camera revised

Science.gov (United States)

Willstrop, R. V.

2004-03-01

Karl Schwarzschild identified a system of two mirrors, each defined by conic sections, free of third-order spherical aberration, coma and astigmatism, and with a flat focal surface. He considered it impractical, because the field was too restricted. This system was rediscovered as a quadratic approximation to one of Lynden-Bell's `exact optics' designs which have wider fields. Thus the `exact optics' version has a moderate but useful field, with excellent definition, suitable for a spectrograph camera. The mirrors are strongly aspheric in both the Schwarzschild design and the exact optics version.

1st Karl Schwarzschild Meeting on Gravitational Physics

CERN Document Server

Kaminski, Matthias; Mureika, Jonas; Bleicher, Marcus

2016-01-01

These proceedings collect the selected contributions of participants of the First Karl Schwarzschild Meeting on Gravitational Physics, held in Frankfurt, Germany to celebrate the 140th anniversary of Schwarzschild's birth. They are grouped into 4 main themes: I. The Life and Work of Karl Schwarzschild; II. Black Holes in Classical General Relativity, Numerical Relativity, Astrophysics, Cosmology, and Alternative Theories of Gravity; III. Black Holes in Quantum Gravity and String Theory; IV. Other Topics in Contemporary Gravitation. Inspired by the foundational principle ``By acknowledging the past, we open a route to the future",  the week-long meeting, envisioned as a forum for exchange between scientists from all locations and levels of education, drew participants from 15 countries across 4 continents. In addition to plenary talks from leading researchers, a special focus on young talent was provided, a feature underlined by the Springer Prize for the best student and junior presentations.

Temperature and entropy of Schwarzschild-de Sitter space-time

International Nuclear Information System (INIS)

Shankaranarayanan, S.

2003-01-01

In the light of recent interest in quantum gravity in de Sitter space, we investigate semiclassical aspects of four-dimensional Schwarzschild-de Sitter space-time using the method of complex paths. The standard semiclassical techniques (such as Bogoliubov coefficients and Euclidean field theory) have been useful to study quantum effects in space-times with single horizons; however, none of these approaches seem to work for Schwarzschild-de Sitter space-time or, in general, for space-times with multiple horizons. We extend the method of complex paths to space-times with multiple horizons and obtain the spectrum of particles produced in these space-times. We show that the temperature of radiation in these space-times is proportional to the effective surface gravity--the inverse harmonic sum of surface gravity of each horizon. For the Schwarzschild-de Sitter space-time, we apply the method of complex paths to three different coordinate systems--spherically symmetric, Painleve, and Lemaitre. We show that the equilibrium temperature in Schwarzschild-de Sitter space-time is the harmonic mean of cosmological and event horizon temperatures. We obtain Bogoliubov coefficients for space-times with multiple horizons by analyzing the mode functions of the quantum fields near the horizons. We propose a new definition of entropy for space-times with multiple horizons, analogous to the entropic definition for space-times with a single horizon. We define entropy for these space-times to be inversely proportional to the square of the effective surface gravity. We show that this definition of entropy for Schwarzschild-de Sitter space-time satisfies the D-bound conjecture

Statistical Entropy of Schwarzschild Black Holes

CERN Document Server

Englert, F

1998-01-01

The entropy of a seven dimensional Schwarzschild black hole of arbitrary large radius is obtained by a mapping onto a near extremal self-dual three-brane whose partition function can be evaluated. The three-brane arises from duality after submitting a neutral blackbrane, from which the Schwarzschild black hole can be obtained by compactification, to an infinite boost in non compact eleven dimensional space-time and then to a Kaluza-Klein compactification. This limit can be defined in precise terms and yields the Beckenstein-Hawking value up to a factor of order one which can be set to be exactly one with the extra assumption of keeping only transverse brane excitations. The method can be generalized to five and four dimensional black holes.

Covariant perturbations of Schwarzschild black holes

International Nuclear Information System (INIS)

Clarkson, Chris A; Barrett, Richard K

2003-01-01

We present a new covariant and gauge-invariant perturbation formalism for dealing with spacetimes having spherical symmetry (or some preferred spatial direction) in the background, and apply it to the case of gravitational wave propagation in a Schwarzschild black-hole spacetime. The 1 + 3 covariant approach is extended to a '1 + 1 + 2 covariant sheet' formalism by introducing a radial unit vector in addition to the timelike congruence, and decomposing all covariant quantities with respect to this. The background Schwarzschild solution is discussed and a covariant characterization is given. We give the full first-order system of linearized 1 + 1 + 2 covariant equations, and we show how, by introducing (time and spherical) harmonic functions, these may be reduced to a system of first-order ordinary differential equations and algebraic constraints for the 1 + 1 + 2 variables which may be solved straightforwardly. We show how both odd- and even-parity perturbations may be unified by the discovery of a covariant, frame- and gauge-invariant, transverse-traceless tensor describing gravitational waves, which satisfies a covariant wave equation equivalent to the Regge-Wheeler equation for both even- and odd-parity perturbations. We show how the Zerilli equation may be derived from this tensor, and derive a similar transverse-traceless tensor equation equivalent to this equation. The so-called special quasinormal modes with purely imaginary frequency emerge naturally. The significance of the degrees of freedom in the choice of the two frame vectors is discussed, and we demonstrate that, for a certain frame choice, the underlying dynamics is governed purely by the Regge-Wheeler tensor. The two transverse-traceless Weyl tensors which carry the curvature of gravitational waves are discussed, and we give the closed system of four first-order ordinary differential equations describing their propagation. Finally, we consider the extension of this work to the study of

Traversable Schwarzschild-like wormholes

Energy Technology Data Exchange (ETDEWEB)

Cataldo, Mauricio [Universidad del Bio-Bio, Departamento de Fisica, Facultad de Ciencias, Concepcion (Chile); Grupo de Cosmologia y Gravitacion-UBB, Concepcion (Chile); Liempi, Luis [Universidad de Concepcion, Departamento de Fisica, Concepcion (Chile); Universidad San Sebastian, Facultad de Ingenieria y Tecnologia, Concepcion (Chile); Rodriguez, Pablo [Universidad de Concepcion, Departamento de Fisica, Concepcion (Chile)

2017-11-15

In this paper we study relativistic static traversable wormhole solutions which are a slight generalization of Schwarzschild wormholes. In order to do this we assume a shape function with a linear dependence on the radial coordinate r. This linear shape function generates wormholes whose asymptotic spacetime is not flat: they are asymptotically locally flat, since in the asymptotic limit r → ∞ spacetimes exhibiting a solid angle deficit (or excess) are obtained. In particular, there exist wormholes which connect two asymptotically non-flat regions with a solid angle deficit. For these wormholes the size of their embeddings in a three-dimensional Euclidean space extends from the throat to infinity. A new phantom zero-tidal-force wormhole exhibiting such asymptotic is obtained. On the other hand, if a solid angle excess is present, the size of the wormhole embeddings depends on the amount of this angle excess, and the energy density is negative everywhere. We discuss the traversability conditions and study the impact of the β-parameter on the motion of a traveler when the wormhole throat is crossed. A description of the geodesic behavior for the wormholes obtained is also presented. (orig.)

Traversable Schwarzschild-like wormholes

International Nuclear Information System (INIS)

Cataldo, Mauricio; Liempi, Luis; Rodriguez, Pablo

2017-01-01

In this paper we study relativistic static traversable wormhole solutions which are a slight generalization of Schwarzschild wormholes. In order to do this we assume a shape function with a linear dependence on the radial coordinate r. This linear shape function generates wormholes whose asymptotic spacetime is not flat: they are asymptotically locally flat, since in the asymptotic limit r → ∞ spacetimes exhibiting a solid angle deficit (or excess) are obtained. In particular, there exist wormholes which connect two asymptotically non-flat regions with a solid angle deficit. For these wormholes the size of their embeddings in a three-dimensional Euclidean space extends from the throat to infinity. A new phantom zero-tidal-force wormhole exhibiting such asymptotic is obtained. On the other hand, if a solid angle excess is present, the size of the wormhole embeddings depends on the amount of this angle excess, and the energy density is negative everywhere. We discuss the traversability conditions and study the impact of the β-parameter on the motion of a traveler when the wormhole throat is crossed. A description of the geodesic behavior for the wormholes obtained is also presented. (orig.)

Kerr generalized solution

International Nuclear Information System (INIS)

Papoyan, V.V.

1989-01-01

A Kerr generalized solution for a stationary axially-symmetric gravitational field of rotating self-gravitational objects is given. For solving the problem Einstein equations and their combinations are used. The particular cases: internal and external Schwarzschild solutions are considered. The external solution of the stationary problem is a Kerr solution generalization. 3 refs

Quantum field theory in Schwarzschild and Rindler spaces

International Nuclear Information System (INIS)

Boulware, D.G.

1975-01-01

The problem of defining a scalar quantum field in the space-times described by the Schwarzschild and Rindler metrics is discussed. The matrix elements of the field operators are found by calculating the Green's functions for the fields. The requirement of positive frequencies for asymptotic timelike separations combined with a careful analysis of the continuity conditions at the event horizons yields a unique prescription for the Green's function. This in turn defines the vacuum state. In the Schwarzschild space the vacuum is shown to be stable and the lowest-energy state. In the Rindler space the quantization procedure yields the same results as quantization in Minkowski coordinates

Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole

Directory of Open Access Journals (Sweden)

G. Abbas

2014-01-01

Full Text Available Few years ago, Setare (2006 has investigated the Cardy-Verlinde formula of noncommutative black hole obtained by noncommutativity of coordinates. In this paper, we apply the same procedure to a noncommutative black hole obtained by the coordinate coherent approach. The Cardy-Verlinde formula is entropy formula of conformal field theory in an arbitrary dimension. It relates the entropy of conformal field theory to its total energy and Casimir energy. In this paper, we have calculated the total energy and Casimir energy of noncommutative Schwarzschild black hole and have shown that entropy of noncommutative Schwarzschild black hole horizon can be expressed in terms of Cardy-Verlinde formula.

Quantitative properties of the Schwarzschild metric

Czech Academy of Sciences Publication Activity Database

Křížek, Michal; Křížek, Filip

2018-01-01

Roč. 2018, č. 1 (2018), s. 1-10 Institutional support: RVO:67985840 Keywords : exterior and interior Schwarzschild metric * proper radius * coordinate radius Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics http://astro.shu-bg.net/pasb/index_files/Papers/2018/SCHWARZ8.pdf

Circular orbits in cosmic string and Schwarzschild-AdS spacetime with Fermi-Walker transport

International Nuclear Information System (INIS)

Bakke, K.; Furtado, C.; Carvalho, A.M. de

2009-01-01

In this paper we discuss the Fermi-Walker transport of vectors along orbits in cosmic string and Schwarzschild-AdS spacetimes. We analyze the influence of acceleration on these holonomies. An effect similar to Thomas precession is observed within the process of Fermi-Walker transport along these circular orbits which are studied in the limit of vanishing cosmological constant in Schwarzschild-AdS case; also we obtain Fermi-Walker transport in a Schwarzschild background. In the case of a Schwarzschild spacetime, we analyze the quantized band holonomy invariance. In the limit of zero acceleration we recover the well-known results for holonomy matrix obtained by parallel transport in all these spacetimes. (orig.)

Un-graviton corrections to the Schwarzschild black hole

International Nuclear Information System (INIS)

Gaete, Patricio; Helayel-Neto, Jose A.; Spallucci, Euro

2010-01-01

We introduce an effective action smoothly extending the standard Einstein-Hilbert action to include un-gravity effects. The improved field equations are solved for the un-graviton corrected Schwarzschild geometry reproducing the Mureika result. This is an important test to confirm the original 'guess' of the form of the un-Schwarzschild metric. Instead of working in the weak field approximation and 'dressing' the Newtonian potential with un-gravitons, we solve the 'effective Einstein equations' including all order un-gravity effects. An unexpected 'bonus' of accounting un-gravity effects is the fractalisation of the event horizon. In the un-gravity dominated regime the event horizon thermodynamically behaves as fractal surface of dimensionality twice the scale dimension d U .

Classical solutions in supergravity

International Nuclear Information System (INIS)

Baaklini, N.S.; Ferrara, S.; Nieuwenhuizen Van, P.

1977-06-01

Classical solutions of supergravity are obtained by making finite global supersymmetry rotation on known solutions of the field equations of the bosonic sector. The Schwarzschild and the Reissner-Nordstoem solutions of general relativity are extended to various supergravity systems and the modification to the perihelion precession of planets is discussed

3rd Karl Schwarzschild Meeting - Gravity and the Gauge/Gravity Correspondence

Science.gov (United States)

Nicolini, Piero; Kaminski, Matthias; Mureika, Jonas; Bleicher, Marcus

2018-01-01

The Karl Schwarzschild Meeting 2017 (KSM2017) has been the third instalment of the conference dedicated to the great Frankfurter scientist, who derived the first black hole solution of Einstein's equations about 100 years ago. The event has been a 5 day meeting in the field of black holes, AdS/CFT correspondence and gravitational physics. Like the two previous instalments, the conference continued to attract a stellar ensemble of participants from the world's most renowned institutions. The core of the meeting has been a series of invited talks from eminent experts (keynote speakers) as well as the presence of plenary research talks by students and junior speakers.

The stable problem of the black-hole connected region in the Schwarzschild black hole

OpenAIRE

Tian, Guihua

2005-01-01

The stability of the Schwarzschild black hole is studied. Using the Painlev\\'{e} coordinate, our region can be defined as the black-hole-connected region(r>2m, see text) of the Schwarzschild black hole or the white-hole-connected region(r>2m, see text) of the Schwarzschild black hole. We study the stable problems of the black-hole-connected region. The conclusions are: (1) in the black-hole-connected region, the initially regular perturbation fields must have real frequency or complex frequen...

Curved spaces before Einstein: Karl Schwarzschild's cosmological speculations and the beginnings of relativistic cosmology (German Title: Gekrümmte Universen vor Einstein: Karl Schwarzschilds kosmologische Spekulationen und die Anfänge der relativistischen Kosmologie)

Science.gov (United States)

Schemmel, Matthias

In contrast to most of his collegues in astronomy and physics, the German astronomer Karl Schwarzschild immediately recognized the significance of general relativity for physics and astronomy, and played a pioneering role in its early development. In this contribution, it is argued that the clue for understanding Schwarzschild's exceptional reaction to general relativity lies in the study of his prerelativistic work. Long before the rise of general relativity, Schwarzschild occupied himself with foundational problems on the borderline of physics, astronomy, and mathematics that, from today's perspective, belong to the field of problems of that theory. In this contribution, the example of Schwarzschild's early speculations about the non-Euclidean nature of physical space on cosmological scales is presented and their reflection in his reception of general relativity is discussed.

Hawking radiation from four-dimensional Schwarzschild black holes in M theory

International Nuclear Information System (INIS)

Das, S.R.; Mathur, S.D.; Ramadevi, P.

1999-01-01

Recently a method has been developed for relating four dimensional Schwarzschild black holes in M theory to near-extremal black holes in string theory with four charges, using suitably defined open-quotes boostsclose quotes and T dualities. We show that this method can be extended to obtain the emission rate of low energy massless scalars for the four dimensional Schwarzschild hole from the microscopic picture of radiation from the near extremal hole. copyright 1999 The American Physical Society

Characteristics of transonic spherical symmetric accretion flow in Schwarzschild-de Sitter and Schwarzschild anti-de Sitter backgrounds, in pseudo-general relativistic paradigm

Science.gov (United States)

Ghosh, Shubhrangshu; Banik, Prabir

2015-07-01

In this paper, we present a complete work on steady state spherically symmetric Bondi type accretion flow in the presence of cosmological constant (Λ) in both Schwarzschild-de Sitter (SDS) and Schwarzschild anti-de Sitter (SADS) backgrounds considering an isolated supermassive black hole (SMBH), with the inclusion of a simple radiative transfer scheme, in the pseudo-general relativistic paradigm. We do an extensive analysis on the transonic behavior of the Bondi type accretion flow onto the cosmological BHs including a complete analysis of the global parameter space and the stability of flow, and do a complete study of the global family of solutions for a generic polytropic flow. Bondi type accretion flow in SADS background renders multiplicity in its transonic behavior with inner "saddle" type and outer "center" type sonic points, with the transonic solutions forming closed loops or contours. There is always a limiting value for ∣Λ∣ up to which we obtain valid stationary transonic solutions, which correspond to both SDS and SADS geometries; this limiting value moderately increases with the increasing radiative efficiency of the flow, especially correspond to Bondi type accretion flow in SADS background. Repulsive Λ suppresses the Bondi accretion rate by an order of magnitude for relativistic Bondi type accretion flow for a certain range in temperature, and with a marginal increase in the Bondi accretion rate if the corresponding accretion flow occurs in SADS background. However, for a strongly radiative Bondi type accretion flow with high mass accretion rate, the presence of cosmological constant do not much influence the corresponding Bondi accretion rate of the flow. Our analysis show that the relic cosmological constant has a substantial effect on Bondi type accretion flow onto isolated SMBHs and their transonic solutions beyond length-scale of kiloparsecs, especially if the Bondi type accretion occurs onto the host supergiant ellipticals or central

Ricci solitons, Ricci flow and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua

International Nuclear Information System (INIS)

Figueras, Pau; Lucietti, James; Wiseman, Toby

2011-01-01

The elliptic Einstein-DeTurck equation may be used to numerically find Einstein metrics on Riemannian manifolds. Static Lorentzian Einstein metrics are considered by analytically continuing to Euclidean time. The Ricci-DeTurck flow is a constructive algorithm to solve this equation, and is simple to implement when the solution is a stable fixed point, the only complication being that Ricci solitons may exist which are not Einstein. Here we extend previous work to consider the Einstein-DeTurck equation for Riemannian manifolds with boundaries, and those that continue to static Lorentzian spacetimes which are asymptotically flat, Kaluza-Klein, locally AdS or have extremal horizons. Using a maximum principle, we prove that Ricci solitons do not exist in these cases and so any solution is Einstein. We also argue that the Ricci-DeTurck flow preserves these classes of manifolds. As an example, we simulate the Ricci-DeTurck flow for a manifold with asymptotics relevant for AdS 5 /CFT 4 . Our maximum principle dictates that there are no soliton solutions, and we give strong numerical evidence that there exists a stable fixed point of the flow which continues to a smooth static Lorentzian Einstein metric. Our asymptotics are such that this describes the classical gravity dual relevant for the CFT on a Schwarzschild background in either the Unruh or Boulware vacua. It determines the leading O(N 2 c ) part of the CFT stress tensor, which interestingly is regular on both the future and past Schwarzschild horizons. (paper)

Quasinormal modes of Schwarzschild black holes: Defined and calculated via Laplace transformation

International Nuclear Information System (INIS)

Nollert, H.; Schmidt, B.G.

1992-01-01

Quasinormal modes play a prominent role in the literature when dealing with the propagation of linearized perturbations of the Schwarzschild geometry. We show that space-time properties of the solutions of the perturbation equation imply the existence of a unique Green's function of the Laplace-transformed wave equation. This Green's function may be constructed from solutions of the homogeneous time-independent equation, which are uniquely characterized by the boundary conditions they satisfy. These boundary conditions are identified as the boundary conditions usually imposed for quasinormal-mode solutions. It turns out that solutions of the homogeneous equation exist which satisfy these boundary conditions at the horizon and at spatial infinity simultaneously, leading to poles of the Green's function. We therefore propose to define quasinormal-mode frequencies as the poles of the Green's function for the Laplace-transformed equation. On the basis of this definition a new technique for the numerical calculation of quasinormal frequencies is developed. The results agree with computations of Leaver, but not with more recent results obtained by Guinn, Will, Kojima, and Schutz

Gauge-invariant non-spherical metric perturbations of Schwarzschild black-hole spacetimes

International Nuclear Information System (INIS)

Nagar, Alessandro; Rezzolla, Luciano

2005-01-01

The theory of gauge-invariant non-spherical metric perturbations of Schwarzschild black-hole spacetimes is now well established. Yet, as different notations and conventions have been used throughout the years, the literature on the subject is often confusing and sometimes confused. The purpose of this review is to review and collect the relevant expressions related to the Regge-Wheeler and Zerilli equations for the odd and even-parity perturbations of a Schwarzschild spacetime. Special attention is paid to the form they assume in the presence of matter-sources and, for the two most popular conventions in the literature, to the asymptotic expressions and gravitational-wave amplitudes. Besides pointing out some inconsistencies in the literature, the expressions collected here could serve as a quick reference for the calculation of the perturbations of a Schwarzschild black-hole spacetime driven by generic sources and for those approaches in which gravitational waves are extracted from numerically generated spacetimes. (topical review)

Scattering and absorption of electromagnetic waves by a Schwarzschild black hole

International Nuclear Information System (INIS)

Fabbri, R.

1975-01-01

The scattering and absorption of electromagnetic waves by a spherically symmetric nonrotating black hole is studied in the Schwarzschild background, by means of the known expansion of the modified Debye potentials in partial waves. The power reflection coefficients and the phase shifts of the partial waves are evaluated at both high and low frequencies. Then the scattering and absorption cross sections of the black hole are determined. It is shown that the black hole is almost unable to absorb electromagnetic waves when the wave length of the radiation is greater than the Schwarzschild radius

The Schwarzschild effect of the dosimetry film Kodak EDR 2.

Science.gov (United States)

Djouguela, A; Kollhoff, R; Rubach, A; Harder, D; Poppe, B

2005-11-07

The magnitude of the Schwarzschild effect or failure of the reciprocity law has been experimentally investigated for the dosimetry film EDR 2 from Kodak. When the dose rate applied to achieve a given dose was reduced by a factor of 12, the net optical density was reduced by up to 5%. The clinical importance of this effect is negligible as long as the films are calibrated at a value of the dose rate approximately representative of the dose rates occurring in the target volume, but in target regions of strongly reduced dose rate the Schwarzschild effect should be allowed for by a correction of the net optical density.

Taub-NUT spinless particles and Schwarzschild spinning particles

International Nuclear Information System (INIS)

Bini, D.; La Sapienza Univ., Rome

2005-01-01

The effect of a small gravitomagnetic monopole on (accelerated) circular orbits in the equatorial plane of the Taub-NUT space-time is compared to the corresponding (accelerated) orbits pushed slightly off the equatorial plane in the absence of the monopole (Schwarzschild space-time)

Quasinormal Modes of a Quantum-Corrected Schwarzschild Black ...

Indian Academy of Sciences (India)

Chunyan Wang

2017-11-27

Nov 27, 2017 ... Abstract. In this work, we investigate the electromagnetic perturbation around a quantum-corrected. Schwarzschild black hole. The complex frequencies of the quasinormal modes are evaluated by the third- order WKB approximation. The numerical results obtained showed that the complex frequencies ...

Space–time and spatial geodesic orbits in Schwarzschild geometry

Science.gov (United States)

Resca, Lorenzo

2018-05-01

Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit equations for a proper spatial submanifold of Schwarzschild metric at any given coordinate-time correspond to an unphysical gravitational repulsion in the non-relativistic limit. This demonstrates at a basic level the centrality and critical role of relativistic time and its intimate pseudo-Riemannian connection with space. Correspondingly, a commonly popularised depiction of geodesic orbits of planets as resulting from the curvature of space produced by the Sun, represented as a rubber sheet dipped in the middle by the weighing of that massive body, is mistaken and misleading for the essence of relativity, even in the non-relativistic limit.

Embeddings for the Schwarzschild metric: classification and new results

International Nuclear Information System (INIS)

Paston, S A; Sheykin, A A

2012-01-01

We suggest a method to search the embeddings of Riemannian spaces with a high enough symmetry in a flat ambient space. It is based on a procedure of construction surfaces with a given symmetry. The method is used to classify the embeddings of the Schwarzschild metric which have the symmetry of this solution, and all such embeddings in a six-dimensional ambient space (i.e. a space with a minimal possible dimension) are constructed. Four of the six possible embeddings are already known, while the two others are new. One of the new embeddings is asymptotically flat, while the other embeddings in a six-dimensional ambient space do not have this property. The asymptotically flat embedding can be of use in the analysis of the many-body problem, as well as for the development of gravity description as a theory of a surface in a flat ambient space. (paper)

Constant scalar curvature hypersurfaces in extended Schwarzschild space-time

International Nuclear Information System (INIS)

Pareja, M. J.; Frauendiener, J.

2006-01-01

We present a class of spherically symmetric hypersurfaces in the Kruskal extension of the Schwarzschild space-time. The hypersurfaces have constant negative scalar curvature, so they are hyperboloidal in the regions of space-time which are asymptotically flat

Karl Schwarzschild and the professionalization of astrophysics. (German Title: Karl Schwarzschild und die Professionalisierung der Astrophysik)

Science.gov (United States)

Schmidt-Kaler, Theodor

Professionalization is characteristic for physics and astronomy since 1830, and forms the basis for their rapid evolution in the 20th century. Karl Schwarzschild's contributions to professionalization of astronomy are presented: the introduction of course lectures in a repeating cycle, a permanent astrophysical laboratory, a tight connection between teaching and research, simulations and suggestions for astronomy at high schools and for the training of high school teachers, an interest in international organisation, and the initiative and planning of a southern observatory.

Singular Minkowski and Euclidean solutions for SU(2) Yang-Mills theory

International Nuclear Information System (INIS)

Singleton, D.

1996-01-01

In this paper it is examined a solution to the SU(2) Yang-Mills-Higgs system, which is a trivial mathematical extension of recently discovered Schwarzschild- like solutions (Singleton D., Phys. Rev. D, 51 (1955) 5911). Physically, however, this new solution has drastically different properties from the Schwarzschild-like solutions. It is also studied a new classical solution for Euclidean SU(2) Yang-Mills theory. Again this new solution is a mathematically trivial extension of the Belavin-Polyakov-Schwartz-Tyupkin (BPST) (Belavin A. A. et al., Phys. Lett. B, 59 (1975) 85) instanton, but is physically very different. Unlike the usual instanton solution, the present solution is singular on a sphere of arbitrary radius in Euclidean space. Both of these solutions are infinite-energy solutions, so their practical value is somewhat unclear. However, they may be useful in exploring some of the mathematical aspects of classical Yang-Mills theory

Three Göttingen lectures by Karl Schwarzschild, 1904-1905. (German Title: Drei Göttinger Vorlesungen Karl Schwarzschilds 1904-1905)

Science.gov (United States)

Schmidt-Kaler, Theodor

Karl Schwarzschild (1873-1916), perhaps the most eminent astronomer of his time, was professor at Göttingen University from 1901 to 1909. Three of his lectures from the years 1904 to 1906 are available in the form of copy-books written by his students Arnold Kohlschütter (1883-1969) and Max Born (1882-1970). Here, an overview of these lectures is given.

Classroom reconstruction of the Schwarzschild metric

OpenAIRE

Kassner, Klaus

2015-01-01

A promising way to introduce general relativity in the classroom is to study the physical implications of certain given metrics, such as the Schwarzschild one. This involves lower mathematical expenditure than an approach focusing on differential geometry in its full glory and permits to emphasize physical aspects before attacking the field equations. Even so, in terms of motivation, lacking justification of the metric employed may pose an obstacle. The paper discusses how to establish the we...

Isotropic extensions of the vacuum solutions in general relativity

Energy Technology Data Exchange (ETDEWEB)

Molina, C. [Universidade de Sao Paulo (USP), SP (Brazil); Martin-Moruno, Prado [Victoria University of Wellington (New Zealand); Gonzalez-Diaz, Pedro F. [Consejo Superior de Investigaciones Cientificas, Madrid (Spain)

2012-07-01

Full text: Spacetimes described by spherically symmetric solutions of Einstein's equations are of paramount importance both in astrophysical applications and theoretical considerations. And among those, black holes are highlighted. In vacuum, Birkhoff's theorem and its generalizations to non-asymptotically flat cases uniquely fix the metric as the Schwarzschild, Schwarzschild-de Sitter or Schwarzschild-anti-de Sitter geometries, the vacuum solutions of the usual general relativity with zero, positive or negative values for the cosmological constant, respectively. In this work we are mainly interested in black holes in a cosmological environment. Of the two main assumptions of the cosmological principle, homogeneity is lost when compact objects are considered. Nevertheless isotropy is still possible, and we enforce this condition. Within this context, we investigate spatially isotropic solutions close - continuously deformable - to the usual vacuum solutions. We obtain isotropic extensions of the usual spherically symmetric vacuum geometries in general relativity. Exact and perturbative solutions are derived. Maximal extensions are constructed and their causal structures are discussed. The classes of geometries obtained include black holes in compact and non-compact universes, wormholes in the interior region of cosmological horizons, and anti-de Sitter geometries with excess/deficit solid angle. The tools developed here are applicable in more general contexts, with extensions subjected to other constraints. (author)

Resolving the Schwarzschild singularity in both classic and quantum gravity

Directory of Open Access Journals (Sweden)

Ding-fang Zeng

2017-04-01

Full Text Available The Schwarzschild singularity's resolution has key values in cracking the key mysteries related with black holes, the origin of their horizon entropy and the information missing puzzle involved in their evaporations. We provide in this work the general dynamic inner metric of collapsing stars with horizons and with non-trivial radial mass distributions. We find that static central singularities are not the final state of the system. Instead, the final state of the system is a periodically zero-cross breathing ball. Through 3+1 decomposed general relativity and its quantum formulation, we establish a functional Schrödinger equation controlling the micro-state of this breathing ball and show that, the system configuration with all the matter concentrating on the central point is not the unique eigen-energy-density solution. Using a Bohr–Sommerfield like “orbital” quantisation assumption, we show that for each black hole of horizon radius rh, there are about erh2/ℓpl2 allowable eigen-energy-density profiles. This naturally leads to physic interpretations for the micro-origin of horizon entropy, as well as solutions to the information missing puzzle involved in Hawking radiations.

The golden ratio in Schwarzschild-Kottler black holes

Energy Technology Data Exchange (ETDEWEB)

Cruz, Norman [Universidad de Santiago de Chile, Departamento de Fisica, Facultad de Ciencia, Santiago 2 (Chile); Olivares, Marco [Universidad Diego Portales, Facultad de Ingenieria, Santiago (Chile); Villanueva, J.R. [Universidad de Valparaiso, Instituto de Fisica y Astronomia, Valparaiso (Chile)

2017-02-15

In this paper we show that the golden ratio is present in the Schwarzschild-Kottler metric. For null geodesics with maximal radial acceleration, the turning points of the orbits are in the golden ratio Φ = (√(5)-1)/2. This is a general result which is independent of the value and sign of the cosmological constant Λ. (orig.)

Thermodynamic phase transition in the rainbow Schwarzschild black hole

International Nuclear Information System (INIS)

Gim, Yongwan; Kim, Wontae

2014-01-01

We study the thermodynamic phase transition in the rainbow Schwarzschild black hole where the metric depends on the energy of the test particle. Identifying the black hole temperature with the energy from the modified dispersion relation, we obtain the modified entropy and thermodynamic energy along with the modified local temperature in the cavity to provide well defined black hole states. It is found that apart from the conventional critical temperature related to Hawking-Page phase transition there appears an additional critical temperature which is of relevance to the existence of a locally stable tiny black hole; however, the off-shell free energy tells us that this black hole should eventually tunnel into the stable large black hole. Finally, we discuss the reason why the temperature near the horizon is finite in the rainbow black hole by employing the running gravitational coupling constant, whereas it is divergent near the horizon in the ordinary Schwarzschild black hole

Static Solutions of Einstein's Equations with Cylindrical Symmetry

Science.gov (United States)

Trendafilova, C. S.; Fulling, S. A.

2011-01-01

In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well-known cone solution, which is locally flat, but others in which the metric coefficients are powers of the radial coordinate and the spacetime is…

Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

International Nuclear Information System (INIS)

Dappiaggi, Claudio; Pinamonti, Nicola

2009-07-01

The discovery of the radiation properties of black holes prompted the search for a natural candidate quantum ground state for a massless scalar field theory on Schwarzschild spacetime, here considered in the Eddington-Finkelstein representation. Among the several available proposals in the literature, an important physical role is played by the so-called Unruh state which is supposed to be appropriate to capture the physics of a black hole formed by spherically symmetric collapsing matter. Within this respect, we shall consider a massless Klein-Gordon field and we shall rigorously and globally construct such state, that is on the algebra of Weyl observables localised in the union of the static external region, the future event horizon and the non-static black hole region. Eventually, out of a careful use of microlocal techniques, we prove that the built state fulfils, where defined, the so-called Hadamard condition; hence, it is perturbatively stable, in other words realizing the natural candidate with which one could study purely quantum phenomena such as the role of the back reaction of Hawking's radiation. From a geometrical point of view, we shall make a profitable use of a bulk-to-boundary reconstruction technique which carefully exploits the Killing horizon structure as well as the conformal asymptotic behaviour of the underlying background. From an analytical point of view, our tools will range from Hoermander's theorem on propagation of singularities, results on the role of passive states, and a detailed use of the recently discovered peeling behaviour of the solutions of the wave equation in Schwarzschild spacetime. (orig.)

Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

Energy Technology Data Exchange (ETDEWEB)

Dappiaggi, Claudio; Pinamonti, Nicola [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Moretti, Valter [Trento Univ., Povo (Italy). Dipt. di Matematica; Istituto Nazionale di Fisica Nucleare, Povo (Italy); Istituto Nazionale di Alta Matematica ' ' F. Severi' ' , GNFM, Sesto Fiorentino (Italy)

2009-07-15

The discovery of the radiation properties of black holes prompted the search for a natural candidate quantum ground state for a massless scalar field theory on Schwarzschild spacetime, here considered in the Eddington-Finkelstein representation. Among the several available proposals in the literature, an important physical role is played by the so-called Unruh state which is supposed to be appropriate to capture the physics of a black hole formed by spherically symmetric collapsing matter. Within this respect, we shall consider a massless Klein-Gordon field and we shall rigorously and globally construct such state, that is on the algebra of Weyl observables localised in the union of the static external region, the future event horizon and the non-static black hole region. Eventually, out of a careful use of microlocal techniques, we prove that the built state fulfils, where defined, the so-called Hadamard condition; hence, it is perturbatively stable, in other words realizing the natural candidate with which one could study purely quantum phenomena such as the role of the back reaction of Hawking's radiation. From a geometrical point of view, we shall make a profitable use of a bulk-to-boundary reconstruction technique which carefully exploits the Killing horizon structure as well as the conformal asymptotic behaviour of the underlying background. From an analytical point of view, our tools will range from Hoermander's theorem on propagation of singularities, results on the role of passive states, and a detailed use of the recently discovered peeling behaviour of the solutions of the wave equation in Schwarzschild spacetime. (orig.)

Quantum correlator outside a Schwarzschild black hole

Directory of Open Access Journals (Sweden)

Claudia Buss

2018-01-01

Full Text Available We calculate the quantum correlator in Schwarzschild black hole space–time. We perform the calculation for a scalar field in three different quantum states: Boulware, Unruh and Hartle–Hawking, and for points along a timelike circular geodesic. The results show that the correlator presents a global fourfold singularity structure, which is state-independent. Our results also show the different correlations in the three different quantum states arising in-between the singularities.

Thermodynamics of the Schwarzschild and the Reissner–Nordström black holes with quintessence

Directory of Open Access Journals (Sweden)

K. Ghaderi

2016-02-01

Full Text Available In this paper, we study the thermodynamics of the Schwarzschild and the Reissner–Nordström black holes surrounded by quintessence. By using the thermodynamical laws of the black holes, we derive the thermodynamic properties of these black holes and we compare the results with each other. We investigate the mass, temperature and heat capacity as functions of entropy for these black holes. We also discuss the equation of state of the Schwarzschild and the Reissner–Nordström black holes surrounded by quintessence.

Effective Stringy Description of Schwarzschild Black Holes

OpenAIRE

Krasnov , Kirill; Solodukhin , Sergey N.

2004-01-01

We start by pointing out that certain Riemann surfaces appear rather naturally in the context of wave equations in the black hole background. For a given black hole there are two closely related surfaces. One is the Riemann surface of complexified ``tortoise'' coordinate. The other Riemann surface appears when the radial wave equation is interpreted as the Fuchsian differential equation. We study these surfaces in detail for the BTZ and Schwarzschild black holes in four and higher dimensions....

The Planck Vacuum and the Schwarzschild Metrics

Directory of Open Access Journals (Sweden)

Daywitt W. C.

2009-07-01

Full Text Available The Planck vacuum (PV is assumed to be the source of the visible universe. So under conditions of sufficient stress, there must exist a pathway through which energy from the PV can travel into this universe. Conversely, the passage of energy from the visible universe to the PV must also exist under the same stressful conditions. The following examines two versions of the Schwarzschild metric equation for compatability with this open-pathway idea.

Accretion-induced quasinormal mode excitation of a Schwarzschild black hole

International Nuclear Information System (INIS)

Nagar, Alessandro; Zanotti, Olindo; Font, Jose A.; Rezzolla, Luciano

2007-01-01

By combining the numerical solution of the nonlinear hydrodynamics equations with the solution of the linear inhomogeneous Zerilli-Moncrief and Regge-Wheeler equations, we investigate the properties of the gravitational radiation emitted during the axisymmetric accretion of matter onto a Schwarzschild black hole. The matter models considered include quadrupolar dust shells and thick accretion disks, permitting us to simulate situations which may be encountered at the end stages of stellar gravitational collapse or binary neutron star merger. We focus on the interference pattern appearing in the energy spectra of the emitted gravitational waves and on the amount of excitation of the quasinormal modes of the accreting black hole. We show that, quite generically in the presence of accretion, the black-hole ringdown is not a simple superposition of quasinormal modes, although the fundamental mode is usually present and often dominates the gravitational-wave signal. We interpret this as due to backscattering of waves off the nonexponentially decaying part of the black-hole potential and to the finite spatial extension of the accreting matter. Our results suggest that the black-hole QNM contributions to the full gravitational-wave signal should be extremely small and possibly not detectable in generic astrophysical scenarios involving the accretion of extended distributions of matter

A Statistical Mechanical Problem in Schwarzschild Spacetime

OpenAIRE

Collas, Peter; Klein, David

2006-01-01

We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit increases to infinity. We also discuss how the method can be extended to the non ideal gas case.

Entanglement redistribution in the Schwarzschild spacetime

International Nuclear Information System (INIS)

Wang, Jieci; Pan, Qiyuan; Jing, Jiliang

2010-01-01

The effect of Hawking radiation on the redistribution of the entanglement and mutual information in the Schwarzschild spacetime is investigated. Our analysis shows that the physically accessible correlations degrade while the unaccessible correlations increase as the Hawking temperature increases because the initial correlations described by inertial observers are redistributed between all the bipartite modes. It is interesting to note that, in the limit case that the temperature tends to infinity, the accessible mutual information equals to just half of its initial value, and the unaccessible mutual information between mode A and II also equals to the same value.

Karl Schwarzschild's investigations of `out-of-focus photometry' between 1897 and 1899 at Kuffner Observatory in Vienna

Science.gov (United States)

Habison, Peter

From 1897 to 1899 Karl Schwarzschild worked at the Kuffner Observatory in Vienna. During these years he developed new measuring techniques in the field of photographic photometry, where he studied particularly the quantitative determination of the departure from the reciprocity law during photographic exposure. This paper concentrates on Schwarzschild's early work in this field and gives an overview of his important Viennese years.

Lemaître-Tolman-Bondi dust solutions in f (R) gravity

Science.gov (United States)

Sussman, Roberto A.; Jaime, Luisa G.

2017-12-01

We derive a class of non-static inhomogeneous dust solutions in f(R) gravity described by the Lemaître-Tolman-Bondi (LTB) metric. The field equations are fully integrated for all parameter subcases and compared with analogous subcases of LTB dust solutions of GR. Since the solutions do not admit regular symmetry centres, we have two possibilities: (i) a spherical dust cloud with angle deficit acting as the source of a vacuum Schwarzschild-like solution associated with a global monopole, or (ii) fully regular dust wormholes without angle deficit, whose rest frames are homeomorphic to the Schwarzschild-Kruskal manifold or to a 3d torus. The compatibility between the LTB metric and generic f(R) ansatzes furnishes an ‘inverse procedure’ to generate LTB solutions whose sources are found from the f(R) geometry. While the resulting fluids may have an elusive physical interpretation, they can be used as exact non-perturbative toy models in theoretical and cosmological applications of f(R) theories.

Schwarzschild black holes can wear scalar wigs.

Science.gov (United States)

Barranco, Juan; Bernal, Argelia; Degollado, Juan Carlos; Diez-Tejedor, Alberto; Megevand, Miguel; Alcubierre, Miguel; Núñez, Darío; Sarbach, Olivier

2012-08-24

We study the evolution of a massive scalar field surrounding a Schwarzschild black hole and find configurations that can survive for arbitrarily long times, provided the black hole or the scalar field mass is small enough. In particular, both ultralight scalar field dark matter around supermassive black holes and axionlike scalar fields around primordial black holes can survive for cosmological times. Moreover, these results are quite generic in the sense that fairly arbitrary initial data evolve, at late times, as a combination of those long-lived configurations.

All the Four-Dimensional Static, Spherically Symmetric Solutions of Abelian Kaluza-Klein Theory

International Nuclear Information System (INIS)

Cvetic, M.; Youm, D.

1995-01-01

We present the explicit form for all the four-dimensional, static, spherically symmetric solutions in (4+n)-d Abelian Kaluza-Klein theory by performing a subset of SO(2,n) transformations corresponding to four SO(1,1) boosts on the Schwarzschild solution, supplemented by SO(n)/SO(n-2) transformations. The solutions are parametrized by the mass M, Taub-NUT charge a, and n electric rvec Q and n magnetic rvec P charges. Nonextreme black holes (with zero Taub-NUT charge) have either the Reissner-Nordstroem or Schwarzschild global space-time. Supersymmetric extreme black holes have a null or naked singularity, while nonsupersymmetric extreme ones have a global space-time of extreme Reissner-Nordstroem black holes. copyright 1995 The American Physical Society

FRW cosmological model inside an isolated Schwarzschild black hole

OpenAIRE

Ortiz, C.; Rosales, J. J.; Socorro, J.; Tkach, V. I.

2004-01-01

Using the canonical quantum theory of spherically symmetric pure gravitational systems, we present a direct correspondence between the Friedmann-Robertson-Walker (FRW) cosmological model in the interior of a Schwarzschild black hole and the nth energy eigenstate of a linear harmonic oscillator. Such type of universe has a quantized mass of the order of the Planck mass and harmonic oscillator wave functions

Anisotropic solutions by gravitational decoupling

Science.gov (United States)

Ovalle, J.; Casadio, R.; da Rocha, R.; Sotomayor, A.

2018-02-01

We investigate the extension of isotropic interior solutions for static self-gravitating systems to include the effects of anisotropic spherically symmetric gravitational sources by means of the gravitational decoupling realised via the minimal geometric deformation approach. In particular, the matching conditions at the surface of the star with the outer Schwarzschild space-time are studied in great detail, and we describe how to generate, from a single physically acceptable isotropic solution, new families of anisotropic solutions whose physical acceptability is also inherited from their isotropic parent.

Anisotropic solutions by gravitational decoupling

Energy Technology Data Exchange (ETDEWEB)

Ovalle, J. [Silesian University in Opava, Institute of Physics and Research Centre of Theoretical Physics and Astrophysics, Faculty of Philosophy and Science, Opava (Czech Republic); Universidad Simon Bolivar, Departamento de Fisica, Caracas (Venezuela, Bolivarian Republic of); Casadio, R. [Alma Mater Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); Istituto Nazionale di Fisica Nucleare, Bologna (Italy); Rocha, R. da [Universidade Federal do ABC (UFABC), Centro de Matematica, Computacao e Cognicao, Santo Andre, SP (Brazil); Sotomayor, A. [Universidad de Antofagasta, Departamento de Matematicas, Antofagasta (Chile)

2018-02-15

We investigate the extension of isotropic interior solutions for static self-gravitating systems to include the effects of anisotropic spherically symmetric gravitational sources by means of the gravitational decoupling realised via the minimal geometric deformation approach. In particular, the matching conditions at the surface of the star with the outer Schwarzschild space-time are studied in great detail, and we describe how to generate, from a single physically acceptable isotropic solution, new families of anisotropic solutions whose physical acceptability is also inherited from their isotropic parent. (orig.)

Schwarzschild black hole encircled by a rotating thin disc: Properties of perturbative solution

Science.gov (United States)

Kotlařík, P.; Semerák, O.; Čížek, P.

2018-04-01

Will [Astrophys. J. 191, 521 (1974), 10.1086/152992] solved the perturbation of a Schwarzschild black hole due to a slowly rotating light concentric thin ring, using Green's functions expressed as infinite-sum expansions in multipoles and in the small mass and rotational parameters. In a previous paper [P. Čížek and O. Semerák, Astrophys. J. Suppl. Ser. 232, 14 (2017), 10.3847/1538-4365/aa876b], we expressed the Green functions in closed form containing elliptic integrals, leaving just summation over the mass expansion. Such a form is more practical for numerical evaluation, but mainly for generalizing the problem to extended sources where the Green functions have to be integrated over the source. We exemplified the method by computing explicitly the first-order perturbation due to a slowly rotating thin disc lying between two finite radii. After finding basic parameters of the system—mass and angular momentum of the black hole and of the disc—we now add further properties, namely those which reveal how the disc gravity influences geometry of the black-hole horizon and those of circular equatorial geodesics (specifically, radii of the photon, marginally bound and marginally stable orbits). We also realize that, in the linear order, no ergosphere occurs and the central singularity remains pointlike, and check the implications of natural physical requirements (energy conditions and subluminal restriction on orbital speed) for the single-stream as well as counter-rotating double-stream interpretations of the disc.

Thermodynamic stability of modified Schwarzschild-AdS black hole in rainbow gravity

Energy Technology Data Exchange (ETDEWEB)

Kim, Yong-Wan [Chonbuk National University, Research Institute of Physics and Chemistry, Jeonju (Korea, Republic of); Kim, Seung Kook [Seonam University, Department of Physical Therapy, Namwon (Korea, Republic of); Park, Young-Jai [Sogang University, Department of Physics, Seoul (Korea, Republic of)

2016-10-15

In this paper, we have extended the previous study of the thermodynamics and phase transition of the Schwarzschild black hole in the rainbow gravity to the Schwarzschild-AdS black hole where metric depends on the energy of a probe. Making use of the Heisenberg uncertainty principle and the modified dispersion relation, we have obtained the modified local Hawking temperature and thermodynamic quantities in an isothermal cavity. Moreover, we carry out the analysis of constant temperature slices of a black hole. As a result, we have shown that there also exists another Hawking-Page-like phase transition in which case a locally stable small black hole tunnels into a globally stable large black hole as well as the standard Hawking-Page phase transition from a hot flat space to a black hole. (orig.)

(Anti-)Evaporation of Schwarzschild-de Sitter Black Holes

OpenAIRE

Bousso, Raphael; Hawking, Stephen

1997-01-01

We study the quantum evolution of black holes immersed in a de Sitter background space. For black holes whose size is comparable to that of the cosmological horizon, this process differs significantly from the evaporation of asymptotically flat black holes. Our model includes the one-loop effective action in the s-wave and large N approximation. Black holes of the maximal mass are in equilibrium. Unexpectedly, we find that nearly maximal quantum Schwarzschild-de Sitter black holes anti-evapor...

The 100th birthday of the conic constant and Schwarzschild's revolutionary papers in optics

Science.gov (United States)

Rakich, Andrew

2005-08-01

In 1905 Karl Schwarzschild published three papers on optics, two of which revolutionized the field of reflecting telescope optics. In his first paper he developed a full theory of the aberrations of reflecting telescopes, generalizing the Eikonal of Bruns to take into account systems with an infinite long conjugate. In the second paper Schwarzschild applied his formulation to a masterful analysis of 2 mirror anastigmatic systems, along the way discovering the so called Ritchey-Chretien aplanat, 18 years Ritchey and Chretien's announcement. Numerous other innovations are given in what must be seen as being among the most important papers on the aberrations of optical systems ever written.

Explanation of Rotation Curves in Galaxies and Clusters of them, by Generalization of Schwarzschild Metric and Combination with MOND, eliminating Dark Matter

Science.gov (United States)

Vossos, Spyridon; Vossos, Elias

2017-12-01

Schwarzschild Metric is the first and the most important solution of Einstein vacuum field equations. This is associated with Lorentz metric of flat spacetime and produces the relativistic potential (Φ) and the field strength (g) outside a spherically symmetric mass or a non-rotating black hole. It has many applications such as gravitational red shift, the precession of Mercury’s orbit, Shapiro time delay etc. However, it is inefficient to explain the rotation curves in large galaxies and clusters of them, causing the necessity for dark matter. On the other hand, Modified Newtonian Dynamics (MOND) has already explained these rotation curves in many cases, using suitable interpolating function (μ) in Milgrom’s Law. In this presentation, we initially produce a Generalized Schwarzschild potential and the corresponding Metric of spacetime, in order to be in accordance with any isotropic metric of flat spacetime (including Galilean Metric of spacetime which is associated with Galilean Transformation of spacetime). From this Generalized Schwarzschild potential (Φ), we calculate the corresponding field strength (g), which is associated with the interpolating function (μ). In this way, a new relativistic potential is obtained (let us call 2nd Generalized Schwarzschild potential) which describes the gravitational interaction at any distance and for any metric of flat spacetime. Thus, not only the necessity for Dark Matter is eliminated, but also MOND becomes a pure Relativistic Theory of Gravitational Interaction. Then, we pass to the case of flat spacetime with Lorentz metric (Minkowski space), because the experimental data have been extracted using the Relativistic Doppler Shift and the gravitational red shift of Classic Relativity (CR). Thus, we Explain the Rotation Curves in Galaxies (e.g. NGC 3198) and Clusters of them as well as the Solar system, eliminating Dark Matter. This relativistic potential and the corresponding metric of spacetime have been obtained

Initial value formulation for the spherically symmetric dust solution

International Nuclear Information System (INIS)

Liu, H.

1990-01-01

An initial value formulation for the dust solution with spherical symmetry is given explicitly in which the initial distributions of dust and its velocity on an initial surface are chosen to be the initial data. As special cases, the Friedmann universe, the Schwarzschild solution in comoving coordinates, and a spherically symmetric and radially inhomogeneous cosmological model are derived

Scattering of Ricci scalar perturbations from Schwarzschild black holes in modified gravity

Energy Technology Data Exchange (ETDEWEB)

Sibandze, Dan B.; Goswami, Rituparno; Maharaj, Sunil D.; Nzioki, Anne Marie [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics Statistics and Computer Science, Private Bag X54001, Durban (South Africa); Dunsby, Peter K.S. [University of Cape Town, Department of Mathematics and Applied Mathematics and ACGC, Cape Town (South Africa)

2017-06-15

It has already been shown that the gravitational waves emitted from a Schwarzschild black hole in f(R) gravity have no signatures of the modification of gravity from General Relativity, as the Regge-Wheeler equation remains invariant. In this paper we consider the perturbations of Ricci scalar in a vacuum Schwarzschild spacetime, which is unique to higher order theories of gravity and is absent in General Relativity. We show that the equation that governs these perturbations can be reduced to a Volterra integral equation. We explicitly calculate the reflection coefficients for the Ricci scalar perturbations, when they are scattered by the black hole potential barrier. Our analysis shows that a larger fraction of these Ricci scalar waves are reflected compared to the gravitational waves. This may provide a novel observational signature for fourth order gravity. (orig.)

Solution of the stationary vacuum equations of relativity for conformally flat 3-spaces

International Nuclear Information System (INIS)

Perjes, Z.; Lukacs, B.; Sebestyen, A.; Valentini, A.; Sparling, G.A.J.

1983-08-01

The solution of Einstein's vacuum gravitational equations for stationary space-times with a conformally flat 3-space is presented. There is no other solution of this problem than the Ehlers-rotation generalizations of the three conformastat space-times including the Schwarzschild metric. (author)

On scattering of scalar waves in static space-times, particularly Schwarzschild

International Nuclear Information System (INIS)

Beig, R.

1982-01-01

This paper aims at laying foundations of a rigorous scattering theory for scalar waves in a static space-time. The treatment includes geometries which can be thought of as representing the exterior of a black hole. Schwarzschild space-time, as a particular example, is studied in more detail. (Auth.)

The stability of vacuum solutions in generalised gravity

Energy Technology Data Exchange (ETDEWEB)

Madsen, M.S. (Sussex Univ., Brighton (UK). Astronomy Centre); Low, R.J. (Coventry (Lanchester) Polytechnic (UK). Dept. of Mathematics)

1990-05-10

The stability of the Ricci-flat solutions of a large class of generalised gravity theories is examined. It is shown by use of complementary methods that all such solutions are stable in a given theory if that theory admits a truncation to a quadratic theory in which the solution is stable. In particular, this means that the exterior Schwarzschild solution is stable in any gravity theory constructed purely from the Ricci scalar, provided that it exists in that theory. (orig.).

The stability of vacuum solutions in generalised gravity

International Nuclear Information System (INIS)

Madsen, M.S.; Low, R.J.

1990-01-01

The stability of the Ricci-flat solutions of a large class of generalised gravity theories is examined. It is shown by use of complementary methods that all such solutions are stable in a given theory if that theory admits a truncation to a quadratic theory in which the solution is stable. In particular, this means that the exterior Schwarzschild solution is stable in any gravity theory constructed purely from the Ricci scalar, provided that it exists in that theory. (orig.)

Schwarzschild black hole in the background of the Einstein universe: some physical effects

International Nuclear Information System (INIS)

Ramachandra, B S; Vishveshwara, C V

2002-01-01

A prototype of an asymptotically non-flat black hole spacetime is that of a Schwarzschild black hole in the background of the Einstein universe, which is a special case of the representation of a black hole in a cosmological background given by Vaidya. Recently, this spacetime has been studied in detail by Nayak et al. They constructed a composite spacetime called the Vaidya-Einstein-Schwarzschild (VES) spacetime. We investigate some of the physical effects inherent to this spacetime. We carry out a background-black hole decomposition of the spacetime in order to separate out the effects due to the background spacetime and the black hole. The physical effects we study include the classical tests - the gravitational redshift, perihelion precession and light bending - and circular geodesics. A detailed classification of geodesics, in general, is also given

Dirac perturbations on Schwarzschild-anti-de Sitter spacetimes: Generic boundary conditions and new quasinormal modes

Science.gov (United States)

Wang, Mengjie; Herdeiro, Carlos; Jing, Jiliang

2017-11-01

We study Dirac quasinormal modes of Schwarzschild-anti-de Sitter (Schwarzschild-AdS) black holes, following the generic principle for allowed boundary conditions proposed in [M. Wang, C. Herdeiro, and M. O. P. Sampaio, Phys. Rev. D 92, 124006 (2015)., 10.1103/PhysRevD.92.124006]. After deriving the equations of motion for Dirac fields on the aforementioned background, we impose vanishing energy flux boundary conditions to solve these equations. We find a set of two Robin boundary conditions are allowed. These two boundary conditions are used to calculate Dirac normal modes on empty AdS and quasinormal modes on Schwarzschild-AdS black holes. In the former case, we recover the known normal modes of empty AdS; in the latter case, the two sets of Robin boundary conditions lead to two different branches of quasinormal modes. The impact on these modes of the black hole size, the angular momentum quantum number and the overtone number are discussed. Our results show that vanishing energy flux boundary conditions are a robust principle, applicable not only to bosonic fields but also to fermionic fields.

Exact vacuum solution to conformal Weyl gravity and galactic rotation curves

International Nuclear Information System (INIS)

Mannheim, P.D.; Kazanas, D.

1989-01-01

The complete, exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented. The solution includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance. The obtained solution provides a potential explanation for observed galactic rotation curves without the need for dark matter. The solution also has some interesting implications for cosmology. 9 refs

A class of solutions for the strong gravity equations

International Nuclear Information System (INIS)

Salam, A.; Strathdee, J.

1976-12-01

We solve the Einstein equation for strong gravity in the limit that weak gravity is neglected. The class of solutions we find reduces to the Schwarzschild solution (with the weak gravity Newtonian constant replaced by a strong coupling parameter) in the limit M 2 →0 where M is the mass of the strong gravity spin-2 meson. These solutions may be of relevance for the problem of defining temperature in hadronic physics

Hawking radiation inside a Schwarzschild black hole

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Hamilton, Andrew J. S.

2018-05-01

The boundary of any observer's spacetime is the boundary that divides what the observer can see from what they cannot see. The boundary of an observer's spacetime in the presence of a black hole is not the true (future event) horizon of the black hole, but rather the illusory horizon, the dimming, redshifting surface of the star that collapsed to the black hole long ago. The illusory horizon is the source of Hawking radiation seen by observers both outside and inside the true horizon. The perceived acceleration (gravity) on the illusory horizon sets the characteristic frequency scale of Hawking radiation, even if that acceleration varies dynamically, as it must do from the perspective of an infalling observer. The acceleration seen by a non-rotating free-faller both on the illusory horizon below and in the sky above is calculated for a Schwarzschild black hole. Remarkably, as an infaller approaches the singularity, the acceleration becomes isotropic, and diverging as a power law. The isotropic, power-law character of the Hawking radiation, coupled with conservation of energy-momentum, the trace anomaly, and the familiar behavior of Hawking radiation far from the black hole, leads to a complete description of the quantum energy-momentum inside a Schwarzschild black hole. The quantum energy-momentum near the singularity diverges as r^{-6}, and consists of relativistic Hawking radiation and negative energy vacuum in the ratio 3 : - 2. The classical back reaction of the quantum energy-momentum on the geometry, calculated using the Einstein equations, serves merely to exacerbate the singularity. All the results are consistent with traditional calculations of the quantum energy-momentum in 1 + 1 spacetime dimensions.

Regular coordinate systems for Schwarzschild and other spherical spacetimes

OpenAIRE

Martel, Karl; Poisson, Eric

2000-01-01

The continuation of the Schwarzschild metric across the event horizon is almost always (in textbooks) carried out using the Kruskal-Szekeres coordinates, in terms of which the areal radius r is defined only implicitly. We argue that from a pedagogical point of view, using these coordinates comes with several drawbacks, and we advocate the use of simpler, but equally effective, coordinate systems. One such system, introduced by Painleve and Gullstrand in the 1920's, is especially simple and pe...

Statistical metastability of a classical ideal gas in the Schwarzschild gravitational field

International Nuclear Information System (INIS)

Gaina, A.B.; Zaslavskii, O.B.

1990-01-01

A classical ideal gas in the Schwarzschild gravitational field is considered. The lifetime of a gas influenced by thermal fluctuations has been calculated. It is shown that thermal effects can lead to the electric charging of a black hole in a plasma containing particles with different masses. (author)

An absence theorem for static wave maps in the Schwarzschild-AdS spacetime

International Nuclear Information System (INIS)

Xie Naqing

2005-01-01

In this Letter, we obtain an absence theorem for static wave maps defined from the Schwarzschild-anti de Sitter spacetime into any Riemannian manifold. This work extends the results in [Chinese Ann. Math. B 5 (1984) 737, Lett. Math. Phys. 14 (1987) 343

QFT holography near the horizon of Schwarzschild-like spacetimes

OpenAIRE

Moretti, Valter; Pinamonti, Nicola

2003-01-01

It is argued that free QFT can be defined on the event horizon of a Schwarzschild-like spacetime and that this theory is unitarily and algebraically equivalent to QFT in the bulk (near the horizon). Under that unitary equivalence the bulk hidden SL(2,R) symmetry found in a previous work becomes manifest on the event horizon, it being induced by a group of horizon diffeomorphisms. The class of generators of that group can be enlarged to include a full Virasoro algebra of fields which are defin...

Geometric extension through Schwarzschild r = 0

International Nuclear Information System (INIS)

Lynden-Bell, D.; Katz, J.; Hebrew Univ., Jerusalem

1990-01-01

Singularities in space-time are not necessarily cancers in the manifold but can herald interesting topological change in the space-time at places where there are several different tangent Minkowski spaces. Most discussions of gravitational collapse cease when space-time becomes singular. In the 'hour-glass' universe we have an example where the singularity develops in empty space; here we give a geometrical extension through the singularity in which geodesics that enter it emerge into a new space. The result extends Schwarzschild space and is periodic in 'extended' Penrose coordinates. There is a topological singularity but no mass at r = 0. The extension is mildly nonanalytic but unique. It is based on the concept that time does not stop and that empty space-times which develop singularities must still have zero Ricci tensors even where the Riemann tensor becomes infinite. (author)

Astronomy from Olbers to Schwarzschild. (German Title: Astronomie von Olbers bis Schwarzschild)

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Dick, Wolfgang R.; Hamel, Jürgen

This issue comprises talks presented 2000 September 18 at the colloquium ``International relations in astronomy'' it is supplemented by additional articles about this topic. The foundation of the international ``Vereinigte Astronomische Gesellschaft'', which took place in 1800 in Bremen, prompted us to investigate the development of astronomy in German-speaking regions, and its international relations during the 19th century. We investigate the activities of famous astronomers like W. Olbers, J.E. Bode, F.X. von Zach, J.H. Schroeter, H.C. Schumacher and K. Schwarzschild, as well as those of their less famous professional colleagues like J.G. Schrader and L. de Ball. The geographical spectrum extends from Bremen and Lilienthal over Kiel, Gotha and Dresden to Copenhagen, Vienna and Chile. Among the topics are: telescope construction, including telescopes made by Herschel, the rediscovery of the minor planet Ceres 1801/02, the Berlin ``Astronomisches Jahrbuch'', the foundation of the ``Astronomische Nachrichten'', the evolution from the ``Vereinigte Astronomische Gesellschaft'' to the present-day ``Astronomische Gesellschaft'', the research at the Kuffner Observatory in Vienna, the professionalization in astronomy, and the attempts of many countries to establish a southern observatory in Chile. A listing of astronomical monuments in Lilienthal and Bremen concludes the book. All papers are written in German with English abstracts.

Can one increase the luminosity of a Schwarzschild black hole?

OpenAIRE

Mayo, Avraham E.

2000-01-01

We illustrate how Hawking's radiance from a Schwarzschild black hole is modified by the electrostatic self-interaction of the emitted charged particles. A W.K.B approximation shows that the probability for a self-interacting charged particle to propagate from the interior to the exterior of the horizon is increased relative to the corresponding probability for neutral particles. We also demonstrate how the electric potential of a charged test object in the black hole's vicinity gives rise to ...

Canonical quantization inside the Schwarzschild black hole

Science.gov (United States)

Yajnik, U. A.; Narayan, K.

1998-05-01

We propose a scheme for quantizing a scalar field over the Schwarzschild manifold including the interior of the horizon. On the exterior, the timelike Killing vector and on the horizon the isometry corresponding to restricted Lorentz boosts can be used to enforce the spectral condition. For the interior we appeal to CPT invariance to construct an explicitly positive-definite operator which allows identification of positive and negative frequencies. This operator is the translation operator corresponding to the inexorable propagation to smaller radii as expected from the classical metric. We also propose an expression for the propagator in the interior and express it as a mode sum. The field theory thus obtained is meaningful for small curvatures far from the classical singularity.

Perturbative calculation of quasinormal modes of AdS Schwarzschild black holes

International Nuclear Information System (INIS)

Musiri, Suphot; Ness, Scott; Siopsis, George

2006-01-01

We calculate analytically quasinormal modes of AdS Schwarzschild black holes including first-order corrections. We consider massive scalar, gravitational and electromagnetic perturbations. Our results are in good agreement with numerical calculations. In the case of electromagnetic perturbations, ours is the first calculation to provide an analytic expression for quasinormal frequencies, because the effective potential vanishes at zeroth order. We show that the first-order correction is logarithmic

Spherically symmetric solution and a satisfactory energy-momentum complex

International Nuclear Information System (INIS)

Nashed, G.G.L.

2005-01-01

Mikhail et al. obtained two spherically symmetric solution in Moeller tetrad theory of gravitation. They calculated their energy content and obtained a strange value for the second solution, in spite that the associated metric of these solutions is the same (the Schwarzschild metric). We use another method given bu Gibbons and Hawking to calculate the energy content of these solutions. We also obtained a strange value of energy for the second solution. Studying the requirements of the satisfactory energy-momentum complex given by Moeller we find that the second solution which behaves as 1/√r does not transform as a four-vector under Lorentz transformation

Thermal properties of Green's functions in Rindler, de Sitter, and Schwarzschild spaces

International Nuclear Information System (INIS)

Dowker, J.S.

1978-01-01

The conventional massless scalar Green's functions in the Minkowski, de Sitter, and two-dimensional Schwarzschild spaces are reinterpreted as finite-temperature Green's functions and the corresponding averages of the stress-energy operator are calculated. The renormalization adopted consists of subtracting the zero-temperature quantities. In all cases the averages give the stress tensor of a purely Planck-type perfect gas

Geometry of deformed black holes. II. Schwarzschild hole surrounded by a Bach-Weyl ring

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Basovník, M.; Semerák, O.

2016-08-01

We continue to study the response of black-hole space-times on the presence of additional strong sources of gravity. Restricting ourselves to static and axially symmetric (electro)vacuum exact solutions of Einstein's equations, we first considered the Majumdar-Papapetrou solution for a binary of extreme black holes in a previous paper, while here we deal with a Schwarzschild black hole surrounded by a concentric thin ring described by the Bach-Weyl solution. The geometry is again revealed on the simplest invariants determined by the metric (lapse function) and its gradient (gravitational acceleration), and by curvature (Kretschmann scalar). Extending the metric inside the black hole along null geodesics tangent to the horizon, we mainly focus on the black-hole interior (specifically, on its sections at constant Killing time) where the quantities behave in a way indicating a surprisingly strong influence of the external source. Being already distinct on the level of potential and acceleration, this is still more pronounced on the level of curvature: for a sufficiently massive and/or nearby (small) ring, the Kretschmann scalar even becomes negative in certain toroidal regions mostly touching the horizon from inside. Such regions have been interpreted as those where magnetic-type curvature dominates, but here we deal with space-times which do not involve rotation and the negative value is achieved due to the electric-type components of the Riemann/Weyl tensor. The Kretschmann scalar also shapes rather nontrivial landscapes outside the horizon.

Two fluid plasmas in the vicinity of a Schwarzschild black hole

International Nuclear Information System (INIS)

Buzzi, V.; Hines, K.C.

1992-01-01

The 3+1 split of general relativity has been used to investigate the dispersion relation for certain plasma waves, together with the two stream instability, in the vicinity of a Schwarzschild black hole horizon. In contrast to the special relativistic results, the dispersion relations discussed here contain additional terms involving the gravitational acceleration, a, and the lapse function α. Some of these terms are imaginary and should correspond to gravitational damping effects. 5 refs

Drude-Schwarzschild Metric and the Electrical Conductivity of Metals

Directory of Open Access Journals (Sweden)

Silva P. R.

2014-07-01

Full Text Available Starting from a string with a length equal to the electron mean free path and having a unit cell equal to the Compton length of the electron, we construct a Schwarzschild-like metric. We found that this metric has a surface horizon with radius equal to the electron mean free path and its Bekenstein-like entropy is proportional to the number of squared unit cells contained in this spherical surface. The Hawking temperature is inversely proportional to the perimeter of the maximum circle of this sphere. Also, interesting analogies on some features of the particle physics are examined.

Accretion onto a noncommutative-inspired Schwarzschild black hole

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Gangopadhyay, Sunandan; Paik, Biplab; Mandal, Rituparna

2018-05-01

In this paper, we investigate the problem of ordinary baryonic matter accretion onto the noncommutative (NC) geometry-inspired Schwarzschild black hole. The fundamental equations governing the spherically symmetric steady state matter accretion are deduced. These equations are seen to be modified due to the presence of noncommutativity. The matter accretion rate is computed and is found to increase rapidly with the increase in strength of the NC parameter. The sonic radius reduces while the sound speed at the sonic point increases with the increase in the strength of noncommutativity. The profile of the thermal environment is finally investigated below the sonic radius and at the event horizon and is found to be affected by noncommutativity.

Gravitational perturbations of the Schwarzschild spacetime: A practical covariant and gauge-invariant formalism

International Nuclear Information System (INIS)

Martel, Karl; Poisson, Eric

2005-01-01

We present a formalism to study the metric perturbations of the Schwarzschild spacetime. The formalism is gauge invariant, and it is also covariant under two-dimensional coordinate transformations that leave the angular coordinates unchanged. The formalism is applied to the typical problem of calculating the gravitational waves produced by material sources moving in the Schwarzschild spacetime. We examine the radiation escaping to future null infinity as well as the radiation crossing the event horizon. The waveforms, the energy radiated, and the angular-momentum radiated can all be expressed in terms of two gauge-invariant scalar functions that satisfy one-dimensional wave equations. The first is the Zerilli-Moncrief function, which satisfies the Zerilli equation, and which represents the even-parity sector of the perturbation. The second is the Cunningham-Price-Moncrief function, which satisfies the Regge-Wheeler equation, and which represents the odd-parity sector of the perturbation. The covariant forms of these wave equations are presented here, complete with covariant source terms that are derived from the stress-energy tensor of the matter responsible for the perturbation

Exact Mathisson-Papapetrou equations in the Schwarzschild metric with integrals of motion

International Nuclear Information System (INIS)

Plyatsko, R.M.; Stefanishin, O.B.

2011-01-01

A new representation for exact Mathisson-Papapetrou equations under the Mathisson-Pirani condition in the Schwarzschild gravitational field, which does not contain third-order derivatives with respect to spinning particle coordinates, has been obtained. For this purpose, the integrals of energy and angular momentum of a spinning particle, as well as a differential relation following from the Mathisson-Papapetrou equations for an arbitrary metric, are used.

The Event Horizon of The Schwarzschild Black Hole in Noncommutative Spaces

OpenAIRE

Nasseri, Forough

2005-01-01

The event horizon of Schwarzschild black hole is obtained in noncommutative spaces up to the second order of perturbative calculations. Because this type of black hole is non-rotating, to the first order there is no any effect on the event horizon due to the noncommutativity of space. A lower limit for the noncommutativity parameter is also obtained. As a result, the event horizon in noncommutative spaces is less than the event horizon in commutative spaces.

Quasinormal modes of the near extremal Schwarzschild-de Sitter black hole

International Nuclear Information System (INIS)

Cardoso, Vitor; Lemos, Jose P.S.

2003-01-01

We present an exact expression for the quasinormal modes of scalar, electromagnetic, and gravitational perturbations of a near extremal Schwarzschild-de Sitter black hole and we show that is why a previous approximation holds exactly in this near extremal regime. In particular, our results give the asymptotic behavior of the quasinormal frequencies for highly damped modes, which has recently attracted much attention due to the proposed identification of its real part with the Barbero-Immirzi parameter

Quantum corrections to the thermodynamics of Schwarzschild-Tangherlini black hole and the generalized uncertainty principle

Energy Technology Data Exchange (ETDEWEB)

Feng, Z.W.; Zu, X.T. [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Li, H.L. [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Shenyang Normal University, College of Physics Science and Technology, Shenyang (China); Yang, S.Z. [China West Normal University, Physics and Space Science College, Nanchong (China)

2016-04-15

We investigate the thermodynamics of Schwarzschild-Tangherlini black hole in the context of the generalized uncertainty principle (GUP). The corrections to the Hawking temperature, entropy and the heat capacity are obtained via the modified Hamilton-Jacobi equation. These modifications show that the GUP changes the evolution of the Schwarzschild-Tangherlini black hole. Specially, the GUP effect becomes susceptible when the radius or mass of the black hole approaches the order of Planck scale, it stops radiating and leads to a black hole remnant. Meanwhile, the Planck scale remnant can be confirmed through the analysis of the heat capacity. Those phenomena imply that the GUP may give a way to solve the information paradox. Besides, we also investigate the possibilities to observe the black hole at the Large Hadron Collider (LHC), and the results demonstrate that the black hole cannot be produced in the recent LHC. (orig.)

Comment on ;Acceleration of particles to high energy via gravitational repulsion in the Schwarzschild field; [Astropart. Phys. 86 (2017) 18-20

Science.gov (United States)

Spallicci, Alessandro D. A. M.

2017-09-01

Comments are due on a recent paper by McGruder III (2017) in which the author deals with the concept of gravitational repulsion in the context of the Schwarzschild-Droste solution. Repulsion (deceleration) for ingoing particles into a black hole is a concept proposed several times starting from Droste himself in 1916. It is a coordinate effect appearing to an observer at a remote distance from the black hole and when coordinate time is employed. Repulsion has no bearing and relation to the local physics of the black hole, and moreover it cannot be held responsible for accelerating outgoing particles. Thereby, the energy boost of cosmic rays cannot be produced by repulsion.

The Compton-Schwarzschild correspondence from extended de Broglie relations

Energy Technology Data Exchange (ETDEWEB)

Lake, Matthew J. [The Institute for Fundamental Study, “The Tah Poe Academia Institute' ,Naresuan University, Phitsanulok 65000 (Thailand); Thailand Center of Excellence in Physics, Ministry of Education,Bangkok 10400 (Thailand); Carr, Bernard [School of Physics and Astronomy, Queen Mary University of London,Mile End Road, London E1 4NS (United Kingdom)

2015-11-17

The Compton wavelength gives the minimum radius within which the mass of a particle may be localized due to quantum effects, while the Schwarzschild radius gives the maximum radius within which the mass of a black hole may be localized due to classial gravity. In a mass-radius diagram, the two lines intersect near the Planck point (l{sub P},m{sub P}), where quantum gravity effects become significant. Since canonical (non-gravitational) quantum mechanics is based on the concept of wave-particle duality, encapsulated in the de Broglie relations, these relations should break down near (l{sub P},m{sub P}). It is unclear what physical interpretation can be given to quantum particles with energy E≫m{sub P}c{sup 2}, since they correspond to wavelengths λ≪l{sub P} or time periods τ≪t{sub P} in the standard theory. We therefore propose a correction to the standard de Broglie relations, which gives rise to a modified Schrödinger equation and a modified expression for the Compton wavelength, which may be extended into the region E≫m{sub P}c{sup 2}. For the proposed modification, we recover the expression for the Schwarzschild radius for E≫m{sub P}c{sup 2} and the usual Compton formula for E≪m{sub P}c{sup 2}. The sign of the inequality obtained from the uncertainty principle reverses at m≈m{sub P}, so that the Compton wavelength and event horizon size may be interpreted as minimum and maximum radii, respectively. We interpret the additional terms in the modified de Broglie relations as representing the self-gravitation of the wave packet.

Spherically symmetric solutions in abelian Kaluza-Klein theories

International Nuclear Information System (INIS)

Angus, I.G.

1986-01-01

We present the most general spherically symmetric solution to the field equations of the truncated five-dimensional Kaluza-Klein theory. We also detail some of the special forms of this solution. With the exception of the Gross-Perry-Sorkin monopole and the Schwarzschild solutions we find that most, and we conjecture all, of the solutions have naked curvature singularities. We then proceed to consider higher-dimensional theories with toroidal compactification and we exhibit a class of nonsingular monopole solutions which are the natural generalization of the Gross-Perry-Sorkin monopole to more than five dimensions. We also present some selected solutions including a solution pertaining to a model with a Ricci-flat, but not curvature-flat, internal manifold. All of these other solutions have naked curvature singularities. (orig.)

Perturbation of a Schwarzschild Black Hole Due to a Rotating Thin Disk

Energy Technology Data Exchange (ETDEWEB)

Čížek, P.; Semerák, O., E-mail: oldrich.semerak@mff.cuni.cz [Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, Prague (Czech Republic)

2017-09-01

Will, in 1974, treated the perturbation of a Schwarzschild black hole due to a slowly rotating, light, concentric thin ring by solving the perturbation equations in terms of a multipole expansion of the mass-and-rotation perturbation series. In the Schwarzschild background, his approach can be generalized to perturbation by a thin disk (which is more relevant astrophysically), but, due to rather bad convergence properties, the resulting expansions are not suitable for specific (numerical) computations. However, we show that Green’s functions, represented by Will’s result, can be expressed in closed form (without multipole expansion), which is more useful. In particular, they can be integrated out over the source (a thin disk in our case) to yield good converging series both for the gravitational potential and for the dragging angular velocity. The procedure is demonstrated, in the first perturbation order, on the simplest case of a constant-density disk, including the physical interpretation of the results in terms of a one-component perfect fluid or a two-component dust in a circular orbit about the central black hole. Free parameters are chosen in such a way that the resulting black hole has zero angular momentum but non-zero angular velocity, as it is just carried along by the dragging effect of the disk.

Exact solutions, numerical relativity and gravitational radiation

International Nuclear Information System (INIS)

Winicour, J.

1986-01-01

In recent years, there has emerged a new use for exact solutions to Einstein's equation as checks on the accuracy of numerical relativity codes. Much has already been written about codes based upon the space-like Cauchy problem. In the case of two Killing vectors, a numerical characteristic initial value formulation based upon two intersecting families of null hypersurfaces has successfully evolved the Schwarzschild and the colliding plane wave vacuum solutions. Here the author discusses, in the context of exact solutions, numerical studies of gravitational radiation based upon the null cone initial value problem. Every stage of progress in the null cone approach has been associated with exact solutions in some sense. He begins by briefly recapping this history. Then he presents two new examples illustrating how exact solutions can be useful

An exact solution in Einstein-Cartan

International Nuclear Information System (INIS)

Roque, W.L.

1982-01-01

The exact solution of the field equations of the Einstein-Cartan theory is obtained for an artificial dust of radially polarized spins, with spherical symmetry and static. For a best estimation of the effect due the spin, the energy-momentum metric tensor is considered null. The gravitational field dynamics is studied for several torsion strengths, through the massive and spinless test-particle moviment, in particular for null torsion Schwarzschild solutions is again obtained. It is observed that the gravitational effects related to the torsin (spin) sometimes are attractives sometimes are repulsives, depending of the torsion values and of the test-particle position and velocity. (L.C.) [pt

Geometric Description of the Thermodynamics of the Noncommutative Schwarzschild Black Hole

Directory of Open Access Journals (Sweden)

Alexis Larrañaga

2013-01-01

Full Text Available The thermodynamics of the noncommutative Schwarzschild black hole is reformulated within the context of the recently developed formalism of geometrothermodynamics (GTD. Using a thermodynamic metric which is invariant with respect to Legendre transformations, we determine the geometry of the space of equilibrium states and show that phase transitions, which correspond to divergencies of the heat capacity, are represented geometrically as singularities of the curvature scalar. This further indicates that the curvature of the thermodynamic metric is a measure of thermodynamic interaction.

Relativistic gas in a Schwarzschild metric

International Nuclear Information System (INIS)

Kremer, Gilberto M

2013-01-01

A relativistic gas in a Schwarzschild metric is studied within the framework of a relativistic Boltzmann equation in the presence of gravitational fields, where Marle’s model for the collision operator of the Boltzmann equation is employed. The transport coefficients of the bulk and shear viscosities and thermal conductivity are determined from the Chapman–Enskog method. It is shown that the transport coefficients depend on the gravitational potential. Expressions for the transport coefficients in the presence of weak gravitational fields in the non-relativistic (low temperature) and ultra-relativistic (high temperature) limiting cases are given. Apart from the temperature gradient the heat flux has two relativistic terms. The first one, proposed by Eckart, is due to the inertia of energy and represents an isothermal heat flux when matter is accelerated. The other, suggested by Tolman, is proportional to the gravitational potential gradient and indicates that—in the absence of an acceleration field—a state of equilibrium of a relativistic gas in a gravitational field can be attained only if the temperature gradient is counterbalanced by a gravitational potential gradient. (paper)

Quantum tunneling effect of Dirac particles in a Schwarzschild-Godel space-time

Energy Technology Data Exchange (ETDEWEB)

Qi, D.-J.; Li, S.-M., E-mail: qidejiang0504@126.com [Shenyang Inst. of Engineering, Shenyang (China); Ru, H.-Q. [Northeastern Univ., Shenyang (China)

2010-11-15

In this paper, motivated by the Kerner and Man fermion tunneling method of 4-dimensional black holes, we further improve the analysis to investigate the quantum tunneling effect of Dirac particles from the five-dimensional Schwarzschild-Godel black hole. We successfully construct a set of appropriate matrices γ{sup μ} for the general covariant Dirac equation and derive the tunneling probability and Hawking temperature, which is exactly the same as that obtained by other methods. (author)

The Cardy-Verlinde formula and topological AdS-Schwarzschild black holes

International Nuclear Information System (INIS)

Youm, Donam

2001-05-01

We consider the brane universe in the background of the topological AdS-Schwarzschild black holes. The induced geometry of the brane is that of a flat or an open radiation dominated FRW-universe. Just like the case of a closed radiation dominated FRW-universe, the temperature and entropy are simply expressed in terms of the Hubble parameter and its time derivative when the brane crosses the black hole horizon. We propose the modified Cardy-Verlinde formula which is valid for any values of the curvature parameter k in the Friedmann equations. (author)

Anomalies, effective action and Hawking temperatures of a Schwarzschild black hole in the isotropic coordinates

International Nuclear Information System (INIS)

Wu Shuangqing; Peng Junjin; Zhao Zhanyue

2008-01-01

Motivated by the universality of Hawking radiation and that of the anomaly cancellation technique as well as the effective action method, we investigate the Hawking radiation of a Schwarzschild black hole in the isotropic coordinates via the cancellation of gravitational anomaly. After performing a dimensional reduction from the four-dimensional isotropic Schwarzschild metric, we show that this reduction procedure will, in general, result in two classes of two-dimensional effective metrics: the conformal equivalent and the inequivalent ones. For the physically equivalent class, the two-dimensional effective metric displays such a distinct feature that the determinant is not equal to the unity √(-g)≠1, but also vanishes at the horizon, the latter of which possibly invalidates the anomaly analysis there. Nevertheless, in this paper we adopt the effective action method to prove that the consistent energy-momentum tensor T r t is divergent on the horizon but √(-g)T t r remains finite there. Meanwhile, through an explicit calculation we show that the covariant energy-momentum tensor T-tilde t r equals zero at the horizon. Therefore the validity of the covariant regularity condition that demands that T-tilde t r = 0 at the horizon has been justified, indicating that the gravitational anomaly analysis can be safely extrapolated to the case where the metric determinant vanishes at the horizon. It is then demonstrated that for the physically equivalent reduced metric, both methods can give the correct Hawking temperature of the isotropic Schwarzschild black hole, while for the inequivalent one with the determinant √(-g) = 1 it can only give half of the correct temperature. We further exclude the latter undesired result by taking into account the general covariance of the energy-momentum tensor under the isotropic coordinate transformation

Hawking radiation spectra for scalar fields by a higher-dimensional Schwarzschild-de Sitter black hole

Science.gov (United States)

Pappas, T.; Kanti, P.; Pappas, N.

2016-07-01

In this work, we study the propagation of scalar fields in the gravitational background of a higher-dimensional Schwarzschild-de Sitter black hole as well as on the projected-on-the-brane four-dimensional background. The scalar fields have also a nonminimal coupling to the corresponding, bulk or brane, scalar curvature. We perform a comprehensive study by deriving exact numerical results for the greybody factors, and study their profile in terms of particle and spacetime properties. We then proceed to derive the Hawking radiation spectra for a higher-dimensional Schwarzschild-de Sitter black hole, and we study both bulk and brane channels. We demonstrate that the nonminimal field coupling, which creates an effective mass term for the fields, suppresses the energy emission rates while the cosmological constant assumes a dual role. By computing the relative energy rates and the total emissivity ratio for bulk and brane emission, we demonstrate that the combined effect of a large number of extra dimensions and value of the field coupling gives to the bulk channel the clear domination in the bulk-brane energy balance.

Effective temperatures and radiation spectra for a higher-dimensional Schwarzschild-de Sitter black hole

Science.gov (United States)

Kanti, P.; Pappas, T.

2017-07-01

The absence of a true thermodynamical equilibrium for an observer located in the causal area of a Schwarzschild-de Sitter spacetime has repeatedly raised the question of the correct definition of its temperature. In this work, we consider five different temperatures for a higher-dimensional Schwarzschild-de Sitter black hole: the bare T0, the normalized TBH, and three effective ones given in terms of both the black-hole and cosmological horizon temperatures. We find that these five temperatures exhibit similarities but also significant differences in their behavior as the number of extra dimensions and the value of the cosmological constant are varied. We then investigate their effect on the energy emission spectra of Hawking radiation. We demonstrate that the radiation spectra for the normalized temperature TBH—proposed by Bousso and Hawking over twenty years ago—leads to the dominant emission curve, while the other temperatures either support a significant emission rate only in a specific Λ regime or have their emission rates globally suppressed. Finally, we compute the bulk-over-brane emissivity ratio and show that the use of different temperatures may lead to different conclusions regarding the brane or bulk dominance.

Accretion of new variable modified Chaplygin gas and generalized cosmic Chaplygin gas onto Schwarzschild and Kerr-Newman black holes

International Nuclear Information System (INIS)

Bhadra, Jhumpa; Debnath, Ujjal

2012-01-01

In this work, we have studied accretion of the dark energies in new variable modified Chaplygin gas (NVMCG) and generalized cosmic Chaplygin gas (GCCG) models onto Schwarzschild and Kerr-Newman black holes. We find the expression of the critical four velocity component which gradually decreases for the fluid flow towards the Schwarzschild as well as the Kerr-Newman black hole. We also find the expression for the change of mass of the black hole in both cases. For the Kerr-Newman black hole, which is rotating and charged, we calculate the specific angular momentum and total angular momentum. We showed that in both cases, due to accretion of dark energy, the mass of the black hole increases and angular momentum increases in the case of a Kerr-Newman black hole. (orig.)

Bi-conformal symmetry and static Green functions in the Schwarzschild-Tangherlini spacetimes

International Nuclear Information System (INIS)

Frolov, Valeri P.; Zelnikov, Andrei

2015-01-01

We study a static massless minimally coupled scalar field created by a source in a static D-dimensional spacetime. We demonstrate that the corresponding equation for this field is invariant under a special transformation of the background metric. This transformation consists of the static conformal transformation of the spatial part of the metric accompanied by a properly chosen transformation of the red-shift factor. Both transformations are determined by one function Ω of the spatial coordinates. We show that in a case of higher dimensional spherically symmetric black holes one can find such a bi-conformal transformation that the symmetry of the D-dimensional metric is enhanced after its application. Namely, the metric becomes a direct sum of the metric on a unit sphere and the metric of 2D anti-de Sitter space. The method of the heat kernels is used to find the Green function in this new space, which allows one, after dimensional reduction, to obtain a static Green function in the original space of the static black hole. The general useful representation of static Green functions is obtained in the Schwarzschild-Tangherlini spacetimes of arbitrary dimension. The exact explicit expressions for the static Green functions are obtained in such metrics for D<6. It is shown that in the four dimensional case the corresponding Green function coincides with the Copson solution.

Touching Ghosts: Observing Free Fall from an Infalling Frame of Reference into a Schwarzschild Black Hole

Science.gov (United States)

Augousti, A. T.; Gawelczyk, M.; Siwek, A.; Radosz, A.

2012-01-01

The problem of communication between observers in the vicinity of a black hole in a Schwarzschild metric is considered. The classic example of an infalling observer Alice and a static distant mother station (MS) is extended to include a second infalling observer Bob, who follows Alice in falling towards the event horizon. Kruskal coordinates are…

Mode coupling of Schwarzschild perturbations: Ringdown frequencies

International Nuclear Information System (INIS)

Pazos, Enrique; Brizuela, David; Martin-Garcia, Jose M.; Tiglio, Manuel

2010-01-01

Within linearized perturbation theory, black holes decay to their final stationary state through the well-known spectrum of quasinormal modes. Here we numerically study whether nonlinearities change this picture. For that purpose we study the ringdown frequencies of gauge-invariant second-order gravitational perturbations induced by self-coupling of linearized perturbations of Schwarzschild black holes. We do so through high-accuracy simulations in the time domain of first and second-order Regge-Wheeler-Zerilli type equations, for a variety of initial data sets. We consider first-order even-parity (l=2, m=±2) perturbations and odd-parity (l=2, m=0) ones, and all the multipoles that they generate through self-coupling. For all of them and all the initial data sets considered we find that--in contrast to previous predictions in the literature--the numerical decay frequencies of second-order perturbations are the same ones of linearized theory, and we explain the observed behavior. This would indicate, in particular, that when modeling or searching for ringdown gravitational waves, appropriately including the standard quasinormal modes already takes into account nonlinear effects.

On the world function of the Schwarzschild field

International Nuclear Information System (INIS)

Buchdahl, H.A.; Warner, N.P.

1979-01-01

The representation of the world function Ω of the Schwarzschild field as a power series is investigated. The initial concern is with a neighbourhood of the event horizon. The symmetries of the metric are invoked effectively to reduce the number of independent variables upon which Ω depends from eight to four, and to show that when these are sufficiently small in magnitude Ω is an analytic function of them. A fairly large number of the early terms of the power series for Ω is found explicitly. The condition that one is to remain sufficiently close to the event horizon is then relaxed, it being merely stipulated that the endpoints shall be sufficiently close to each other. Finally, using other variables, the early terms of a series for Ω are obtained for the case in which the endpoints are restricted to lie outside the event horizon and sufficiently close to each other. (author)

High overtones of Schwarzschild-de-Sitter quasinormal spectrum

International Nuclear Information System (INIS)

Konoplya, R.A.; Zhidenko, A.

2004-01-01

We find the high overtones of gravitational and electromagnetic quasinormal spectrum of the Schwarzschild-de Sitter black hole. The calculations show that the real parts of the electromagnetic modes asymptotically approach zero. The gravitational modes show more peculiar behavior at large n: the real part oscillates as a function of imaginary even for very high overtones and these oscillations settles to some 'profile' which just repeats itself with further increasing of the overtone number n. This lets us judge that Reω is not a constant as n →∞ but rather some oscillating function. The spacing for imaginary part Imω n+1 -Imω n for electromagnetic perturbations at high n slowly approach k e as n→∞, where k e is the surface gravity. In addition we find the lower QN modes for which the values obtained with numerical methods are in a very good agreement with those obtained through the 6th order WKB technique. (author)

From thermodynamics to the solutions in gravity theory

International Nuclear Information System (INIS)

Zhang, Hongsheng; Li, Xin-Zhou

2014-01-01

In a recent work, we present a new point of view to the relation of gravity and thermodynamics, in which we derive the Schwarzschild solution through thermodynamic considerations by the aid of the Misner–Sharp mass in an adiabatic system. In this Letter we continue to investigate the relation between gravity and thermodynamics for obtaining solutions via thermodynamics. We generalize our studies on gravi-thermodynamics in Einstein gravity to modified gravity theories. By using the first law with the assumption that the Misner–Sharp mass is the mass for an adiabatic system, we reproduce the Boulware–Deser–Cai solution in Gauss–Bonnet gravity. Using this gravi-thermodynamic thought, we obtain a NEW class of solution in F(R) gravity in an n-dimensional (n≥3) spacetime which permits three-type (n−2)-dimensional maximally symmetric subspace, as an extension of our recent three-dimensional black hole solution, and four-dimensional Clifton–Barrow solution in F(R) gravity

From thermodynamics to the solutions in gravity theory

Directory of Open Access Journals (Sweden)

Hongsheng Zhang

2014-10-01

Full Text Available In a recent work, we present a new point of view to the relation of gravity and thermodynamics, in which we derive the Schwarzschild solution through thermodynamic considerations by the aid of the Misner–Sharp mass in an adiabatic system. In this Letter we continue to investigate the relation between gravity and thermodynamics for obtaining solutions via thermodynamics. We generalize our studies on gravi-thermodynamics in Einstein gravity to modified gravity theories. By using the first law with the assumption that the Misner–Sharp mass is the mass for an adiabatic system, we reproduce the Boulware–Deser–Cai solution in Gauss–Bonnet gravity. Using this gravi-thermodynamic thought, we obtain a NEW class of solution in F(R gravity in an n-dimensional (n≥3 spacetime which permits three-type (n−2-dimensional maximally symmetric subspace, as an extension of our recent three-dimensional black hole solution, and four-dimensional Clifton–Barrow solution in F(R gravity.

From geodesics of the multipole solutions to the perturbed Kepler problem

International Nuclear Information System (INIS)

Hernandez-Pastora, J. L.; Ospino, J.

2010-01-01

A static and axisymmetric solution of the Einstein vacuum equations with a finite number of relativistic multipole moments (RMM) is written in multipole symmetry adapted (MSA) coordinates up to certain order of approximation, and the structure of its metric components is explicitly shown. From the equation of equatorial geodesics, we obtain the Binet equation for the orbits and it allows us to determine the gravitational potential that leads to the equivalent classical orbital equations of the perturbed Kepler problem. The relativistic corrections to Keplerian motion are provided by the different contributions of the RMM of the source starting from the monopole (Schwarzschild correction). In particular, the perihelion precession of the orbit is calculated in terms of the quadrupole and 2 4 -pole moments. Since the MSA coordinates generalize the Schwarzschild coordinates, the result obtained allows measurement of the relevance of the quadrupole moment in the first order correction to the perihelion frequency-shift.

Thermodynamics of the Schwarzschild-de Sitter black hole: Thermal stability of the Nariai black hole

International Nuclear Information System (INIS)

Myung, Yun Soo

2008-01-01

We study the thermodynamics of the Schwarzschild-de Sitter black hole in five dimensions by introducing two temperatures based on the standard and Bousso-Hawking normalizations. We use the first-law of thermodynamics to derive thermodynamic quantities. The two temperatures indicate that the Nariai black hole is thermodynamically unstable. However, it seems that black hole thermodynamics favors the standard normalization and does not favor the Bousso-Hawking normalization

Black hole solutions in mimetic Born-Infeld gravity.

Science.gov (United States)

Chen, Che-Yu; Bouhmadi-López, Mariam; Chen, Pisin

2018-01-01

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. We find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in this case, the maximal proper time for a timelike radially-infalling observer to reach the singularity is found to be infinite.

Black hole solutions in mimetic Born-Infeld gravity

Energy Technology Data Exchange (ETDEWEB)

Chen, Che-Yu [National Taiwan University, Department of Physics and Center for Theoretical Sciences, Taipei (China); LeCosPA, National Taiwan University, Taipei (China); Bouhmadi-Lopez, Mariam [University of the Basque Country UPV/EHU, Department of Theoretical Physics, Bilbao (Spain); IKERBASQUE, Basque Foundation for Science, Bilbao (Spain); Chen, Pisin [National Taiwan University, Department of Physics and Center for Theoretical Sciences, Taipei (China); LeCosPA, National Taiwan University, Taipei (China); Stanford University, Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory, Stanford, CA (United States)

2018-01-15

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. We find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in this case, the maximal proper time for a timelike radially-infalling observer to reach the singularity is found to be infinite. (orig.)

A detailed analytic study of the asymptotic quasinormal modes of Schwarzschild-anti de Sitter black holes

International Nuclear Information System (INIS)

Daghigh, Ramin G; Green, Michael D

2009-01-01

We analyze analytically the asymptotic regions of the quasinormal mode frequency spectra with infinitely large overtone numbers for D-dimensional Schwarzschild black holes in anti de Sitter spacetimes. In this limit, we confirm the analytic results obtained previously in the literature using different methods. In addition, we show that in certain spacetime dimensions these techniques imply the existence of other regions of the asymptotic quasinormal mode frequency spectrum which have not previously appeared in the literature. For large black holes, some of these modes have a damping rate of 1.2T H , where T H is the Hawking temperature. This is less than the damping rate of the lowest overtone quasinormal mode calculated by other authors. It is not completely clear whether these modes actually exist or are an artifact of an unknown flaw in the analytic techniques being used. We discuss the possibility of the existence of these modes and explore some of the consequences. We also examine the possible connection between the asymptotic quasinormal modes of Schwarzschild-anti de Sitter black holes and the quantum level spacing of their horizon area spectrum.

Gravitational waveforms from a point particle orbiting a Schwarzschild black hole

International Nuclear Information System (INIS)

Martel, Karl

2004-01-01

We numerically solve the inhomogeneous Zerilli-Moncrief and Regge-Wheeler equations in the time domain. We obtain the gravitational waveforms produced by a point particle of mass μ traveling around a Schwarzschild black hole of mass M on arbitrary bound and unbound orbits. Fluxes of energy and angular momentum at infinity and the event horizon are also calculated. Results for circular orbits, selected cases of eccentric orbits, and parabolic orbits are presented. The numerical results from the time-domain code indicate that, for all three types of orbital motion, black hole absorption contributes less than 1% of the total flux, so long as the orbital radius r p (t) satisfies r p (t)>5M at all times

K. Schwarzschild's problem in radiation transfer theory

International Nuclear Information System (INIS)

Rutily, B.; Chevallier, L.; Pelkowski, J.

2006-01-01

We solve exactly the problem of a finite slab receiving an isotropic radiation on one side and no radiation on the other side. This problem-to be more precise the calculation of the source function within the slab-was first formulated by K. Schwarzschild in 1914. We first solve it for unspecified albedos and optical thicknesses of the atmosphere, in particular for an albedo very close to 1 and a very large optical thickness in view of some astrophysical applications. Then we focus on the conservative case (albedo=1), which is of great interest for the modeling of grey atmospheres in radiative equilibrium. Ten-figure tables of the conservative source function are given. From the analytical expression of this function, we deduce (1) a simple relation between the effective temperature of a grey atmosphere in radiative equilibrium and the temperature of the black body that irradiates it (2) the temperature at any point of the atmosphere when it is in local thermodynamical equilibrium. This temperature distribution is the counterpart, for a finite slab, of Hopf's distribution in a half-space. Its graphical representation is given for various optical thicknesses of the atmosphere

Generalized transformations and coordinates for static spherically symmetric general relativity

Science.gov (United States)

Hill, James M.; O'Leary, Joseph

2018-04-01

We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington-Finkelstein transformation and the Kruskal-Szekeres coordinates.

Generalized transformations and coordinates for static spherically symmetric general relativity.

Science.gov (United States)

Hill, James M; O'Leary, Joseph

2018-04-01

We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington-Finkelstein transformation and the Kruskal-Szekeres coordinates.

Magnetized particle motion and acceleration around a Schwarzschild black hole in a magnetic field

International Nuclear Information System (INIS)

Abdujabbarov, Ahmadjon; Bobomurat Ahmedov; Rahimov, Ozodbek; Salikhbaev, Umar

2014-01-01

The capture cross section of magnetized particles with nonvanishing magnetic moment by a Schwarzschild black hole immersed in an asymptotically uniform magnetic field has been studied as an extension of the approach developed in Zakharov (1994 Class. Quantum Grav. 11 1027) for neutral unmagnetized particles in the Reissner–Nordström spacetime. The magnetic moment of the particle is chosen as in de Felice and Sorge (2003 Class. Quantum Grav. 20 469). It is shown that the spin of the particle sustains the stability of particles circularly orbiting around the black hole immersed in a magnetic field, i.e., a spinning particle's motion near the Schwarzschild black hole horizon is more stable than that of a particle with zero spin. It is shown that the magnetic parameter essentially changes the value of the critical angular momentum and affects the process of capture of the particles by the central black hole. Furthermore, the interaction between the magnetic moment of the particle and the magnetic field forces stable circular orbits to shift to the central object, and this effect should be taken into account in astrophysical scenarios related to the accretion discs and in measuring the spin of the black holes. The magnetized particle's acceleration mechanism near the black hole in an external magnetic field is studied. It is shown that due to the presence of a magnetic field, magnetized particles can accelerate to unlimited high energies. (paper)

Hawking Radiation Spectra for Scalar Fields by a Higher-Dimensional Schwarzschild-de-Sitter Black Hole

OpenAIRE

Pappas, T.; Kanti, P.; Pappas, N.

2016-01-01

In this work, we study the propagation of scalar fields in the gravitational background of a higher-dimensional Schwarzschild-de-Sitter black hole as well as on the projected-on-the-brane 4-dimensional background. The scalar fields have also a non-minimal coupling to the corresponding, bulk or brane, scalar curvature. We perform a comprehensive study by deriving exact numerical results for the greybody factors, and study their profile in terms of particle and spacetime properties. We then pro...

A proposal of the gauge theory description of the small Schwarzschild black hole in AdS5×S5

International Nuclear Information System (INIS)

Hanada, Masanori; Maltz, Jonathan

2017-01-01

Based on 4d N=4 SYM on ℝ 1 ×S 3 , a gauge theory description of a small black hole in AdS 5 ×S 5 is proposed. The change of the number of dynamical degrees of freedom associated with the emission of the scalar fields’ eigenvalues plays a crucial role in this description. By analyzing the microcanonical ensemble, the Hagedorn behavior of long strings at low energy is obtained. Modulo an assumption based on the AdS/CFT duality for a large black hole, the energy of the small ten-dimensional Schwarzschild black hole E∼1/(G 10,N T 7 ) is derived. A heuristic gauge theory argument supporting this assumption is also given. The same argument applied to the ABJM theory correctly reproduces the relation for the eleven-dimensional Schwarzschild black hole. One of the consequences of our proposal is that the small and large black holes are very similar when seen from the gauge theory point of view.

The self-force on a non-minimally coupled static scalar charge outside a Schwarzschild black hole

International Nuclear Information System (INIS)

Cho, Demian H J; Tsokaros, Antonios A; Wiseman, Alan G

2007-01-01

The finite part of the self-force on a static, non-minimally coupled scalar test charge outside a Schwarzschild black hole is zero. This result is determined from the work required to slowly raise or lower the charge through an infinitesimal distance. Unlike similar force calculations for minimally-coupled scalar charges or electric charges, we find that we must account for a flux of field energy that passes through the horizon and changes the mass and area of the black hole when the charge is displaced. This occurs even for an arbitrarily slow displacement of the non-minimally coupled scalar charge. For a positive coupling constant, the area of the hole increases when the charge is lowered and decreases when the charge is raised. The fact that the self-force vanishes for a static, non-minimally coupled scalar charge in Schwarzschild spacetime agrees with a simple prediction of the Quinn-Wald axioms. However, Zel'nikov and Frolov computed a non-vanishing self-force for a non-minimally coupled charge. Our method of calculation closely parallels the derivation of Zel'nikov and Frolov, and we show that their omission of this unusual flux is responsible for their (incorrect) result. When the flux is accounted for, the self-force vanishes. This correction eliminates a potential counter example to the Quinn-Wald axioms. The fact that the area of the black hole changes when the charge is displaced brings up two interesting questions that did not arise in similar calculations for static electric charges and minimally coupled scalar charges. (1) How can we reconcile a decrease in the area of the black hole horizon with the area theorem which concludes that δArea horizon ≥ 0? The key hypothesis of the area theorem is that the stress-energy tensor must satisfy a null-energy condition T αβ l α l β ≥ 0 for any null vector l α . We explicitly show that the stress-energy associated with a non-minimally coupled field does not satisfy this condition, and this violation of

Torsion induces gravity

International Nuclear Information System (INIS)

Aros, Rodrigo; Contreras, Mauricio

2006-01-01

In this work the Poincare-Chern-Simons and anti-de Sitter-Chern-Simons gravities are studied. For both, a solution that can be cast as a black hole with manifest torsion is found. Those solutions resemble Schwarzschild and Schwarzschild-AdS solutions, respectively

Linearized stability analysis of thin-shell wormholes with a cosmological constant

International Nuclear Information System (INIS)

Lobo, Francisco S N; Crawford, Paulo

2004-01-01

Spherically symmetric thin-shell wormholes in the presence of a cosmological constant are constructed applying the cut-and-paste technique implemented by Visser. Using the Darmois-Israel formalism the surface stresses, which are concentrated at the wormhole throat, are determined. This construction allows us to apply a dynamical analysis to the throat, considering linearized radial perturbations around static solutions. For a large positive cosmological constant, i.e., for the Schwarzschild-de Sitter solution, the region of stability is significantly increased, relatively to the null cosmological constant case, analysed by Poisson and Visser. With a negative cosmological constant, i.e., the Schwarzschild-anti de Sitter solution, the region of stability is decreased. In particular, considering static solutions with a generic cosmological constant, the weak and dominant energy conditions are violated, while for a 0 ≤ 3M the null and strong energy conditions are satisfied. The surface pressure of the static solution is strictly positive for the Schwarzschild and Schwarzschild-anti de Sitter spacetimes, but takes negative values, assuming a surface tension in the Schwarzschild-de Sitter solution, for high values of the cosmological constant and the wormhole throat radius

Null geodesics and embedding diagrams of the interior Schwarzschild--de Sitter spacetimes with uniform density

International Nuclear Information System (INIS)

Stuchlik, Zdenek; Hledik, Stanislav; Soltes, Jiri; Ostgaard, Erlend

2001-01-01

Null geodesics and embedding diagrams of central planes in the ordinary space geometry and the optical reference geometry of the interior Schwarzschild--de Sitter spacetimes with uniform density are studied. For completeness, both positive and negative values of the cosmological constant are considered. The null geodesics are restricted to the central planes of these spacetimes, and their properties can be reflected by an 'effective potential.' If the interior spacetime is extremely compact, the effective potential has a local maximum corresponding to a stable circular null geodesic around which bound null geodesics are concentrated. The upper limit on the size of the interior spacetimes containing bound null geodesics is R=3M, independently of the value of the cosmological constant. The embedding diagrams of the central planes of the ordinary geometry into three-dimensional Euclidean space are well defined for the complete interior of all spacetimes with a repulsive cosmological constant, but the planes cannot be embedded into the Euclidean space in the case of spacetimes with subcritical values of an attractive cosmological constant. On the other hand, the embedding diagrams of the optical geometry are well defined for all of the spacetimes, and the turning points of these diagrams correspond to the radii of the circular null geodesics. All the embedding diagrams, for both the ordinary and optical geometry, are smoothly matched to the corresponding embedding diagrams of the external vacuum Schwarzschild--de Sitter spacetimes

Large N phase transitions and the fate of small Schwarzschild-AdS black holes

Science.gov (United States)

Yaffe, Laurence G.

2018-01-01

Sufficiently small Schwarzschild-AdS black holes in asymptotically global AdS5×S5 spacetime are known to become dynamically unstable toward deformation of the internal S5 geometry. The resulting evolution of such an unstable black hole is related, via holography, to the dynamics of supercooled plasma which has reached the limit of metastability in maximally supersymmetric large-N Yang-Mills theory on R ×S3. Puzzles related to the resulting dynamical evolution are discussed, with a key issue involving differences between the large-N limit in the dual field theory and typical large volume thermodynamic limits.

One-parameter family of time-symmetric initial data for the radial infall of a particle into a Schwarzschild black hole

International Nuclear Information System (INIS)

Martel, Karl; Poisson, Eric

2002-01-01

A one-parameter family of time-symmetric initial data for the radial infall of a particle into a Schwarzschild black hole is constructed within the framework of black-hole perturbation theory. The parameter measures the amount of gravitational radiation present on the initial spacelike surface. These initial data sets are then evolved by integrating the Zerilli-Moncrief wave equation in the presence of the particle. Numerical results for the gravitational waveforms and their power spectra are presented; we show that the choice of initial data strongly influences the waveforms, both in their shapes and their frequency content. We also calculate the total energy radiated by the particle-black-hole system, as a function of the initial separation between the particle and the black hole, and as a function of the choice of initial data. Our results confirm that for large initial separations, a conformally flat initial three-geometry minimizes the initial gravitational-wave content, so that the total energy radiated is also minimized. For small initial separations, however, we show that the conformally flat solution no longer minimizes the energy radiated

Accretion of a symmetry-breaking scalar field by a Schwarzschild black hole.

Science.gov (United States)

Traykova, Dina; Braden, Jonathan; Peiris, Hiranya V

2018-03-06

We simulate the behaviour of a Higgs-like field in the vicinity of a Schwarzschild black hole using a highly accurate numerical framework. We consider both the limit of the zero-temperature Higgs potential and a toy model for the time-dependent evolution of the potential when immersed in a slowly cooling radiation bath. Through these numerical investigations, we aim to improve our understanding of the non-equilibrium dynamics of a symmetry-breaking field (such as the Higgs) in the vicinity of a compact object such as a black hole. Understanding this dynamics may suggest new approaches for studying properties of scalar fields using black holes as a laboratory.This article is part of the Theo Murphy meeting issue 'Higgs Cosmology'. © 2018 The Author(s).

Comment on "Comments on `The Euclidean gravitational action as black hole entropy, singularities and space-time voids'" [J. Math. Phys. 50, 042502 (2009)]-Schwarzschild black hole lives to fight another day

Science.gov (United States)

Kundu, Prasun K.

2017-11-01

In a comment published several years ago in this journal, Mitra [J. Math. Phys. 50, 042502 (2009)] has claimed to prove that a neutral point particle in general relativity as described by the Schwarzschild metric must have zero gravitational mass, i.e., the mass parameter M0 of a Schwarzschild black hole necessarily vanishes. It is shown that the purported proof is incorrect. The error stems from a basic misunderstanding of the mathematical description of coordinate volume element in a differentiable manifold.

Uber das Gravitationsfeld eines Massenpunktes nach der Einstenschen Theorie

OpenAIRE

Bel, Ll.

2007-01-01

Schwarzschild's solution of Einstein's field equations in vacuum can be written in many different forms. Unfortunately Schwarzschild's own original form is less nice looking and simple than that latter derived by Droste and Hilbert. We prove here that we can have both: a nice looking simple form and the meaning that Schwarzschild wanted to give to his solution, i.e., that of describing the gravitational field of a massive point particle.

Solutions of the linearized Bach-Einstein equation in the static spherically symmetric case

International Nuclear Information System (INIS)

Schmidt, H.J.

1985-01-01

The Bach-Einstein equation linearized around Minkowski space-time is completely solved. The set of solutions depends on three parameters; a two-parameter subset of it becomes asymptotically flat. In that region the gravitational potential is of the type phi = -m/r + epsilon exp (-r/l). Because of the different asymptotic behaviour of both terms, it became necessary to linearize also around the Schwarzschild solution phi = -m/r. The linearized equation resulting in this case is discussed using qualitative methods. The result is that for m = 2l phi = -m/r + epsilon r -2 exp (-r/l) u, where u is some bounded function; m is arbitrary and epsilon again small. Further, the relation between the solution of the linearized and the full equation is discussed. (author)

Book Review:

Science.gov (United States)

Ernst, Frederick J.

2007-06-01

Shortly after Einstein published his general theory of relativity, the spherically symmetric solution of the vacuum field equations was discovered by Karl Schwarzschild, while Hermann Weyl showed that from any axisymmetric solution ψ of the Laplace equation ∇²ψ = 0 (satisfying appropriate boundary conditions) the metric tensor of a static axisymmetric vacuum spacetime can be constructed. In particular, the Schwarzschild solution corresponds to a rather trivial solution of Laplace's equation expressed in terms of prolate spheroidal coordinates. It took about 45 years before Roy Kerr discovered what he called the 'rotating Schwarzschild solution', and an additional five years before I established that from any complex axisymmetric solution \\E of the nonlinear equation (\\Re E)\

Probing quantum entanglement in the Schwarzschild space-time beyond the single-mode approximation

Science.gov (United States)

He, Juan; Ding, Zhi-Yong; Ye, Liu

2018-05-01

In this paper, we deduce the vacuum structure for Dirac fields in the background of Schwarzschild space-time beyond the single-mode approximation and discuss the performance of quantum entanglement between particle and antiparticle modes of a Dirac field with Hawking effect. It is shown that Hawking radiation does not always destroy the physically accessible entanglement, and entanglement amplification may happen in some cases. This striking result is different from that of the single-mode approximation, which holds that the Hawking radiation can only destroy entanglement. Lastly, we analyze the physically accessible entanglement relation outside the event horizon and demonstrate that the monogamy inequality is constantly established regardless of the choice of given parameters.

Black holes in the Universe: Generalized Lemaitre-Tolman-Bondi solutions

International Nuclear Information System (INIS)

Gao Changjun; Chen Xuelei; Shen Yougen; Faraoni, Valerio

2011-01-01

We present new exact solutions which presumably describe black holes in the background of a spatially flat, pressureless dark-matter- or dark matter plus dark energy (DM+DE)- or quintom-dominated Universe. These solutions generalize Lemaitre-Tolman-Bondi metrics. For a dark-matter- or (DM+DE)-dominated universe, the area of the black hole apparent horizon (AH) decreases with the expansion of the Universe while that of the cosmic AH increases. However, for a quintom-dominated universe, the black hole AH first shrinks and then expands, while the cosmic AH first expands and then shrinks. A (DM+DE)-dominated universe containing a black hole will evolve to the Schwarzschild-de Sitter solution with both AHs approaching constant size. In a quintom-dominated universe, the black hole and cosmic AHs will coincide at a certain time, after which the singularity becomes naked, violating cosmic censorship.

Dirac equation for massive neutrinos in a Schwarzschild-de Sitter spacetime from a 5D vacuum

International Nuclear Information System (INIS)

Sánchez, Pablo Alejandro; Anabitarte, Mariano; Bellini, Mauricio

2011-01-01

Starting from a Dirac equation for massless neutrino in a 5D Ricci-flat background metric, we obtain the effective 4D equation for massive neutrino in a Schwarzschild-de Sitter (SdS) background metric from an extended SdS 5D Ricci-flat metric. We use the fact that the spin connection is defined to an accuracy of a vector, so that the covariant derivative of the spinor field is strongly dependent of the background geometry. We show that the mass of the neutrino can be induced from the extra space-like dimension.

Fabrication of nanoscale patterns in lithium fluoride crystal using a 13.5 nm Schwarzschild objective and a laser produced plasma source

International Nuclear Information System (INIS)

Wang Xin; Mu Baozhong; Jiang Li; Zhu Jingtao; Yi Shengzhen; Wang Zhanshan; He Pengfei

2011-01-01

Lithium fluoride (LiF) crystal is a radiation sensitive material widely used as EUV and soft x-ray detector. The LiF-based detector has high resolution, in principle limited by the point defect size, large field of view, and wide dynamic range. Using LiF crystal as an imaging detector, a resolution of 900 nm was achieved by a projection imaging of test meshes with a Schwarzschild objective operating at 13.5 nm. In addition, by imaging of a pinhole illuminated by the plasma, an EUV spot of 1.5 μm diameter in the image plane of the objective was generated, which accomplished direct writing of color centers with resolution of 800 nm. In order to avoid sample damage and contamination due to the influence of huge debris flux produced by the plasma source, a spherical normal-incidence condenser was used to collect EUV radiation. Together with a description of experimental results, the development of the Schwarzschild objective, the influence of condenser on energy density and the alignment of the imaging system are also reported.

Spectroscopy of the Schwarzschild black hole at arbitrary frequencies.

Science.gov (United States)

Casals, Marc; Ottewill, Adrian

2012-09-14

Linear field perturbations of a black hole are described by the Green function of the wave equation that they obey. After Fourier decomposing the Green function, its two natural contributions are given by poles (quasinormal modes) and a largely unexplored branch cut in the complex frequency plane. We present new analytic methods for calculating the branch cut on a Schwarzschild black hole for arbitrary values of the frequency. The branch cut yields a power-law tail decay for late times in the response of a black hole to an initial perturbation. We determine explicitly the first three orders in the power-law and show that the branch cut also yields a new logarithmic behavior T(-2ℓ-5)lnT for late times. Before the tail sets in, the quasinormal modes dominate the black hole response. For electromagnetic perturbations, the quasinormal mode frequencies approach the branch cut at large overtone index n. We determine these frequencies up to n(-5/2) and, formally, to arbitrary order. Highly damped quasinormal modes are of particular interest in that they have been linked to quantum properties of black holes.

Do static atoms outside a Schwarzschild black hole spontaneously excite?

International Nuclear Information System (INIS)

Yu Hongwei; Zhou Wenting

2007-01-01

The spontaneous excitation of a two-level atom held static outside a four dimensional Schwarzschild black hole and in interaction with a massless scalar field in the Boulware, Unruh, and Hartle-Hawking vacuums is investigated, and the contributions of the vacuum fluctuations and radiation reaction to the rate of change of the mean atomic energy are calculated separately. We find that, for the Boulware vacuum, the spontaneous excitation does not occur and the ground-state atoms are stable, while the spontaneous emission rate for excited atoms in the Boulware vacuum, which is well behaved at the event horizon, is not the same as that in the usual Minkowski vacuum. However, for both the Unruh vacuum and the Hartle-Hawking vacuum, our results show that the atom would spontaneously excite, as if there were an outgoing thermal flux of radiation or as if it were in a thermal bath of radiation at a proper temperature which reduces to the Hawking temperature in the spatial asymptotic region, depending on whether the scalar field is in the Unruh or Hartle-Hawking vacuum

A generalized sine condition and performance comparison of Wolter type II and Wolter-Schwarzschild extreme ultraviolet telescopes

Science.gov (United States)

Saha, T. T.

1984-01-01

An equation similar to the Abbe sine condition is derived for a Wolter type II telescope. This equation and the sine condition are then combined to produce a so called generalized sine condition. Using the law of reflection, Fermat's principle, the generalized sine condition, and simple geometry the surface equations for a Wolter type II telescope and an equivalent Wolter-Schwarzschild telescope are calculated. The performances of the telescopes are compared in terms of rms blur circle radius at the Gaussian focal plane and at best focus.

Ineffective higher derivative black hole hair

Science.gov (United States)

Goldstein, Kevin; Mashiyane, James Junior

2018-01-01

Inspired by the possibility that the Schwarzschild black hole may not be the unique spherically symmetric vacuum solution to generalizations of general relativity, we consider black holes in pure fourth order higher derivative gravity treated as an effective theory. Such solutions may be of interest in addressing the issue of higher derivative hair or during the later stages of black hole evaporation. Non-Schwarzschild solutions have been studied but we have put earlier results on a firmer footing by finding a systematic asymptotic expansion for the black holes and matching them with known numerical solutions obtained by integrating out from the near-horizon region. These asymptotic expansions can be cast in the form of trans-series expansions which we conjecture will be a generic feature of non-Schwarzschild higher derivative black holes. Excitingly we find a new branch of solutions with lower free energy than the Schwarzschild solution, but as found in earlier work, solutions only seem to exist for black holes with large curvatures, meaning that one should not generically neglect even higher derivative corrections. This suggests that one effectively recovers the nonhair theorems in this context.

A complete solution for GP-B's gyroscopic precession by retarded gravitational theory

Science.gov (United States)

Tang, Keyun

Mainstream physicists generally believe that Mercury’s Perihelion precession and GP-B’ gyroscopic precession are two of the strongest evidences supporting Einstein’ curved spacetime and general relativity. However, most classical literatures and textbooks (e.g. Ohanain: Gravitation and Spacetime) paint an incorrect picture of Mercury’s orbit anomaly, namely Mercury’s perihelion precessed 43 arc-seconds per century; a correct picture should be that Mercury rotated 43 arc-seconds per century more than along Newtonian theoretical orbit. The essence of Le Verrier’s and Newcomb’s observation and analysis is that the angular speed of Mercury is slightly faster than the Newtonian theoretical value. The complete explanation to Mercury’s orbit anomaly should include two factors, perihelion precession is one of two factors, in addition, the change of orbital radius will also cause a change of angular speed, which is another component of Mercury's orbital anomaly. If Schwarzschild metric is correct, then the solution of the Schwarzschild orbit equation must contain three non-ignorable items. The first corresponds to Newtonian ellipse; the second is a nonlinear perturbation with increasing amplitude, which causes the precession of orbit perihelion; this is just one part of the angular speed anomaly of Mercury; the third part is a linear perturbation, corresponding to a similar figure of the Newton's ellipse, but with a minimal radius; this makes no contribution to the perihelion precession of the Schwarzschild orbit, but makes the Schwarzschild orbital radius slightly smaller, leading to a slight increase in Mercury’s angular speed. All classical literatures of general relativity ignored this last factor, which is a gross oversight. If you correctly take all three factors into consideration, the final result is that the difference between the angles rotated along Schwarzschild’s orbit and the angle rotated along Newton’s orbit for one hundred years should

Schwarzschild-de Sitter spacetime: The role of temperature in the emission of Hawking radiation

Science.gov (United States)

Pappas, Thomas; Kanti, Panagiota

2017-12-01

We consider a Schwarzschild-de Sitter (SdS) black hole, and focus on the emission of massless scalar fields either minimally or non-minimally coupled to gravity. We use six different temperatures, two black-hole and four effective ones for the SdS spacetime, as the question of the proper temperature for such a background is still debated in the literature. We study their profiles under the variation of the cosmological constant, and derive the corresponding Hawking radiation spectra. We demonstrate that only few of these temperatures may support significant emission of radiation. We finally compute the total emissivities for each temperature, and show that the non-minimal coupling constant of the scalar field to gravity also affects the relative magnitudes of the energy emission rates.

Numerical simulation of electromagnetic waves in Schwarzschild space-time by finite difference time domain method and Green function method

Science.gov (United States)

Jia, Shouqing; La, Dongsheng; Ma, Xuelian

2018-04-01

The finite difference time domain (FDTD) algorithm and Green function algorithm are implemented into the numerical simulation of electromagnetic waves in Schwarzschild space-time. FDTD method in curved space-time is developed by filling the flat space-time with an equivalent medium. Green function in curved space-time is obtained by solving transport equations. Simulation results validate both the FDTD code and Green function code. The methods developed in this paper offer a tool to solve electromagnetic scattering problems.

Fermion tunnels of higher-dimensional anti-de Sitter Schwarzschild black hole and its corrected entropy

Energy Technology Data Exchange (ETDEWEB)

Lin Kai, E-mail: lk314159@126.co [Institute of Theoretical Physics, China West Normal University, NanChong, SiChuan 637002 (China); Yang Shuzheng, E-mail: szyangcwnu@126.co [Institute of Theoretical Physics, China West Normal University, NanChong, SiChuan 637002 (China)

2009-10-12

Applying the method beyond semiclassical approximation, fermion tunneling from higher-dimensional anti-de Sitter Schwarzschild black hole is researched. In our work, the 'tortoise' coordinate transformation is introduced to simplify Dirac equation, so that the equation proves that only the (r-t) sector is important to our research. Because we only need to study the (r-t) sector, the Dirac equation is decomposed into several pairs of equations spontaneously, and we then prove the components of wave functions are proportional to each other in every pair of equations. Therefore, the suitable action forms of the wave functions are obtained, and finally the correctional Hawking temperature and entropy can be determined via the method beyond semiclassical approximation.

Detection of Intrinsic Source Structure at ∼3 Schwarzschild Radii with Millimeter-VLBI Observations of SAGITTARIUS A*

Science.gov (United States)

Lu, Ru-Sen; Krichbaum, Thomas P.; Roy, Alan L.; Fish, Vincent L.; Doeleman, Sheperd S.; Johnson, Michael D.; Akiyama, Kazunori; Psaltis, Dimitrios; Alef, Walter; Asada, Keiichi; Beaudoin, Christopher; Bertarini, Alessandra; Blackburn, Lindy; Blundell, Ray; Bower, Geoffrey C.; Brinkerink, Christiaan; Broderick, Avery E.; Cappallo, Roger; Crew, Geoffrey B.; Dexter, Jason; Dexter, Matt; Falcke, Heino; Freund, Robert; Friberg, Per; Greer, Christopher H.; Gurwell, Mark A.; Ho, Paul T. P.; Honma, Mareki; Inoue, Makoto; Kim, Junhan; Lamb, James; Lindqvist, Michael; Macmahon, David; Marrone, Daniel P.; Martí-Vidal, Ivan; Menten, Karl M.; Moran, James M.; Nagar, Neil M.; Plambeck, Richard L.; Primiani, Rurik A.; Rogers, Alan E. E.; Ros, Eduardo; Rottmann, Helge; SooHoo, Jason; Spilker, Justin; Stone, Jordan; Strittmatter, Peter; Tilanus, Remo P. J.; Titus, Michael; Vertatschitsch, Laura; Wagner, Jan; Weintroub, Jonathan; Wright, Melvyn; Young, Ken H.; Zensus, J. Anton; Ziurys, Lucy M.

2018-05-01

We report results from very long baseline interferometric (VLBI) observations of the supermassive black hole in the Galactic center, Sgr A*, at 1.3 mm (230 GHz). The observations were performed in 2013 March using six VLBI stations in Hawaii, California, Arizona, and Chile. Compared to earlier observations, the addition of the APEX telescope in Chile almost doubles the longest baseline length in the array, provides additional uv coverage in the N–S direction, and leads to a spatial resolution of ∼30 μas (∼3 Schwarzschild radii) for Sgr A*. The source is detected even at the longest baselines with visibility amplitudes of ∼4%–13% of the total flux density. We argue that such flux densities cannot result from interstellar refractive scattering alone, but indicate the presence of compact intrinsic source structure on scales of ∼3 Schwarzschild radii. The measured nonzero closure phases rule out point-symmetric emission. We discuss our results in the context of simple geometric models that capture the basic characteristics and brightness distributions of disk- and jet-dominated models and show that both can reproduce the observed data. Common to these models are the brightness asymmetry, the orientation, and characteristic sizes, which are comparable to the expected size of the black hole shadow. Future 1.3 mm VLBI observations with an expanded array and better sensitivity will allow more detailed imaging of the horizon-scale structure and bear the potential for a deep insight into the physical processes at the black hole boundary.

Fluid/gravity correspondence and the CFM black brane solutions

Energy Technology Data Exchange (ETDEWEB)

Casadio, R. [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, Bologna (Italy); Cavalcanti, R.T. [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); Universidade Federal do ABC-UFABC, Centro de Ciencias Naturais e Humanas, Santo Andre (Brazil); Rocha, Roldao da [Universidade Federal do ABC-UFABC, Centro de Matematica, Computacao e Cognicao, Santo Andre (Brazil)

2016-10-15

We consider the lower bound for the shear viscosity-to-entropy density ratio, obtained from the fluid/gravity correspondence, in order to constrain the post-Newtonian parameter of brane-world metrics. In particular, we analyse the Casadio-Fabbri-Mazzacurati (CFM) effective solutions for the gravity side of the correspondence and argue that including higher-order terms in the hydrodynamic expansion can lead to a full agreement with the experimental bounds, for the Eddington-Robertson-Schiff post-Newtonian parameter in the CFM metrics. This lends further support to the physical relevance of the viscosity-to-entropy ratio lower bound and fluid/gravity correspondence. Hence we show that CFM black branes are, effectively, Schwarzschild black branes. (orig.)

The initial value problem for linearized gravitational perturbations of the Schwarzschild naked singularity

Energy Technology Data Exchange (ETDEWEB)

Dotti, Gustavo; Gleiser, Reinaldo J [Facultad de Matematica, AstronomIa y Fisica (FaMAF), Universidad Nacional de Cordoba, Ciudad Universitaria, 5000 Cordoba (Argentina)

2009-11-07

The coupled equations for the scalar modes of the linearized Einstein equations around Schwarzschild's spacetime were reduced by Zerilli to a (1+1) wave equation partial deriv{sup 2}PSI{sub z} /partial derivt{sup 2} +HPSI{sub z} =0, where H= -partial deriv{sup 2} /partial derivx{sup 2} + V(x) is the Zerilli 'Hamiltonian' and x is the tortoise radial coordinate. From its definition, for smooth metric perturbations the field PSI{sub z} is singular at r{sub s} = -6M/(l - 1)(l +2), with l being the mode harmonic number. The equation PSI{sub z} obeys is also singular, since V has a second-order pole at r{sub s}. This is irrelevant to the black hole exterior stability problem, where r > 2M > 0, and r{sub s} < 0, but it introduces a non-trivial problem in the naked singular case where M < 0, then r{sub s} > 0, and the singularity appears in the relevant range of r (0 < r < infinity). We solve this problem by developing a new approach to the evolution of the even mode, based on a new gauge invariant function, PSI-circumflex, that is a regular function of the metric perturbation for any value of M. The relation of PSI-circumflex to PSI{sub z} is provided by an intertwiner operator. The spatial pieces of the (1 + 1) wave equations that PSI-circumflex and PSI{sub z} obey are related as a supersymmetric pair of quantum Hamiltonians H and H-circumflex. For M < 0,H-circumflex has a regular potential and a unique self-adjoint extension in a domain D defined by a physically motivated boundary condition at r = 0. This allows us to address the issue of evolution of gravitational perturbations in this non-globally hyperbolic background. This formulation is used to complete the proof of the linear instability of the Schwarzschild naked singularity, by showing that a previously found unstable mode belongs to a complete basis of H-circumflex in D, and thus is excitable by generic initial data. This is further illustrated by numerically solving the linearized equations for

Schwarzschild black holes as unipolar inductors: Expected electromagnetic power of a merger

International Nuclear Information System (INIS)

Lyutikov, Maxim

2011-01-01

The motion of a Schwarzschild black hole with velocity v 0 =β 0 c through a constant magnetic field B 0 in vacuum induces a component of the electric field along the magnetic field, generating a nonzero second Poincare electromagnetic invariant * F·F≠0. This will produce (e.g., via radiative effects and vacuum breakdown) an electric charge density of the order of ρ ind =B 0 β 0 /(2πeR G ), where R G =2GM/c 2 is the Schwarzschild radius and M is the mass of the black hole; the charge density ρ ind is similar to the Goldreich-Julian density. The magnetospheres of moving black holes resemble in many respects the magnetospheres of rotationally-powered pulsars, with pair formation fronts and outer gaps, where the sign of the induced charge changes. As a result, the black hole will generate bipolar electromagnetic jets each consisting of two counter-aligned current flows (four current flows total), each carrying an electric current of the order I≅eB 0 R G β 0 . The electromagnetic power of the jets is L≅(GM) 2 B 0 2 β 0 2 /c 3 ; for a particular case of merging black holes the resulting Poynting power is L≅(GM) 3 B 0 2 /(c 5 R), where R is the radius of the orbit. In addition, in limited regions near the horizon the first electromagnetic invariant changes sign, so that the induced electric field becomes larger than the magnetic field, E>B. As a result, there will be local dissipation of the magnetic field close to the horizon, within a region with the radial extent ΔR≅R G β 0 . The total energy loss from a system of merging black holes is a sum of two components with similar powers, one due to the rotation of space-time within the orbit, driven by the nonzero angular momentum in the system, and the other due to the linear motion of the black holes through the magnetic field. Since the resulting electrodynamics is in many respects similar to pulsars, merging black holes may generate coherent radio and high energy emission beamed approximately along the

Quantum gravity of Kerr-Schild spacetimes and the logarithmic correction to Schwarzschild black hole entropy

Energy Technology Data Exchange (ETDEWEB)

El-Menoufi, Basem Kamal [Department of Physics, University of Massachusetts,Amherst, MA 01003 (United States)

2016-05-05

In the context of effective field theory, we consider quantum gravity with minimally coupled massless particles. Fixing the background geometry to be of the Kerr-Schild type, we fully determine the one-loop effective action of the theory whose finite non-local part is induced by the long-distance portion of quantum loops. This is accomplished using the non-local expansion of the heat kernel in addition to a non-linear completion technique through which the effective action is expanded in gravitational curvatures. Via Euclidean methods, we identify a logarithmic correction to the Bekenstein-Hawking entropy of Schwarzschild black hole. Using dimensional transmutation the result is shown to exhibit an interesting interplay between the UV and IR properties of quantum gravity.

Thermodynamics of black-holes in Brans-Dicke gravity

International Nuclear Information System (INIS)

Kim, H.; Kim, Y.

1997-01-01

It is recently been argued that non-trivial Brans-Dicke black-hole solutions different from the usual Schwarzschild solution could exist. The authors attempt here to 'censor' these non-trivial Brans-Dicke black-hole solutions by examining their thermodynamics properties. Quantities like Hawking temperature and entropy of the black holes are computed. The analysis of the behaviors of these thermodynamic quantities appears to show that even in Brans-Dicke gravity, the usual Schwarzschild space-time turns out to be the only physically relevant uncharged black-hole solution

Thermodynamics of the Schwarzschild-AdS Black Hole with a Minimal Length

Directory of Open Access Journals (Sweden)

Yan-Gang Miao

2017-01-01

Full Text Available Using the mass-smeared scheme of black holes, we study the thermodynamics of black holes. Two interesting models are considered. One is the self-regular Schwarzschild-AdS black hole whose mass density is given by the analogue to probability densities of quantum hydrogen atoms. The other model is the same black hole but whose mass density is chosen to be a rational fractional function of radial coordinates. Both mass densities are in fact analytic expressions of the δ-function. We analyze the phase structures of the two models by investigating the heat capacity at constant pressure and the Gibbs free energy in an isothermal-isobaric ensemble. Both models fail to decay into the pure thermal radiation even with the positive Gibbs free energy due to the existence of a minimal length. Furthermore, we extend our analysis to a general mass-smeared form that is also associated with the δ-function and indicate the similar thermodynamic properties for various possible mass-smeared forms based on the δ-function.

Multilayer roughness and image formation in the Schwarzschild objective

International Nuclear Information System (INIS)

Singh, S.; Solak, H.; Cerrina, F.

1996-01-01

We present a study of the effect of multilayer-surface-roughness-induced scattering in the image formation of the Schwarzschild objective (SO) used in the spectromicroscope MAXIMUM. The two mirrors comprising the SO are coated with Ru/B 4 C multilayers that have a peak reflectivity at 130 eV. We had long observed that a diffuse x-ray background surrounds the focused x-ray spot. The spatial resolution remains at 0.1 μm in spite of this. However, since a significant fraction of the flux is lost to the background, since too large an area of the sample is illuminated, and since the S/N ratio is degraded, the origins of this effect merit investigation. This diffuse background resulting from x-ray scattering at the surface of the mirrors was mapped out using bidirectional knife edge scans. Complementary surface roughness simulations were carried out with the ray-tracing program SHADOW. AFM experiments were also done to directly measure the surface roughness and power spectrum of representative multilayers. Following curve fitting, it was possible to classify Gaussian components in both the measured and simulated profiles as arising from scattering occurring at either the convex primary mirror or the concave secondary mirror. Together with geometrical analysis, these techniques permitted us to track the image formation process of an actual optical system in the presence of surface roughness. copyright 1996 American Institute of Physics

Thermodynamics phase transition and Hawking radiation of the Schwarzschild black hole with quintessence-like matter and a deficit solid angle

Science.gov (United States)

Rodrigue, Kamiko Kouemeni Jean; Saleh, Mahamat; Thomas, Bouetou Bouetou; Kofane, Timoleon Crepin

2018-05-01

In this paper, we investigate the thermodynamics and Hawking radiation of Schwarzschild black hole with quintessence-like matter and deficit solid angle. From the metric of the black hole, we derive the expressions of temperature and specific heat using the laws of black hole thermodynamics. Using the null geodesics method and Parikh-Wilczeck tunneling method, we derive the expressions of Boltzmann factor and the change of Bekenstein-Hawking entropy for the black hole. The behaviors of the temperature, specific heat, Boltzmann factor and the change of Bekenstein entropy versus the deficit solid angle (ɛ 2) and the density of static spherically symmetric quintessence-like matter (ρ 0) were explicitly plotted. The results show that, when the deficit solid angle (ɛ 2) and the density of static spherically symmetric quintessence-like matter at r=1 (ρ 0) vanish (ρ 0=ɛ =0), these four thermodynamics quantities are reduced to those obtained for the simple case of Schwarzschild black hole. For low entropies, the presence of quintessence-like matter induces a first order phase transition of the black hole and for the higher values of the entropies, we observe the second order phase transition. When increasing ρ 0, the transition points are shifted to lower entropies. The same thing is observed when increasing ɛ 2. In the absence of quintessence-like matter (ρ 0=0), these transition phenomena disappear. Moreover the rate of radiation decreases when increasing ρ 0 or (ɛ ^2).

Tripartite nonlocality for an open Dirac system in the background of Schwarzschild space-time

Science.gov (United States)

Ding, Zhi-Yong; Shi, Jia-Dong; Wu, Tao; He, Juan

2017-12-01

In this paper, the behavior of the tripartite nonlocality for a Dirac system in the background of Schwarzschild space-time is studied. It is shown that the nonlocality of the ultimate physical accessible state always decreases as the Hawking effect increases monotonically, which is independent of the number of particles located near the event horizon. Besides, the more particles there are located near the event horizon, the more difficult the violation of the Svetlichny inequality becomes. Furthermore, we investigate the property of these particles suffering from a non-Markovian environment, and derive that the nonlocality decreases quickly with the increasing decoherence time accompanied by damping revivals. To preserve tripartite nonlocality in the non-Markovian environment, we propose a scheme by means of prior weak measurement and post measurement reversal. It is worth noticing that the effect is better for larger measurement strengths, while it induces smaller success probability.

'Two-color' reflection multilayers for He-I and He-II resonance lines for micro-UPS using Schwarzschild objective

International Nuclear Information System (INIS)

Ejima, Takeo; Kondo, Yuzi; Watanabe, Makoto

2000-01-01

'Two-color' multilayers reflecting both He-I (58.4 nm) and He-II (30.4 nm) resonance lines have been designed and fabricated for reflection coatings of Schwarzschild objectives of micro-UPS instruments. They are designed so that their reflectances for both He-I and He-II resonance lines are more than 20%. The 'two-color' multilayers are piled double layers coated with top single layers. Fabricated are multilayers of SiC(top layer)-Mg/SiC(double layers) and SiC(top layer)-Mg/Y 2 O 3 (double layers), and their reflectances for the He-I and the He-II are 23% and 17%, and 20% and 23%, respectively

Static spherically symmetric solutions in mimetic gravity: rotation curves and wormholes

International Nuclear Information System (INIS)

Myrzakulov, Ratbay; Sebastiani, Lorenzo; Vagnozzi, Sunny; Zerbini, Sergio

2016-01-01

In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension of general relativity where the conformal degree of freedom of gravity is isolated in a covariant fashion. Here we extend previous works by considering, in addition, a potential for the mimetic field. An appropriate choice of such a potential allows for the reconstruction of a number of interesting cosmological and astrophysical scenarios. We explicitly show how to reconstruct such a potential for a general static spherically symmetric space-time. A number of applications and scenarios are then explored, among which are traversable wormholes. Finally, we analytically reconstruct potentials, which leads to solutions to the equations of motion featuring polynomial corrections to the Schwarzschild space-time. Accurate choices for such corrections could provide an explanation for the inferred flat rotation curves of spiral galaxies within the mimetic gravity framework, without the need for particle dark matter. (paper)

Global solutions to the electrodynamic two-body problem on a straight line

Science.gov (United States)

Bauer, G.; Deckert, D.-A.; Dürr, D.; Hinrichs, G.

2017-06-01

The classical electrodynamic two-body problem has been a long standing open problem in mathematics. For motion constrained to the straight line, the interaction is similar to that of the two-body problem of classical gravitation. The additional complication is the presence of unbounded state-dependent delays in the Coulomb forces due to the finiteness of the speed of light. This circumstance renders the notion of local solutions meaningless, and therefore, straightforward ODE techniques cannot be applied. Here, we study the time-symmetric case, i.e., the Fokker-Schwarzschild-Tetrode (FST) equations, comprising both advanced and retarded delays. We extend the technique developed in Deckert and Hinrichs (J Differ Equ 260:6900-6929, 2016), where existence of FST solutions was proven on the half line, to ensure global existence—a result that had been obtained by Bauer (Ein Existenzsatz für die Wheeler-Feynman-Elektrodynamik, Herbert Utz Verlag, München, 1997). Due to the novel technique, the presented proof is shorter and more transparent but also relies on the idea to employ asymptotic data to characterize solutions.

Relativistic static thin dust disks with an inner edge: An infinite family of new exact solutions

International Nuclear Information System (INIS)

Gonzalez, Guillermo A.; Gutierrez-Pineres, Antonio C.; Vina-Cervantes, Viviana M.

2009-01-01

An infinite family of new exact solutions of the vacuum Einstein equations is presented. The solutions are static and axially symmetric and correspond to an infinite family of thin dust disks with a central inner edge. The metric functions of all the solutions can be explicitly computed, and can be expressed in a simple manner in terms of oblate spheroidal coordinates. The energy density of all the disks of the family is positive everywhere and well behaved, so that the corresponding energy-momentum tensor is in full agreement with all the energy conditions. Moreover, although the total mass of the disks is infinite, the solutions are asymptotically flat and the Riemann tensor is regular everywhere, as it is shown by computing the curvature scalars. Now, besides its importance as a new family of exact solutions of the vacuum Einstein equations, the main importance of this family of solutions is that it can be easily superposed with the Schwarzschild solution in order to describe thin disks surrounding a central black hole. Accordingly, a detailed analysis of this superposition will be presented in a subsequent paper.

Scalar-gravitational perturbations and quasi normal modes in the five dimensional Schwarzschild black hole

International Nuclear Information System (INIS)

Cardoso, Vitor; Lemos, Jose P.S.; Yoshida, Shijun

2003-01-01

We calculate the quasi normal modes (QNMs) for gravitational perturbations of the Schwarzschild black hole in the five dimensional (5D) spacetime with a continued fraction method. For all the types of perturbations (scalar-gravitational, vector-gravitational, and tensor-gravitational perturbations), the QNMs associated with l = 2, l 3, and l = 4 are calculated. Our numerical results are summarized as follows: (i) The three types of gravitational perturbations associated with the same angular quantum number l have a different set of the quasi normal (QN) frequencies; (ii) There is no purely imaginary frequency mode; (iii) The three types of gravitational perturbations have the same asymptotic behavior of the QNMs in the limit of the large imaginary frequencies, which are given by ωT H -1 → log 3+ 2πi(n+1/2) as n → ∞, where ω, T H , and n are the oscillation frequency, the Hawking temperature of the black hole, and the mode number, respectively. (author)

Schwarzschild tests of the Wahlquist-Estabrook-Buchman-Bardeen tetrad formulation for numerical relativity

International Nuclear Information System (INIS)

Buchman, L.T.; Bardeen, J.M.

2005-01-01

A first order symmetric hyperbolic tetrad formulation of the Einstein equations developed by Estabrook and Wahlquist and put into a form suitable for numerical relativity by Buchman and Bardeen (the WEBB formulation) is adapted to explicit spherical symmetry and tested for accuracy and stability in the evolution of spherically symmetric black holes (the Schwarzschild geometry). The lapse and shift, which specify the evolution of the coordinates relative to the tetrad congruence, are reset at frequent time intervals to keep the constant-time hypersurfaces nearly orthogonal to the tetrad congruence and the spatial coordinate satisfying a kind of minimal rate of strain condition. By arranging through initial conditions that the constant-time hypersurfaces are asymptotically hyperbolic, we simplify the boundary value problem and improve stability of the evolution. Results are obtained for both tetrad gauges ('Nester' and 'Lorentz') of the WEBB formalism using finite difference numerical methods. We are able to obtain stable unconstrained evolution with the Nester gauge for certain initial conditions, but not with the Lorentz gauge

Schwarzschild–de Sitter spacetime: The role of temperature in the emission of Hawking radiation

Directory of Open Access Journals (Sweden)

Thomas Pappas

2017-12-01

Full Text Available We consider a Schwarzschild–de Sitter (SdS black hole, and focus on the emission of massless scalar fields either minimally or non-minimally coupled to gravity. We use six different temperatures, two black-hole and four effective ones for the SdS spacetime, as the question of the proper temperature for such a background is still debated in the literature. We study their profiles under the variation of the cosmological constant, and derive the corresponding Hawking radiation spectra. We demonstrate that only few of these temperatures may support significant emission of radiation. We finally compute the total emissivities for each temperature, and show that the non-minimal coupling constant of the scalar field to gravity also affects the relative magnitudes of the energy emission rates.

Magnetized black holes and black rings in the higher dimensional dilaton gravity

International Nuclear Information System (INIS)

Yazadjiev, Stoytcho S.

2006-01-01

In this paper we consider magnetized black holes and black rings in the higher dimensional dilaton gravity. Our study is based on exact solutions generated by applying a Harrison transformation to known asymptotically flat black hole and black ring solutions in higher dimensional spacetimes. The explicit solutions include the magnetized version of the higher dimensional Schwarzschild-Tangherlini black holes, Myers-Perry black holes, and five-dimensional (dipole) black rings. The basic physical quantities of the magnetized objects are calculated. We also discuss some properties of the solutions and their thermodynamics. The ultrarelativistic limits of the magnetized solutions are briefly discussed and an explicit example is given for the D-dimensional magnetized Schwarzschild-Tangherlini black holes

New Gauss-Bonnet Black Holes with Curvature-Induced Scalarization in Extended Scalar-Tensor Theories.

Science.gov (United States)

Doneva, Daniela D; Yazadjiev, Stoytcho S

2018-03-30

In the present Letter, we consider a class of extended scalar-tensor-Gauss-Bonnet (ESTGB) theories for which the scalar degree of freedom is excited only in the extreme curvature regime. We show that in the mentioned class of ESTGB theories there exist new black-hole solutions that are formed by spontaneous scalarization of the Schwarzschild black holes in the extreme curvature regime. In this regime, below certain mass, the Schwarzschild solution becomes unstable and a new branch of solutions with a nontrivial scalar field bifurcates from the Schwarzschild one. As a matter of fact, more than one branch with a nontrivial scalar field can bifurcate at different masses, but only the first one is supposed to be stable. This effect is quite similar to the spontaneous scalarization of neutron stars. In contrast to the standard spontaneous scalarization of neutron stars, which is induced by the presence of matter, in our case, the scalarization is induced by the curvature of the spacetime.

The Advanced Gamma-ray Imaging System (AGIS): Schwarzschild-Couder (SC) Telescope Mechanical and Optical System Design

Science.gov (United States)

Byrum, Karen L.; Vassiliev, V.; AGIS Collaboration

2010-03-01

AGIS is a concept for the next-generation ground-based gamma-ray observatory. It will be an array of 36 imaging atmospheric Cherenkov telescopes (IACTs) sensitive in the energy range from 50 GeV to 200 TeV. The required improvements in sensitivity, angular resolution, and reliability of operation relative to the present generation instruments imposes demanding technological and cost requirements on the design of AGIS telescopes. In this submission, we outline the status of the development of the optical and mechanical systems for a novel Schwarzschild-Couder two-mirror aplanatic telescope. This design can provide a field of view and angular resolution significantly better to those offered by the traditional Davies-Cotton optics utilized in present-day IACTs. Other benefits of the novel design include isochronous focusing and compatibility with cost-effective, high quantum efficiency image sensors such as multi-anode PMTs, silicon PMTs (SiPMs), or image intensifiers.

Development of a mid-sized Schwarzschild-Couder Telescope for the Cherenkov Telescope Array

Energy Technology Data Exchange (ETDEWEB)

Cameron, Robert A.

2012-06-28

The Cherenkov Telescope Array (CTA) is a ground-based observatory for very high-energy (10 GeV to 100 TeV) gamma rays, planned for operation starting in 2018. It will be an array of dozens of optical telescopes, known as Atmospheric Cherenkov Telescopes (ACTs), of 8 m to 24 m diameter, deployed over an area of more than 1 square km, to detect flashes of Cherenkov light from showers initiated in the Earth's atmosphere by gamma rays. CTA will have improved angular resolution, a wider energy range, larger fields of view and an order of magnitude improvement in sensitivity over current ACT arrays such as H.E.S.S., MAGIC and VERITAS. Several institutions have proposed a research and development program to eventually contribute 36 medium-sized telescopes (9 m to 12 m diameter) to CTA to enhance and optimize its science performance. The program aims to construct a prototype of an innovative, Schwarzschild-Couder telescope (SCT) design that will allow much smaller and less expensive cameras and much larger fields of view than conventional Davies-Cotton designs, and will also include design and testing of camera electronics for the necessary advances in performance, reliability and cost. We report on the progress of the mid-sized SCT development program.

Conical Stream of the Two-Sided Jets in NGC 4261 over the Range of 103–109 Schwarzschild Radii

Directory of Open Access Journals (Sweden)

Satomi Nakahara

2016-12-01

Full Text Available We report the jet width profile of of the nearby ( ∼ 30 Mpc AGN NGC 4261 for both the approaching jet and the counter jet at radial distances ranging from ∼ 10 3 – 10 9 Schwarzschild radius ( R S from the central engine. Our Very Large Array (VLA and Very Long Baseline Array (VLBA observations reveal that the jets maintain a conical structure on both sides over the range 10 3 – 10 9 R S without any structural transition (i.e., parabolic to conical like in the approaching jet in M87. Thus, NGC 4261 will provide a unique opportunity to examine the conical jet hypothesis in blazars, while it may require some additional consideration on the acceleration and collimation process in AGN jets.

Scattering of particles by deformed non-rotating black holes

International Nuclear Information System (INIS)

Pei, Guancheng; Bambi, Cosimo

2015-01-01

We study the excitation of axial quasi-normal modes of deformed non-rotating black holes by test particles and we compare the associated gravitational wave signal with that expected in general relativity from a Schwarzschild black hole. Deviations from standard predictions are quantified by an effective deformation parameter, which takes into account deviations from both the Schwarzschild metric and the Einstein equations. We show that, at least in the case of non-rotating black holes, it is possible to test the metric around the compact object, in the sense that the measurement of the gravitational wave spectrum can constrain possible deviations from the Schwarzschild solution. (orig.)

Reversed sense of the ''outward'' direction for dynamical effects of rotation close to a Schwarzschild black hole

International Nuclear Information System (INIS)

Abramowicz, M.A.; Prasanna, A.R.

1988-10-01

Anderson and Lemos (1988) noticed that the direction in which viscous torque transports angular momentum changes, close to a black hole, from outwards to inwards. We find here that close to a black hole the centrifugal force attracts particles towards the hole. We argue that these are particular examples of a general reversal in sense of the inward and outward directions for all dynamical effects of rotation close to the hole. Using results from the recent paper by Abramowicz, Carter and Lasota (1988) we explain that the reversal is not connected with dragging of inertial frames or with the difference between the angular velocities of the hole and of the surrounding matter but rather, it is an effect of curvature. For a Schwarzschild black hole the reversal takes place at the circular photon orbit (r=3M-tilde) because the geodesic curvature, R-tilde=r(1-3M-tilde/r), of the circles r = const. changes its sign there. (author). 13 refs, 7 figs, 1 tab

Development of a SiPM Camera for a Schwarzschild-Couder Cherenkov Telescope for the Cherenkov Telescope Array

CERN Document Server

Otte, A N; Dickinson, H.; Funk, S.; Jogler, T.; Johnson, C.A.; Karn, P.; Meagher, K.; Naoya, H.; Nguyen, T.; Okumura, A.; Santander, M.; Sapozhnikov, L.; Stier, A.; Tajima, H.; Tibaldo, L.; Vandenbroucke, J.; Wakely, S.; Weinstein, A.; Williams, D.A.

2015-01-01

We present the development of a novel 11328 pixel silicon photomultiplier (SiPM) camera for use with a ground-based Cherenkov telescope with Schwarzschild-Couder optics as a possible medium-sized telescope for the Cherenkov Telescope Array (CTA). The finely pixelated camera samples air-shower images with more than twice the optical resolution of cameras that are used in current Cherenkov telescopes. Advantages of the higher resolution will be a better event reconstruction yielding improved background suppression and angular resolution of the reconstructed gamma-ray events, which is crucial in morphology studies of, for example, Galactic particle accelerators and the search for gamma-ray halos around extragalactic sources. Packing such a large number of pixels into an area of only half a square meter and having a fast readout directly attached to the back of the sensors is a challenging task. For the prototype camera development, SiPMs from Hamamatsu with through silicon via (TSV) technology are used. We give ...

Weak deflection gravitational lensing for photons coupled to Weyl tensor in a Schwarzschild black hole

Science.gov (United States)

Cao, Wei-Guang; Xie, Yi

2018-03-01

Beyond the Einstein-Maxwell model, electromagnetic field might couple with gravitational field through the Weyl tensor. In order to provide one of the missing puzzles of the whole physical picture, we investigate weak deflection lensing for photons coupled to the Weyl tensor in a Schwarzschild black hole under a unified framework that is valid for its two possible polarizations. We obtain its coordinate-independent expressions for all observables of the geometric optics lensing up to the second order in the terms of ɛ which is the ratio of the angular gravitational radius to angular Einstein radius of the lens. These observables include bending angle, image position, magnification, centroid and time delay. The contributions of such a coupling on some astrophysical scenarios are also studied. We find that, in the cases of weak deflection lensing on a star orbiting the Galactic Center Sgr A*, Galactic microlensing on a star in the bulge and astrometric microlensing by a nearby object, these effects are beyond the current limits of technology. However, measuring the variation of the total flux of two weak deflection lensing images caused by the Sgr A* might be a promising way for testing such a coupling in the future.

Lovelock black holes with maximally symmetric horizons

Energy Technology Data Exchange (ETDEWEB)

Maeda, Hideki; Willison, Steven; Ray, Sourya, E-mail: hideki@cecs.cl, E-mail: willison@cecs.cl, E-mail: ray@cecs.cl [Centro de Estudios CientIficos (CECs), Casilla 1469, Valdivia (Chile)

2011-08-21

We investigate some properties of n( {>=} 4)-dimensional spacetimes having symmetries corresponding to the isometries of an (n - 2)-dimensional maximally symmetric space in Lovelock gravity under the null or dominant energy condition. The well-posedness of the generalized Misner-Sharp quasi-local mass proposed in the past study is shown. Using this quasi-local mass, we clarify the basic properties of the dynamical black holes defined by a future outer trapping horizon under certain assumptions on the Lovelock coupling constants. The C{sup 2} vacuum solutions are classified into four types: (i) Schwarzschild-Tangherlini-type solution; (ii) Nariai-type solution; (iii) special degenerate vacuum solution; and (iv) exceptional vacuum solution. The conditions for the realization of the last two solutions are clarified. The Schwarzschild-Tangherlini-type solution is studied in detail. We prove the first law of black-hole thermodynamics and present the expressions for the heat capacity and the free energy.

Black Holes: Physics and Astrophysics - Stellar-mass, supermassive and primordial black holes

OpenAIRE

Bekenstein, Jacob D.

2004-01-01

I present an elementary primer of black hole physics, including its general relativity basis, all peppered with astrophysical illustrations. Following a brief review of the process stellar collapse to a black hole, I discuss the gravitational redshift, particle trajectories in gravitational fields, the Schwarzschild and Kerr solutions to Einstein's equations, orbits in Schwarzschild and in Kerr geometry, and the dragging of inertial frames. I follow with a brief review of galactic X-ray binar...

Cosmic strings and black holes

International Nuclear Information System (INIS)

Aryal, M.; Ford, L.H.; Vilenkin, A.

1986-01-01

The metric for a Schwarzschild black hole with a cosmic string passing through it is discussed. The thermodynamics of such an object is considered, and it is shown that S = (1/4)A, where S is the entropy and A is the horizon area. It is noted that the Schwarzschild mass parameter M, which is the gravitational mass of the system, is no longer identical to its energy. A solution representing a pair of black holes held apart by strings is discussed. It is nearly identical to a static, axially symmetric solution given long ago by Bach and Weyl. It is shown how these solutions, which were formerly a mathematical curiosity, may be given a more physical interpretation in terms of cosmic strings

Six-dimensional localized black holes: Numerical solutions

International Nuclear Information System (INIS)

Kudoh, Hideaki

2004-01-01

To test the strong-gravity regime in Randall-Sundrum braneworlds, we consider black holes bound to a brane. In a previous paper, we studied numerical solutions of localized black holes whose horizon radii are smaller than the AdS curvature radius. In this paper, we improve the numerical method and discuss properties of the six-dimensional (6D) localized black holes whose horizon radii are larger than the AdS curvature radius. At a horizon temperature T≅1/2πl, the thermodynamics of the localized black hole undergo a transition with its character changing from a 6D Schwarzschild black hole type to a 6D black string type. The specific heat of the localized black holes is negative, and the entropy is greater than or nearly equal to that of the 6D black strings with the same thermodynamic mass. The large localized black holes show flattened horizon geometries, and the intrinsic curvature of the horizon four-geometry becomes negative near the brane. Our results indicate that the recovery mechanism of lower-dimensional Einstein gravity on the brane works even in the presence of the black holes

Chaos in the motion of a test scalar particle coupling to the Einstein tensor in Schwarzschild-Melvin black hole spacetime

Energy Technology Data Exchange (ETDEWEB)

Wang, Mingzhi [Hunan Normal University, Department of Physics, Institute of Physics, Changsha, Hunan (China); Hunan Normal University, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Changsha, Hunan (China); Chen, Songbai; Jing, Jiliang [Hunan Normal University, Department of Physics, Institute of Physics, Changsha, Hunan (China); Hunan Normal University, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Changsha, Hunan (China); Hunan Normal University, Synergetic Innovation Center for Quantum Effects and Applications, Changsha, Hunan (China)

2017-04-15

We present firstly the equation of motion for a test scalar particle coupling to the Einstein tensor in the Schwarzschild-Melvin black hole spacetime through the short-wave approximation. Through analyzing Poincare sections, the power spectrum, the fast Lyapunov exponent indicator and the bifurcation diagram, we investigate the effects of the coupling parameter on the chaotic behavior of the particles. With the increase of the coupling strength, we find that the motion of the coupled particle for the chosen parameters becomes more regular and order for the negative couple constant. While, for the positive one, the motion of the coupled particles first undergoes a series of transitions betweens chaotic motion and regular motion and then falls into horizon or escapes to spatial infinity. Our results show that the coupling brings about richer effects for the motion of the particles. (orig.)

Property of various correlation measures of open Dirac system with Hawking effect in Schwarzschild space–time

International Nuclear Information System (INIS)

He, Juan; Xu, Shuai; Yu, Yang; Ye, Liu

2015-01-01

We explore the performance of various correlation measures for open Dirac system with Hawking effect in Schwarzschild space–time. Our results indicate that the impact of Hawking effect on physical accessible entanglement is weaker than that of decoherence. For generalized amplitude damping (GAD) channel, the entanglement sudden death (ESD) is analyzed in detail, and the inequivalence of quantization for Dirac particles in the black hole and Kruskal space–time is verified via quantum discord measure. In addition, as an example for interpreting Bell non-locality, we study the GAD channel with Hawking effect. It can be noticed that there is a boundary line of Bell violation for physically accessible states. That is, quantum non-locality would disappear when Hawking temperature exceeds a certain value. This critical temperature increases as a decoherence parameter decreases. In the case of phase damping (PD) channel, the interaction between the particle and noise environment does not produce bipartite system–environment entanglement. Then we discuss entanglement distributions, and find that the reduced physically accessible entanglement can be redistributed to physical inaccessible region. At last, we extend our investigation to an N-qubit system, and obtain a universal expression of the physical accessible entanglement

Bulk and brane decay of a (4+n)-dimensional Schwarzschild-de Sitter black hole: Scalar radiation

International Nuclear Information System (INIS)

Kanti, P.; Grain, J.; Barrau, A.

2005-01-01

In this paper, we extend the idea that the spectrum of Hawking radiation can reveal valuable information on a number of parameters that characterize a particular black hole background--such as the dimensionality of spacetime and the value of coupling constants--to gain information on another important aspect: the curvature of spacetime. We investigate the emission of Hawking radiation from a D-dimensional Schwarzschild-de Sitter black hole emitted in the form of scalar fields, and employ both analytical and numerical techniques to calculate greybody factors and differential energy emission rates on the brane and in the bulk. The energy emission rate of the black hole is significantly enhanced in the high-energy regime with the number of spacelike dimensions. On the other hand, in the low-energy part of the spectrum, it is the cosmological constant that leaves a clear footprint, through a characteristic, constant emission rate of ultrasoft quanta determined by the values of black hole and cosmological horizons. Our results are applicable to 'small' black holes arising in theories with an arbitrary number and size of extra dimensions, as well as to pure 4-dimensional primordial black holes, embedded in a de Sitter spacetime

Exact solution for the interior of a black hole

NARCIS (Netherlands)

Nieuwenhuizen, T.M.

2008-01-01

Within the Relativistic Theory of Gravitation it is shown that the equation of state p = rho holds near the center of a black hole. For the stiff equation of state p = rho - rho(c) the interior metric is solved exactly. It is matched with the Schwarzschild metric, which is deformed in a narrow range

The Kerr/fluid duality and the singularity of solutions to the fluid equation

International Nuclear Information System (INIS)

Fujisawa, Ippei; Nakayama, Ryuichi

2016-01-01

An equation for a viscous incompressible fluid on a spheroidal surface that is dual to the perturbation around the near-near-horizon extreme Kerr (near-NHEK) black hole is derived. It is also shown that an expansion scalar θ of a congruence of null geodesics on the perturbed horizon of the perturbed near-NHEK spacetime, which is dual to a viscous incompressible fluid, is not in general positive semidefinite, even if initial conditions on the velocity are smooth. Unless the initial conditions are appropriately adjusted, caustics of null congruence will occur on the perturbed horizon in the future. A similar result is obtained for a perturbed Schwarzschild black hole spacetime, which is dual to a viscous incompressible fluid on S 2 . An initial condition that θ be positive semidefinite at any point on S 2 is a necessary condition for the existence of smooth solutions to the incompressible Navier-Stokes equation on S 2

Lumpy AdS5× S5 black holes and black belts

International Nuclear Information System (INIS)

Dias, Óscar J.C.; Santos, Jorge E.; Way, Benson

2015-01-01

Sufficiently small Schwarzschild black holes in global AdS 5 ×S 5 are Gregory-Laflamme unstable. We construct new families of black hole solutions that bifurcate from the onset of this instability and break the full SO(6) symmetry group of the S 5 down to SO(5). These new “lumpy" solutions are labelled by the harmonics ℓ. We find evidence that the ℓ=1 branch never dominates the microcanonical/canonical ensembles and connects through a topology-changing merger to a localised black hole solution with S 8 topology. We argue that these S 8 black holes should become the dominant phase in the microcanonical ensemble for small enough energies, and that the transition to Schwarzschild black holes is first order. Furthermore, we find two branches of solutions with ℓ=2. We expect one of these branches to connect to a solution containing two localised black holes, while the other branch connects to a black hole solution with horizon topology S 4 ×S 4 which we call a “black belt”.

Phase transition and thermodynamical geometry for Schwarzschild AdS black hole in AdS_5×S"5 spacetime

International Nuclear Information System (INIS)

Zhang, Jia-Lin; Cai, Rong-Gen; Yu, Hongwei

2015-01-01

We study the thermodynamics and thermodynamic geometry of a five-dimensional Schwarzschild AdS black hole in AdS_5×S"5 spacetime by treating the cosmological constant as the number of colors in the boundary gauge theory and its conjugate quantity as the associated chemical potential. It is found that the chemical potential is always negative in the stable branch of black hole thermodynamics and it has a chance to be positive, but appears in the unstable branch. We calculate the scalar curvatures of the thermodynamical Weinhold metric, Ruppeiner metric and Quevedo metric, respectively and we find that the scalar curvature in the Weinhold metric is always vanishing, while in the Ruppeiner metric the divergence of the scalar curvature is related to the divergence of the heat capacity with fixed chemical potential, and in the Quevedo metric the divergence of the scalar curvature is related to the divergence of the heat capacity with fixed number of colors and to the vanishing of the heat capacity with fixed chemical potential.

Revisiting scalar geodesic synchrotron radiation in Kerr spacetime

International Nuclear Information System (INIS)

Macedo, Caio F.B.; Crispino, Luis C.B.

2011-01-01

Full text: The Kerr solution [R. P. Kerr, Phys. Rev. D 11, 5 (1963)] is one of the most important black hole solutions of Einstein equations. It describes a chargeless rotating black hole, with Schwarzschild black hole as a particular case. It is estimated, inferred using distinct methods, that most black hole candidates have a considerable value of the rotation parameter [E. Berti, V. Cardoso, and A. Starinets, Classical Quantum Gravity 26, 163001 (2009)]. Although the Schwarzschild solution is suitable for a great variety of phenomena in star and black hole physics, the Kerr solution becomes very important in the explanation of the electrodynamical aspects of accretion disks for binary X-ray sources [The Kerr Spacetime: Rotating Black Holes in General Relativity, edited by D. L. Wiltshire, M. Visser, and S. M. Scott (Cambridge University Press, Cambridge, 2009)]. Thus, the investigation of how radiation emission processes are modified by the nontrivial curvature of rotating black holes is particularly important. As a first approximation to the problem, one can consider a moving particle, minimally coupled to the massless scalar field, in circular geodesic motion. The radiation emitted in this configuration is called scalar geodesic synchrotron radiation. In this work, we revisit the main aspects of scalar geodesic synchrotron radiation in Kerr spacetime, including some effects occurring in the high-frequency approximation. Our results can be readily compared with the results of the equivalent phenomena in Schwarzschild spacetime. (author)

Static black hole and vacuum energy: thin shell and incompressible fluid

Science.gov (United States)

Ho, Pei-Ming; Matsuo, Yoshinori

2018-03-01

With the back reaction of the vacuum energy-momentum tensor consistently taken into account, we study static spherically symmetric black-hole-like solutions to the semi-classical Einstein equation. The vacuum energy is assumed to be given by that of 2-dimensional massless scalar fields, as a widely used model in the literature for black holes. The solutions have no horizon. Instead, there is a local minimum in the radius. We consider thin shells as well as incompressible fluid as the matter content of the black-hole-like geometry. The geometry has several interesting features due to the back reaction of vacuum energy. In particular, Buchdahl's inequality can be violated without divergence in pressure, even if the surface is below the Schwarzschild radius. At the same time, the surface of the star can not be far below the Schwarzschild radius for a density not much higher than the Planck scale, and the proper distance from its surface to the origin can be very short even for very large Schwarzschild radius. The results also imply that, contrary to the folklore, in principle the Boulware vacuum can be physical for black holes.

On the localisation of four-dimensional brane-world black holes: II. The general case

Science.gov (United States)

Kanti, P.; Pappas, N.; Pappas, T.

2016-01-01

We perform a comprehensive analysis of a number of scalar field theories in an attempt to find analytically five-dimensional, localised-on-the-brane, black-hole solutions. Extending a previous analysis, we assume a generalised Vaidya ansatz for the five-dimensional metric tensor that allows for a time-dependent, non-trivial profile of the mass function in terms of the bulk coordinate and a deviation from the over-restricting Schwarzschild-type solution on the brane. In order to support such a solution, we study a variety of theories including single or multiple scalar fields, with canonical or non-canonical kinetic terms, minimally or non-minimally coupled to gravity. We demonstrate that for such a metric ansatz and for a carefully chosen energy-momentum tensor which is non-isotropic in five dimensions, solutions that have the form of a Schwarzschild-(anti)de Sitter or Reissner-Nordstrom type of solution do emerge. However, the resulting profile of the mass function along the bulk coordinate, when allowed, is not the correct one for eliminating bulk singularities.

Gravitational nonminimally coupled electromagnetic fields: a possible solution to some idiosincrasies of Einstein-Maxwell theory

International Nuclear Information System (INIS)

Accioly, A.J.

1988-01-01

A theory of nonminimal coupling of electromagnetism and gravitation in the framework of Riomannian geometry is constructed. As a consequence the main difficulties concerning the Einstein-Maxwell theory are cleared away. The theory works as a kind of correction to the Einstein-Maxwell one for regions with strong curvature and for times much greater than the Planck time. A Reissner-Nordstroem-type solution is exhibited and comments are made on a parameter which somewhat resembles the ''Schwarzschild radius''. A mechanism of charge creation via nonminimal coupling is also discussed. We calculate the propagation of photons in a Robertson-Walker background and find that the effect of the nonminimal coupling in this case may be to deviate the photon from the null geodesics, increasing its velocity beyond the flat-space value. Taking into account this results, the observed isotropy of the background radiation can be explained in a simple way, regardless of any assumption about the state of the Universe prior to the Planck time. (author) [pt

Light bending in the galactic halo by Rindler-Ishak method

Energy Technology Data Exchange (ETDEWEB)

Bhattacharya, Amrita; Nandi, Kamal K. [Department of Mathematics, University of North Bengal, Rajarammohunpur, Siliguri 734 013 (India); Isaev, Ruslan [Joint Research Laboratory, Bashkir State Pedagogical University, 3A, October Revolution Street, Ufa 450000 (Russian Federation); Scalia, Massimo; Cattani, Carlo, E-mail: amrita_852003@yahoo.co.in, E-mail: subfear@gmail.com, E-mail: Massimo.Scalia@uniroma1.it, E-mail: ccattani@unisa.it, E-mail: kamalnandi1952@yahoo.co.in [Dipartimento di Matematica, Istituto ' ' G. Castelnuovo' ' , Università La Sapienza, P.le Aldo Moro, 2, Rome (Italy)

2010-09-01

After the work of Rindler and Ishak, it is now well established that the bending of light is influenced by the cosmological constant Λ appearing in the Schwarzschild-de Sitter spacetime. We show that their method, when applied to the exact Mannheim-Kazanas-de Sitter solution of the Weyl conformal gravity, nicely yields the expected answer together with several other physically interesting new terms. Apart from Λ, the solution is parametrized by a conformal parameter γ, which is known to play a dominant role in the galactic halo gravity. The application of the method yields exactly the same γ− correction to Schwarzschild bending as obtained by standard methods. Different cases are analyzed, which include some corrections to the special cases considered in the original paper by Rindler and Ishak.

Light bending in the galactic halo by Rindler-Ishak method

International Nuclear Information System (INIS)

Bhattacharya, Amrita; Nandi, Kamal K.; Isaev, Ruslan; Scalia, Massimo; Cattani, Carlo

2010-01-01

After the work of Rindler and Ishak, it is now well established that the bending of light is influenced by the cosmological constant Λ appearing in the Schwarzschild-de Sitter spacetime. We show that their method, when applied to the exact Mannheim-Kazanas-de Sitter solution of the Weyl conformal gravity, nicely yields the expected answer together with several other physically interesting new terms. Apart from Λ, the solution is parametrized by a conformal parameter γ, which is known to play a dominant role in the galactic halo gravity. The application of the method yields exactly the same γ− correction to Schwarzschild bending as obtained by standard methods. Different cases are analyzed, which include some corrections to the special cases considered in the original paper by Rindler and Ishak

Quantization of the Schwarzschild geometry

International Nuclear Information System (INIS)

Melas, Evangelos

2013-01-01

The conditional symmetries of the reduced Einstein-Hilbert action emerging from a static, spherically symmetric geometry are used as supplementary conditions on the wave function. Based on their integrability conditions, only one of the three existing symmetries can be consistently imposed, while the unique Casimir invariant, being the product of the remaining two symmetries, is calculated as the only possible second condition on the wave function. This quadratic integral of motion is identified with the reparametrization generator, as an implication of the uniqueness of the dynamical evolution, by fixing a suitable parametrization of the r-lapse function. In this parametrization, the determinant of the supermetric plays the role of the mesure. The combined Wheeler – DeWitt and linear conditional symmetry equations are analytically solved. The solutions obtained depend on the product of the two ''scale factors''.

A simple application of the Newman-Penrose spin coefficient formalism

International Nuclear Information System (INIS)

Davis, T.M.

1976-01-01

As a simple application of the Newman-Penrose spin coefficient formalism, useful for beginners, the vacuum symmetry (Schwarzschild) solution is found. The calculations also show that all spherically symmetric metrics are Petrov type D. (author)

Scalar radiation from a radially infalling source into a Schwarzschild black hole in the framework of quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Oliveira, Leandro A. [Campus Salinopolis, Universidade Federal do Para, Salinopolis, Para (Brazil); Universidade Federal do Para, Faculdade de Fisica, Belem, Para (Brazil); Crispino, Luis C.B. [Universidade Federal do Para, Faculdade de Fisica, Belem, Para (Brazil); Higuchi, Atsushi [University of York, Department of Mathematics, Heslington, York (United Kingdom)

2018-02-15

We investigate the radiation to infinity of a massless scalar field from a source falling radially towards a Schwarzschild black hole using the framework of the quantum field theory at tree level. When the source falls from infinity, the monopole radiation is dominant for low initial velocities. Higher multipoles become dominant at high initial velocities. It is found that, as in the electromagnetic and gravitational cases, at high initial velocities the energy spectrum for each multipole with l ≥ 1 approximately is constant up to the fundamental quasinormal frequency and then drops to zero. We also investigate the case where the source falls from rest at a finite distance from the black hole. It is found that the monopole and dipole contributions in this case are dominant. This case needs to be carefully distinguished from the unphysical process where the source abruptly appears at rest and starts falling, which would result in radiation of an infinite amount of energy. We also investigate the radiation of a massless scalar field to the horizon of the black hole, finding some features similar to the gravitational case. (orig.)

Thermodynamic Relations for Kiselev and Dilaton Black Hole

International Nuclear Information System (INIS)

Jamil, Mubasher; Pradhan, Parthapratim; Majeed, Bushra

2015-01-01

We investigate the thermodynamics and phase transition for Kiselev black hole and dilaton black hole. Specifically we consider Reissner-Nordström black hole surrounded by radiation and dust and Schwarzschild black hole surrounded by quintessence, as special cases of Kiselev solution. We have calculated the products relating the surface gravities, surface temperatures, Komar energies, areas, entropies, horizon radii, and the irreducible masses at the Cauchy and the event horizons. It is observed that the product of surface gravities, product of surface temperature, and product of Komar energies at the horizons are not universal quantities for the Kiselev solutions while products of areas and entropies at both the horizons are independent of mass of the above-mentioned black holes (except for Schwarzschild black hole surrounded by quintessence). For charged dilaton black hole, all the products vanish. The first law of thermodynamics is also verified for Kiselev solutions. Heat capacities are calculated and phase transitions are observed, under certain conditions

Quasistationary solutions of scalar fields around accreting black holes

Science.gov (United States)

Sanchis-Gual, Nicolas; Degollado, Juan Carlos; Izquierdo, Paula; Font, José A.; Montero, Pedro J.

2016-08-01

Massive scalar fields can form long-lived configurations around black holes. These configurations, dubbed quasibound states, have been studied both in the linear and nonlinear regimes. In this paper, we show that quasibound states can form in a dynamical scenario in which the mass of the black hole grows significantly due to the capture of infalling matter. We solve the Klein-Gordon equation numerically in spherical symmetry, mimicking the evolution of the spacetime through a sequence of analytic Schwarzschild black hole solutions of increasing mass. It is found that the frequency of oscillation of the quasibound states decreases as the mass of the black hole increases. In addition, accretion leads to an increase of the exponential decay of the scalar field energy. We compare the black hole mass growth rates used in our study with estimates from observational surveys and extrapolate our results to values of the scalar field masses consistent with models that propose scalar fields as dark matter in the universe. We show that, even for unrealistically large mass accretion rates, quasibound states around accreting black holes can survive for cosmological time scales. Our results provide further support to the intriguing possibility of the existence of dark matter halos based on (ultralight) scalar fields surrounding supermassive black holes in galactic centers.

THE INNERMOST COLLIMATION STRUCTURE OF THE M87 JET DOWN TO ∼10 SCHWARZSCHILD RADII

Energy Technology Data Exchange (ETDEWEB)

Hada, Kazuhiro; Giroletti, Marcello; Giovannini, Gabriele [INAF Istituto di Radioastronomia, via Gobetti 101, I-40129 Bologna (Italy); Kino, Motoki; Doi, Akihiro [Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo, Sagamihara 252-5210 (Japan); Nagai, Hiroshi; Honma, Mareki; Hagiwara, Yoshiaki; Kawaguchi, Noriyuki [National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588 (Japan)

2013-09-20

We investigated the detailed inner jet structure of M87 using Very Long Baseline Array data at 2, 5, 8.4, 15, 23.8, 43, and 86 GHz, especially focusing on the multi-frequency properties of the radio core at the jet base. First, we measured the size of the core region transverse to the jet axis, defined as W{sub c}, at each frequency ν, and found a relation between W{sub c} and ν: W{sub c}(ν)∝ν{sup –0.71±0.05}. Then, by combining W{sub c}(ν) and the frequency dependence of the core position r{sub c}(ν), which was obtained in our previous study, we constructed a collimation profile of the innermost jet W{sub c}(r) down to ∼10 Schwarzschild radii (R{sub s}) from the central black hole. We found that W{sub c}(r) smoothly connects with the width profile of the outer edge-brightened, parabolic jet and then follows a similar radial dependence down to several tens of R{sub s}. Closer to the black hole, the measured radial profile suggests a possible change in the jet collimation shape from the outer parabolic one, where the jet shape tends to become more radially oriented. This result could be related to a magnetic collimation process or/and interactions with surrounding materials at the jet base. The present results shed light on the importance of higher-sensitivity/resolution imaging studies of M87 at 86, 43, and 22 GHz; these studies should be examined more rigorously.

Event horizon and scalar potential

International Nuclear Information System (INIS)

Duruisseau, J.P.; Tonnelat, M.A.

1977-01-01

The introduction of a scalar potential with a more general scheme than General Relativity eliminates the event horizon. Among possible solutions, the Schwarzschild one represents a singular case. A study of the geodesic properties of the matching with an approximated interior solution are given. A new definition of the gravitational mass and chi function is deduced. (author)

Electromagnetic radiation from collisions at almost the speed of light: An extremely relativistic charged particle falling into a Schwarzschild black hole

International Nuclear Information System (INIS)

Cardoso, Vitor; Lemos, Jose P.S.; Yoshida, Shijun

2003-01-01

We investigate the electromagnetic radiation released during the high energy collision of a charged point particle with a four-dimensional Schwarzschild black hole. We show that the spectra is flat, and well described by a classical calculation. We also compare the total electromagnetic and gravitational energies emitted, and find that the former is suppressed in relation to the latter for very high energies. These results could apply to the astrophysical world in the case that charged stars and small charged black holes are out there colliding into large black holes, and to a very high energy collision experiment in a four-dimensional world. In this latter scenario the calculation is to be used for the moments just after black hole formation, when the collision of charged debris with the newly formed black hole is certainly expected. Since the calculation is four dimensional, it does not directly apply to TeV-scale gravity black holes, as these inhabit a world of six to eleven dimensions, although our results should qualitatively hold when extrapolated with some care to higher dimensions

Binding Energy and Equilibrium of Compact Objects

Directory of Open Access Journals (Sweden)

Germano M.

2014-04-01

Full Text Available The theoretical analysis of the existence of a limit mass for compact astronomic ob- jects requires the solution of the Einstein’s equations of g eneral relativity together with an appropriate equation of state. Analytical solutions exi st in some special cases like the spherically symmetric static object without energy sou rces that is here considered. Solutions, i.e. the spacetime metrics, can have a singular m athematical form (the so called Schwarzschild metric due to Hilbert or a nonsingula r form (original work of Schwarzschild. The former predicts a limit mass and, conse quently, the existence of black holes above this limit. Here it is shown that, the origi nal Schwarzschild met- ric permits compact objects, without mass limit, having rea sonable values for central density and pressure. The lack of a limit mass is also demonst rated analytically just imposing reasonable conditions on the energy-matter densi ty, of positivity and decreas- ing with radius. Finally the ratio between proper mass and to tal mass tends to 2 for high values of mass so that the binding energy reaches the lim it m (total mass seen by a distant observer. As it is known the negative binding energ y reduces the gravitational mass of the object; the limit of m for the binding energy provides a mechanism for stable equilibrium of any amount of mass to contrast the gravitatio nal collapse.

Classical and quantum gravity of brane black holes

International Nuclear Information System (INIS)

Gregory, Ruth; Ross, Simon F.; Zegers, Robin

2008-01-01

We test the holographic conjecture of brane black holes: that a full classical 5D solution will correspond to a quantum corrected 4D black hole. Using the Schwarzschild-AdS black string, we compare the braneworld back reaction at strong coupling with the calculation of the quantum stress tensor on Schwarzschild-AdS 4 at weak coupling. The two calculations give different results and provide evidence that the stress tensor at strong coupling is indeed different to the weak coupling calculations, and hence does not conform to our notion of a quantum corrected black hole. We comment on the implications for an asymptotically flat black hole.

On algebraically special perturbations of black holes

International Nuclear Information System (INIS)

Chandrasekhar, S.

1984-01-01

Algebraically special perturbations of black holes excite gravitational waves that are either purely ingoing or purely outgoing. Solutions, appropriate to such perturbations of the Kerr, the Schwarzschild, and the Reissner-Nordstroem black-holes, are obtained in explicit forms by different methods. The different methods illustrate the remarkable inner relations among different facets of the mathematical theory. In the context of the Kerr black-hole they derive from the different ways in which the explicit value of the Starobinsky constant emerges, and in the context of the Schwarzschild and the Reissner-Nordstroem black-holes they derive from the potential barriers surrounding them belonging to a special class. (author)

Apparent violation of the principle of equivalence and Killing horizons

International Nuclear Information System (INIS)

Zimmerman, R.L.; Farhoosh, H.; Oregon Univ., Eugene

1980-01-01

By means of the principle of equivalence it is deduced that the qualitative behavior of the Schwarzschild horizon about a uniformly accelerating particle. This result is confirmed for an exact solution of a uniformly accelerating object in the limit of small accelerations. For large accelerations the Schwarzschild horizon appears to violate the qualitative behavior established via the principle of equivalence. When similar arguments are extended to an observable such as the red shift between two observers, there is no departure from the results expected from the principle of equivalence. The resolution of the paradox is brought about by a compensating effect due to the Rindler horizon. (author)

Flat synchronizations in spherically symmetric space-times

International Nuclear Information System (INIS)

Herrero, Alicia; Morales-Lladosa, Juan Antonio

2010-01-01

It is well known that the Schwarzschild space-time admits a spacelike slicing by flat instants and that the metric is regular at the horizon in the associated adapted coordinates (Painleve-Gullstrand metric form). We consider this type of flat slicings in an arbitrary spherically symmetric space-time. The condition ensuring its existence is analyzed, and then, we prove that, for any spherically symmetric flat slicing, the densities of the Weinberg momenta vanish. Finally, we deduce the Schwarzschild solution in the extended Painleve-Gullstrand-LemaItre metric form by considering the coordinate decomposition of the vacuum Einstein equations with respect to a flat spacelike slicing.

Stability of Schwarzschild-like solutions in f(R,G) gravity models

International Nuclear Information System (INIS)

De Felice, Antonio; Suyama, Teruaki; Tanaka, Takahiro

2011-01-01

We study linear metric perturbations around a spherically symmetric static spacetime for general f(R,G) theories, where R is the Ricci scalar and G is the Gauss-Bonnet term. We find that, unless the determinant of the Hessian of f(R,G) is zero, even-type perturbations have a ghost for any multipole mode. In order for these theories to be plausible alternatives to general relativity, the theory should satisfy the condition that the ghost is massive enough to effectively decouple from the other fields. We study the requirement on the form of f(R,G) which satisfies this condition. We also classify the number of propagating modes both for the odd-type and the even-type perturbations and derive the propagation speeds for each mode.

Quasinormal frequencies of Schwarzschild black holes in anti-de Sitter spacetimes: A complete study of the overtone asymptotic behavior

International Nuclear Information System (INIS)

Cardoso, Vitor; Konoplya, Roman; Lemos, Jose P. S.

2003-01-01

We present a thorough analysis of the quasinormal (QN) behavior associated with the decay of scalar, electromagnetic, and gravitational perturbations of Schwarzschild black holes in anti-de Sitter (AdS) spacetimes. As is known, the AdS QN spectrum crucially depends on the relative size of the black hole to the AdS radius. There are three different types of behavior depending on whether the black hole is large, intermediate, or small. The results of previous works, concerning lower overtones for large black holes, are completed here by obtaining higher overtones for all three black hole regimes. There are two major conclusions that one can draw from this work: First, asymptotically for high overtones, all the modes are evenly spaced, and this holds for all three types of regime, large, intermediate, and small black holes, independently of l, where l is the quantum number characterizing the angular distribution; second, the spacing between modes is apparently universal in that it does not depend on the field; i.e., scalar, electromagnetic, and gravitational QN modes all have the same spacing for high overtones. We are also able to prove why scalar and gravitational perturbations are isospectral, asymptotically for high overtones, by introducing appropriate superpartner potentials

Exact solutions of Einstein and Einstein-Maxwell equations in higher-dimensional spacetime

International Nuclear Information System (INIS)

Xu Dianyan; Beijing Univ., BJ

1988-01-01

The D-dimensional Schwarzschild-de Sitter metric and Reissner-Nordstrom-de-Sitter metric are derived directly by solving the Einstein and Einstein-Maxwell equations. The D-dimensional Kerr metric is rederived by using the complex coordinate transformation method and the D-dimensional Kerr-de Sitter metric is also given. The conjecture about the D-dimensional metric of a rotating charged mass is given at the end of this paper. (author)

Confluent Heun functions and the physics of black holes: Resonant frequencies, Hawking radiation and scattering of scalar waves

Energy Technology Data Exchange (ETDEWEB)

Vieira, H.S., E-mail: horacio.santana.vieira@hotmail.com [Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, CEP 58051-970, João Pessoa, PB (Brazil); Centro de Ciências, Tecnologia e Saúde, Universidade Estadual da Paraíba, CEP 58233-000, Araruna, PB (Brazil); Bezerra, V.B., E-mail: valdir@fisica.ufpb.br [Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, CEP 58051-970, João Pessoa, PB (Brazil)

2016-10-15

We apply the confluent Heun functions to study the resonant frequencies (quasispectrum), the Hawking radiation and the scattering process of scalar waves, in a class of spacetimes, namely, the ones generated by a Kerr–Newman–Kasuya spacetime (dyon black hole) and a Reissner–Nordström black hole surrounded by a magnetic field (Ernst spacetime). In both spacetimes, the solutions for the angular and radial parts of the corresponding Klein–Gordon equations are obtained exactly, for massive and massless fields, respectively. The special cases of Kerr and Schwarzschild black holes are analyzed and the solutions obtained, as well as in the case of a Schwarzschild black hole surrounded by a magnetic field. In all these special situations, the resonant frequencies, Hawking radiation and scattering are studied. - Highlights: • Charged massive scalar field in the dyon black hole and massless scalar field in the Ernst spacetime are analyzed. • The confluent Heun functions are applied to obtain the solution of the Klein–Gordon equation. • The resonant frequencies are obtained. • The Hawking radiation and the scattering process of scalar waves are examined.

Exact Solutions of the Field Equations for Empty Space in the Nash Gravitational Theory

Directory of Open Access Journals (Sweden)

Matthew T. Aadne

2017-02-01

Full Text Available John Nash has proposed a new theory of gravity. We define a Nash-tensor equal to the curvature tensor appearing in the Nash field equations for empty space, and calculate its components for two cases: 1. A static, spherically symmetric space; and 2. The expanding, homogeneous and isotropic space of the Friedmann-Lemaitre-Robertson-Walker (FLRW universe models. We find the general, exact solution of Nash’s field equations for empty space in the static case. The line element turns out to represent the Schwarzschild-de Sitter spacetime. Also we find the simplest non-trivial solution of the field equations in the cosmological case, which gives the scale factor corresponding to the de Sitter spacetime. Hence empty space in the Nash theory corresponds to a space with Lorentz Invariant Vacuum Energy (LIVE in the Einstein theory. This suggests that dark energy may be superfluous according to the Nash theory. We also consider a radiation filled universe model in an effort to find out how energy and matter may be incorporated into the Nash theory. A tentative interpretation of the Nash theory as a unified theory of gravity and electromagnetism leads to a very simple form of the field equations in the presence of matter. It should be noted, however, that the Nash theory is still unfinished. A satisfying way of including energy momentum into the theory has yet to be found.

Super-horizon primordial black holes

International Nuclear Information System (INIS)

Harada, Tomohiro; Carr, B.J.

2005-01-01

We discuss a new class of solutions to the Einstein equations which describe a primordial black hole (PBH) in a flat Friedmann background. Such solutions arise if a Schwarzschild black hole is patched onto a Friedmann background via a transition region. They are possible providing the black hole event horizon is larger than the cosmological apparent horizon. Such solutions have a number of strange features. In particular, one has to define the black hole and cosmological horizons carefully and one then finds that the mass contained within the black hole event horizon decreases when the black hole is larger than the Friedmann cosmological apparent horizon, although its area always increases. These solutions involve two distinct future null infinities and are interpreted as the conversion of a white hole into a black hole. Although such solutions may not form from gravitational collapse in the same way as standard PBHs, there is nothing unphysical about them, since all energy and causality conditions are satisfied. Their conformal diagram is a natural amalgamation of the Kruskal diagram for the extended Schwarzschild solution and the conformal diagram for a black hole in a flat Friedmann background. In this paper, such solutions are obtained numerically for a spherically symmetric universe containing a massless scalar field, but it is likely that they exist for more general matter fields and less symmetric systems

Simultaneous baldness and cosmic baldness and the Kottler spacetime

Science.gov (United States)

Faraoni, Valerio; Cardini, Adriana M.; Chung, Wen-Jian

2018-01-01

The uniqueness of the Kottler/Schwarzschild-de Sitter solution (KSdS) of the vacuum Einstein equations with positive cosmological constant is discussed and certain putative alternatives are shown to either solve different equations or to be the KSdS solution in disguise. A simultaneous no-hair and cosmic no-hair theorem for the KSdS geometry in the presence of an imperfect fluid is proved.

Black Hole Information Problem and Wave Bursts

Science.gov (United States)

Gogberashvili, Merab; Pantskhava, Lasha

2018-06-01

By reexamination of the boundary conditions of wave equation on a black hole horizon it is found not harmonic, but real-valued exponentially time-dependent solutions. This means that quantum particles probably do not cross the Schwarzschild horizon, but are absorbed and some are reflected by it, what potentially can solve the famous black hole information paradox. To study this strong gravitational lensing we are introducing an effective negative cosmological constant between the Schwarzschild and photon spheres. It is shown that the reflected particles can obtain their additional energy in this effective AdS space and could explain properties of some unusually strong signals, like LIGO events, gamma ray and fast radio bursts.

Graviton emission from a higher-dimensional black hole

International Nuclear Information System (INIS)

Cornell, Alan S.; Naylor, Wade; Sasaki, Misao

2006-01-01

We discuss the graviton absorption probability (greybody factor) and the cross-section of a higher-dimensional Schwarzschild black hole (BH). We are motivated by the suggestion that a great many BHs may be produced at the LHC and bearing this fact in mind, for simplicity, we shall investigate the intermediate energy regime for a static Schwarzschild BH. That is, for (2M) 1/(n-1) ω ∼ 1, where M is the mass of the black hole and ω is the energy of the emitted gravitons in (2+n)-dimensions. To find easily tractable solutions we work in the limit l >> 1, where l is the angular momentum quantum number of the graviton

Effects of general relativity in the motion of minor planets and comets

International Nuclear Information System (INIS)

Sitarski, G.

1983-01-01

Basing on the solution of one-body Schwarzschild problem, the relativistic terms were included to the equations of motion of a minor planet or comet. It appeared that the using of Painleve's coordinates allowed to write the equations of motion in a very simple form. Equations of motion as well as the commonly used equations based on the Schwarzschild isotropic and nonisotropic line elements were numerically integrated by the recurrent power series method. The results of integration of the motion of Mercury and of the minor planet Icarus show strictly the perihelion motion predicted by the general relativity theory. The relativistic effects in the motion of some minor planets and comets were examined too. (author)

Anisotropic spheres admitting a one-parameter group of conformal motions

International Nuclear Information System (INIS)

Herrera, L.; Ponce de Leon, J.

1985-01-01

The Einstein equations for spherically symmetric distributions of anisotropic matter (principal stresses unequal), are solved, assuming the existence of a one-parameter group of conformal motions. All solutions can be matched with the Schwarzschild exterior metric on the boundary of matter. Two families of solutions represent, respectively, expanding and contracting spheres which asymptotically tend to a static sphere with a surface potential equal to (1)/(3) . A third family of solutions describes ''oscillating black holes.'' All solutions possess a positive energy density larger than the stresses everywhere

Temperature evolution during dissipative collapse

Indian Academy of Sciences (India)

Abstract. We investigate the gravitational collapse of a radiating sphere evolving into a final static configuration described by the interior Schwarzschild solution. The temperature profiles of this par- ticular model are obtained within the framework of causal thermodynamics. The overall temperature evolution is enhanced by ...

The effect of non-sphericity on mass and anisotropy measurements in dSph galaxies with Schwarzschild method

Science.gov (United States)

Kowalczyk, Klaudia; Łokas, Ewa L.; Valluri, Monica

2018-05-01

In our previous work we confirmed the reliability of the spherically symmetric Schwarzschild orbit-superposition method to recover the mass and velocity anisotropy profiles of spherical dwarf galaxies. Here, we investigate the effect of its application to intrinsically non-spherical objects. For this purpose we use a model of a dwarf spheroidal galaxy formed in a numerical simulation of a major merger of two discy dwarfs. The shape of the stellar component of the merger remnant is axisymmetric and prolate which allows us to identify and measure the bias caused by observing the spheroidal galaxy along different directions, especially the longest and shortest principal axis. The modelling is based on mock data generated from the remnant that are observationally available for dwarfs: projected positions and line-of-sight velocities of the stars. In order to obtain a reliable tool while keeping the number of parameters low we parametrize the total mass distribution as a radius-dependent mass-to-light ratio with just two free parameters we aim to constrain. Our study shows that if the total density profile is known, the true, radially increasing anisotropy profile can be well recovered for the observations along the longest axis whereas the data along the shortest axis lead to the inference of an incorrect, isotropic model. On the other hand, if the density profile is derived from the method as well, the anisotropy is always underestimated but the total mass profile is well recovered for the data along the shortest axis whereas for the longest axis the mass content is overestimated.

Papapetrou energy-momentum tensor for Chern-Simons modified gravity

International Nuclear Information System (INIS)

Guarrera, David; Hariton, A. J.

2007-01-01

We construct a conserved, symmetric energy-momentum (pseudo-)tensor for Chern-Simons modified gravity, thus demonstrating that the theory is Lorentz invariant. The tensor is discussed in relation to other gravitational energy-momentum tensors and analyzed for the Schwarzschild, Reissner-Nordstrom, and Friedmann-Robertson-Walker solutions. To our knowledge this is the first confirmation that the Reissner-Nordstrom and Friedmann-Robertson-Walker metrics are solutions of the modified theory

arXiv Supplying Dark Energy from Scalar Field Dark Matter

CERN Document Server

Gogberashvili, Merab

We consider the hypothesis that dark matter and dark energy consists of ultra-light self-interacting scalar particles. It is found that the Klein-Gordon equation with only two free parameters (mass and self-coupling) on a Schwarzschild background, at the galactic length-scales has the solution which corresponds to Bose-Einstein condensate, behaving as dark matter, while the constant solution at supra-galactic scales can explain dark energy.

Supplying Dark Energy from Scalar Field Dark Matter

OpenAIRE

Gogberashvili, Merab; Sakharov, Alexander S.

2017-01-01

We consider the hypothesis that dark matter and dark energy consists of ultra-light self-interacting scalar particles. It is found that the Klein-Gordon equation with only two free parameters (mass and self-coupling) on a Schwarzschild background, at the galactic length-scales has the solution which corresponds to Bose-Einstein condensate, behaving as dark matter, while the constant solution at supra-galactic scales can explain dark energy.

Zero-rest-mass fields in an algebraically special curved space-time

Energy Technology Data Exchange (ETDEWEB)

Fordy, A P [King' s Coll., London (UK). Dept. of Mathematics

1977-04-01

Zero-rest-mass higher-spin fields in algebraically special vacuum back-ground space-times are considered. It is shown that the algebraic speciality of the background metric strongly restricts the form of the solutions of these fields. These results are used to study perturbations of the Schwarzschild black hole.

Higher-dimensional relativistic-fluid spheres

International Nuclear Information System (INIS)

Patel, L. K.; Ahmedabad, Gujarat Univ.

1997-01-01

They consider the hydrostatic equilibrium of relativistic-fluid spheres for a D-dimensional space-time. Three physically viable interior solutions of the Einstein field equations corresponding to perfect-fluid spheres in a D-dimensional space-time are obtained. When D = 4 they reduce to the Tolman IV solution, the Mehra solution and the Finch-Skea solution. The solutions are smoothly matched with the D-dimensional Schwarzschild exterior solution at the boundary r = a of the fluid sphere. Some physical features and other related details of the solutions are briefly discussed. A brief description of two other new solutions for higher-dimensional perfect-fluid spheres is also given

A Non-anthropic Solution to the Cosmological Constant Problem

Directory of Open Access Journals (Sweden)

Spivey R. J.

2016-01-01

Full Text Available Accelerating cosmological expansion is driven by a minuscule vacuum energy density possibly seeking opportunities to decay to a true ground state. Quasar characteristics imply their central engines possess an intrinsic magnetic field compatible with the pres- ence of an electrically charged toroidal dark hole, an eternally collapsing structure lack- ing an event horizon. The possibility is consistent with the inability of black holes to capture particles in a universe of finite age, Einstein’s dismissal of the Schwarzschild metric as unphysical and the implausibility of the various paradoxes invoked by black hole existence. The uncloaked innards of these dark holes would expose immense vac- uum accelerations at their cores, inevitably tempered by Planck scale physics. The Unruh effect predicts that intense yet highly localised heating should occur there. As thermal energy gradually amasses and dissipates, radiation would eventually start to escape into the surrounding environment. Virtual from the d ark hole perspective, the emissions could not decrease the dark hole’s mass: the energy source must instead be the universal vacuum, the likely repository of dark energy. In analogy with core- collapse supernovae, neutrinos should dominate the cooling flows. Red-shifting to low energies upon escape, quantum degenerate haloes should for m predominantly around the largest galaxies. This mechanism is promising from the perspective of enabling the future universe to efficiently sustain aquatic life before stars become scarce, offering a biological yet decidedly non-anthropic solution to the cosmological constant problem.

Tidal Forces in Dyonic Reissner-Nördstrom Black Hole

Science.gov (United States)

Sharif, M.; Kousar, Lubna

2018-03-01

This paper investigates the tidal as well as magnetic charge effects produced in dyonic Reissner-Nordström black hole. We evaluate Newtonian radial acceleration using radial geodesics for freely falling test particles. We establish system of equations governing radial and angular tidal forces using geodesic deviation equation and discuss their solutions for bodies falling freely towards this black hole. The radial tidal force turns out to be compressing outside the event horizon whereas the angular tidal force changes sign between event and Cauchy horizons unlike Schwarzschild black hole. The radial geodesic component starts decreasing in dyonic Reissner-Nordström black hole unlike Schwarzschild case. We conclude that magnetic charge strongly affects the radial as well as angular components of tidal force.

Introduction to General Relativity and Black Holes (5/5)

CERN Multimedia

CERN. Geneva

2001-01-01

Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.

Introduction to General Relativity and Black Holes (3/5)

CERN Multimedia

CERN. Geneva

2001-01-01

Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.

Introduction to General Relativity and Black Holes (1/5)

CERN Multimedia

CERN. Geneva

2001-01-01

Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.

Introduction to General Relativity and Black Holes (2/5)

CERN Multimedia

CERN. Geneva

2001-01-01

Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.

Introduction to General Relativity and Black Holes (4/5)

CERN Multimedia

CERN. Geneva

2001-01-01

Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.

Cosmic frontiers of general relativity

International Nuclear Information System (INIS)

Kaufmann, W.J. III.

1977-01-01

All relevant topics in general astronomy are covered including orientation in space--time, special relativity, gravitation and general relativity, stars and stellar evolution, white dwarfs, pulsars, neutron stars, the black hole, the geometry of the Schwarzschild solution, and electrically charged and rotating black holes. Also the geometry of the Kerr solution, observations of black holes, white holes and particle creation, gravitational waves and lenses, exploding galaxies and massive and primordial black holes are discussed

Instability of enclosed horizons

Science.gov (United States)

Kay, Bernard S.

2015-03-01

We point out that there are solutions to the scalar wave equation on dimensional Minkowski space with finite energy tails which, if they reflect off a uniformly accelerated mirror due to (say) Dirichlet boundary conditions on it, develop an infinite stress-energy tensor on the mirror's Rindler horizon. We also show that, in the presence of an image mirror in the opposite Rindler wedge, suitable compactly supported arbitrarily small initial data on a suitable initial surface will develop an arbitrarily large stress-energy scalar near where the two horizons cross. Also, while there is a regular Hartle-Hawking-Israel-like state for the quantum theory between these two mirrors, there are coherent states built on it for which there are similar singularities in the expectation value of the renormalized stress-energy tensor. We conjecture that in other situations with analogous enclosed horizons such as a (maximally extended) Schwarzschild black hole in equilibrium in a (stationary spherical) box or the (maximally extended) Schwarzschild-AdS spacetime, there will be similar stress-energy singularities and almost-singularities—leading to instability of the horizons when gravity is switched on and matter and gravity perturbations are allowed for. All this suggests it is incorrect to picture a black hole in equilibrium in a box or a Schwarzschild-AdS black hole as extending beyond the past and future horizons of a single Schwarzschild (/Schwarzschild-AdS) wedge. It would thus provide new evidence for 't Hooft's brick wall model while seeming to invalidate the picture in Maldacena's ` Eternal black holes in AdS'. It would thereby also support the validity of the author's matter-gravity entanglement hypothesis and of the paper ` Brick walls and AdS/CFT' by the author and Ortíz.

On stellar collapse: continual or oscillatory. A short comment

International Nuclear Information System (INIS)

Leung, P.T.

1980-01-01

We comment on a previously published paper on the oscillatory dynamics of stellar collapse and conclude that the Schwarzschild interior solution applied to the 'inflection points' can never give rise to a 'turning back' motion, in spite of the fact that the geodesic equation really does not always describe an attractive gravitational acceleration

Antigravity: Spin-gravity coupling in action

Science.gov (United States)

Plyatsko, Roman; Fenyk, Mykola

2016-08-01

The typical motions of a spinning test particle in Schwarzschild's background which show the strong repulsive action of the highly relativistic spin-gravity coupling are considered using the exact Mathisson-Papapetrou equations. An approximated approach to choice solutions of these equations which describe motions of the particle's proper center of mass is developed.

Optics of relativistic sources in a spherically symmetric gravitational field

International Nuclear Information System (INIS)

Campbell, G.A.

1975-01-01

The effects of spectral shifts and gravitational focussing on radiation from sources moving geodesically in the Schwarzschild gravitational field is analyzed using the general-relativistic equations for geodesic motion and for the propagation of radiation along null geodesics in the geometrical optics approximation. The exact solutions of the Schwarzschild geodesic equations are briefly discussed for the null and time-like cases, and the method of classifying the orbital types of motion based on the effective radial potential is presented. A method of finding the stability of these orbits using this technique is discussed. The geometrical optics approximation for the propagation of radiation is discussed, and the area-intensity law for the Schwarzschild field is derived. The particularly interesting region near R = 3m is investigated by means of expansions of the exact equations. Numerical techniques for calculating radiation patterns from the propagation equations are discussed, including techniques for obtaining the time variation along geodesics and differences in propagation time along different null geodesics. Finally, the implications of these calculations for the apparent contradiction in energy requirements set by Joseph Weber's observations of galactic gravitational radiation and by astronomical observation are discussed. (Diss. Abstr. Int., B)

Geometric scalar theory of gravity beyond spherical symmetry

Science.gov (United States)

Moschella, U.; Novello, M.

2017-04-01

We construct several exact solutions for a recently proposed geometric scalar theory of gravity. We focus on a class of axisymmetric geometries and a big-bang-like geometry and discuss their Lorentzian character. The axisymmetric solutions are parametrized by an integer angular momentum l . The l =0 (spherical) case gives rise to the Schwarzschild geometry. The other solutions have naked singular surfaces. While not a priori obvious, all the solutions that we present here are globally Lorentzian. The Lorentzian signature appears to be a robust property of the disformal geometries solving the vacuum geometric scalar theory of gravity equations.

Black holes in loop quantum gravity: the complete space-time.

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Gambini, Rodolfo; Pullin, Jorge

2008-10-17

We consider the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution corresponding to the semiclassical theory. The singularity is eliminated but the space-time still contains a horizon. Although the solution is known partially numerically and therefore a proper global analysis is not possible, a global structure akin to a singularity-free Reissner-Nordström space-time including a Cauchy horizon is suggested.

Local cosmology of the solar system

OpenAIRE

Bel, Ll.

2010-01-01

A time-dependent model of space-time is used to describe the gravitational field of the sun. This model is a spherically symmetric approximate solution of Einstein's equations in vacuum. Near the sun it approximates one of the models derived from the Schwarzschild solution, while at large distances it becomes a milne's-like zero space-time curvature model. Two local cosmology free parameters provide simple descriptions for the secular increasing of the astronomical unit, as well as the "anoma...

Modified gravity in Arnowitt-Deser-Misner formalism

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Gao, Changjun

2010-02-01

Motivated by Hořava-Lifshitz gravity theory, we propose and investigate two kinds of modified gravity theories, the f(R) kind and the K-essence kind, in the Arnowitt-Deser-Misner (ADM) formalism. The f(R) kind includes one ultraviolet (UV) term and one infrared (IR) term together with the Einstein-Hilbert action. We find that these two terms naturally present the ultraviolet and infrared modifications to the Friedmann equation. The UV and IR modifications can avoid the past Big-Bang singularity and the future Big-Rip singularity, respectively. Furthermore, the IR modification can naturally account for the current acceleration of the Universe. The Lagrangian of K-essence kind modified gravity is made up of the three-dimensional Ricci scalar and an arbitrary function of the extrinsic curvature term. We find the cosmic acceleration can also be naturally interpreted without invoking any kind of dark energy. The static, spherically symmetry and vacuum solutions of both theories are Schwarzschild or Schwarzschild-de Sitter solution. Thus these modified gravity theories are viable for solar system tests.

Nonadiabatic charged spherical evolution in the postquasistatic approximation

International Nuclear Information System (INIS)

Rosales, L.; Barreto, W.; Peralta, C.; Rodriguez-Mueller, B.

2010-01-01

We apply the postquasistatic approximation, an iterative method for the evolution of self-gravitating spheres of matter, to study the evolution of dissipative and electrically charged distributions in general relativity. The numerical implementation of our approach leads to a solver which is globally second-order convergent. We evolve nonadiabatic distributions assuming an equation of state that accounts for the anisotropy induced by the electric charge. Dissipation is described by streaming-out or diffusion approximations. We match the interior solution, in noncomoving coordinates, with the Vaidya-Reissner-Nordstroem exterior solution. Two models are considered: (i) a Schwarzschild-like shell in the diffusion limit; and (ii) a Schwarzschild-like interior in the free-streaming limit. These toy models tell us something about the nature of the dissipative and electrically charged collapse. Diffusion stabilizes the gravitational collapse producing a spherical shell whose contraction is halted in a short characteristic hydrodynamic time. The streaming-out radiation provides a more efficient mechanism for emission of energy, redistributing the electric charge on the whole sphere, while the distribution collapses indefinitely with a longer hydrodynamic time scale.

Modified gravity in Arnowitt-Deser-Misner formalism

International Nuclear Information System (INIS)

Gao Changjun

2010-01-01

Motivated by Horava-Lifshitz gravity theory, we propose and investigate two kinds of modified gravity theories, the f(R) kind and the K-essence kind, in the Arnowitt-Deser-Misner (ADM) formalism. The f(R) kind includes one ultraviolet (UV) term and one infrared (IR) term together with the Einstein-Hilbert action. We find that these two terms naturally present the ultraviolet and infrared modifications to the Friedmann equation. The UV and IR modifications can avoid the past Big-Bang singularity and the future Big-Rip singularity, respectively. Furthermore, the IR modification can naturally account for the current acceleration of the Universe. The Lagrangian of K-essence kind modified gravity is made up of the three-dimensional Ricci scalar and an arbitrary function of the extrinsic curvature term. We find the cosmic acceleration can also be naturally interpreted without invoking any kind of dark energy. The static, spherically symmetry and vacuum solutions of both theories are Schwarzschild or Schwarzschild-de Sitter solution. Thus these modified gravity theories are viable for solar system tests.

Beyond the geodesic approximation: Conservative effects of the gravitational self-force in eccentric orbits around a Schwarzschild black hole

International Nuclear Information System (INIS)

Barack, Leor; Sago, Norichika

2011-01-01

We study conservative finite-mass corrections to the motion of a particle in a bound (eccentric) strong-field orbit around a Schwarzschild black hole. We assume the particle's mass μ is much smaller than the black hole mass M, and explore post-geodesic corrections of O(μ/M). Our analysis uses numerical data from a recently developed code that outputs the Lorenz-gauge gravitational self-force (GSF) acting on the particle along the eccentric geodesic. First, we calculate the O(μ/M) conservative correction to the periastron advance of the orbit, as a function of the (gauge-dependent) semilatus rectum and eccentricity. A gauge-invariant description of the GSF precession effect is made possible in the circular-orbit limit, where we express the correction to the periastron advance as a function of the invariant azimuthal frequency. We compare this relation with results from fully nonlinear numerical-relativistic simulations. In order to obtain a gauge-invariant measure of the GSF effect for fully eccentric orbits, we introduce a suitable generalization of Detweiler's circular-orbit ''redshift'' invariant. We compute the O(μ/M) conservative correction to this invariant, expressed as a function of the two invariant frequencies that parametrize the orbit. Our results are in good agreement with results from post-Newtonian calculations in the weak-field regime, as we shall report elsewhere. The results of our study can inform the development of analytical models for the dynamics of strongly gravitating binaries. They also provide an accurate benchmark for future numerical-relativistic simulations.

Surface phenomena and the evolution of radiating fluid spheres in general relativity

International Nuclear Information System (INIS)

Herrera, L.; Jimenez, J.; Esculpi, M.; Ibanez, J.

1989-01-01

A method used to study the evolution of radiating spheres (Herrera, Jimenez, and Ruggeri) is extended to the case in which surface phenomena are taken into account. The equations have been integrated numerically for a model derived from the Schwarzschild interior solution, bringing out the effects of surface tension on the evolution of the spheres. 17 refs

Introduction to gravity and cosmology

International Nuclear Information System (INIS)

Jauneau, L.

1988-09-01

Relativity principles, equivalence principles, and the general covariance principle are introduced. Curved space analysis via tensor calculus and absolute differential calculus is outlined. Einstein's equations are presented. The Schwarzschild solution; tests of general relativity; and black holes are discussed. Application of general relativity to cosmology is considered. The Standard Model of cosmology and its extensions are reviewed

A new possibility of cosmological model construction in Kaluza-Klein theories

International Nuclear Information System (INIS)

Berezin, V.A.; Kuzmin, V.A.; AN SSSR, Moscow. Inst. Yadernykh Issledovanij)

1987-12-01

We studied the dimensional reduction of the 5-dimensional Schwarzschild-deSitter solution and found that the Friedmann-Robertson-Walker cosmological model may be obtained by the dimensional reduction along the Killing vector in the T-region of the 5-manifold. For the Appelquist-Chodos reduction we observed the universal behaviour of the scale factor near the 4-dimensional singularity and found a possibility of cosmological model constructing with induced singularity like the Big Bang from non-singular 5-dimensional solution. (orig.)

Gravitational curvature: an introduction to Einstein's theory

International Nuclear Information System (INIS)

Frankel, T.

1979-01-01

The basic aspects of general relativity are presented from a geometric point of view. The content of the book is well indicated by chapter headings: aspects of special relativity, clocks and gravitational potential, a heuristic derivation of Einstein's equations, the geometry of Einstein's equations, the Schwarzschild solution, the classical motion of a continuum, the relativistic equations of motion, light rays and Fermat's principle, electromagnetism in three-space and Minkowski space, electromagnetism in general relativity, the interior solution, and cosmology. 28 figures

Spacetime Junctions and the Collapse to Black Holes in Higher Dimensions

Directory of Open Access Journals (Sweden)

Filipe C. Mena

2012-01-01

Full Text Available We review recent results about the modelling of gravitational collapse to black holes in higher dimensions. The models are constructed through the junction of two exact solutions of the Einstein field equations: an interior collapsing fluid solution and a vacuum exterior solution. The vacuum exterior solutions are either static or containing gravitational waves. We then review the global geometrical properties of the matched solutions which, besides black holes, may include the existence of naked singularities and wormholes. In the case of radiating exteriors, we show that the data at the boundary can be chosen to be, in some sense, arbitrarily close to the data for the Schwarzschild-Tangherlini solution.

A new class of relativistic stellar models

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Haggag, Salah

1995-03-01

Einstein field equations for a static and spherically symmetric perfect fluid are considered. A formulation given by Patino and Rago is used to obtain a class of nine solutions, two of them are Tolman solutions I, IV and the remaining seven are new. The solutions are the correct ones corresponding to expressions derived by Patino and Rago which have been shown by Knutsen to be incorrect. Similar to Tolan solution IV each of the new solutions satisfies energy conditions inside a sphere in some range of two independent parameters. Besides, each solution could be matched to the exterior Schwarzschild solution at a boundary where the pressure vanishes and thus the solutions constitute a class of new physically reasonable stellar models.

Probing the quantum correlation and Bell non-locality for Dirac particles with Hawking effect in the background of Schwarzschild black hole

International Nuclear Information System (INIS)

Xu, Shuai; Song, Xue-ke; Shi, Jia-dong; Ye, Liu

2014-01-01

In this Letter, we analytically explore the effect of the Hawking radiation on the quantum correlation and Bell non-locality for Dirac particles in the background of Schwarzschild black hole. It is shown that when the Hawking effect is almost nonexistent, corresponding to the case of an almost extreme black hole, the quantum properties of physically accessible state are the same for the initial situation. For finite Hawking temperature T, the accessible quantum correlation monotonously decreases along with increasing T owing to the thermal fields generated by the Hawking effect, and the accessible quantum non-locality will be disappeared when the Hawking temperature is more than a fixed value which increases with the parameter r of Werner state growing. Then we analyze the redistribution of quantum correlation, and find that for the case of the Hawking temperature being infinite, corresponding to the case of the black hole evaporating completely, the quantum correlation of physically accessible state is equal to the one of the inaccessible states. Moreover, due to the Pauli exclusion principle and the differences between Fermi–Dirac and Bose–Einstein statistics, for the Dirac fields the accessible classical correlation decreases with increase of the Hawking temperature, which is different for the scalar fields. For Bell non-locality, we also find that the quantum non-locality is always extinct for physically inaccessible states, and the strength of the non-locality decreases with enlarging intensity of Hawking effect when the non-locality is existent in physically accessible state.

Scalar-tensor theory of gravitation: generalizations and experimental limitations

International Nuclear Information System (INIS)

Duruisseau, J.P.

1983-01-01

Several theories with scalar field can be derived from different variational principles. Here a very general variational principle is considered and it is proved that, in the exterior case without electromagnetic field, the solution for a particular case generates the set of solutions for the general case. This is applied to the exterior solution in the static case with spherical symmetry without electromagnetic field. The predictions are investigated for the classic effects and the event horizons and some limitations for the variational principles which generalize the usual limitations are obtained. In all these cases the Schwarzschild solution with his horizon appears as a very particular case. (author)

Are black holes a serious threat to scalar field dark matter models?

International Nuclear Information System (INIS)

Barranco, Juan; Degollado, Juan Carlos; Bernal, Argelia; Diez-Tejedor, Alberto; Megevand, Miguel; Alcubierre, Miguel; Nunez, Dario; Sarbach, Olivier

2011-01-01

Classical scalar fields have been proposed as possible candidates for the dark matter component of the universe. Given the fact that supermassive black holes seem to exist at the center of most galaxies, in order to be a viable candidate for the dark matter halo a scalar field configuration should be stable in the presence of a central black hole, or at least be able to survive for cosmological time scales. In the present work we consider a scalar field as a test field on a Schwarzschild background, and study under which conditions one can obtain long-lived configurations. We present a detailed study of the Klein-Gordon equation in the Schwarzschild space-time, both from an analytical and numerical point of view, and show that indeed there exist quasistationary solutions that can remain surrounding a black hole for large time scales.

Accretion onto a noncommutative geometry inspired black hole

Energy Technology Data Exchange (ETDEWEB)

Kumar, Rahul [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); Ghosh, Sushant G. [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); Jamia Millia Islamia, Multidisciplinary Centre for Advanced Research and Studies (MCARS), New Delhi (India); University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)

2017-09-15

The spherically symmetric accretion onto a noncommutative (NC) inspired Schwarzschild black hole is treated for a polytropic fluid. The critical accretion rate M, sonic speed a{sub s} and other flow parameters are generalized for the NC inspired static black hole and compared with the results obtained for the standard Schwarzschild black holes. Also explicit expressions for gas compression ratios and temperature profiles below the accretion radius and at the event horizon are derived. This analysis is a generalization of Michel's solution to the NC geometry. Owing to the NC corrected black hole, the accretion flow parameters also have been modified. It turns out that M ∼ M{sup 2} is still achievable but r{sub s} seems to be substantially decreased due to the NC effects. They in turn do affect the accretion process. (orig.)

Black-hole decay and topological stability in quantum gravity

International Nuclear Information System (INIS)

Rodrigues, L.M.C.S.; Soares, I.D.; Zanelli, J.

1988-01-01

In the context of Quantum Gravity, the evolution of Schwarzschild black-holes is studied. The superspace of the theory is restricted to a class of geometries that contains the Schwarzschild solution for different masses as well as other geometries with different topologies. It is shown that, black-holes are topologically stable under quantum fluctuations but unstable under quantum processes of emission and absorption of gravitons. It is found that, the probability of emission behaves as exp (- α (M f - M i ), where M i and M f are the masses associated to the initial and final states, respectively and α is a positive constant of the order of 1. As the black-hole looses mass it evolves towards a state corresponding to a black-hole of very small that cannot be distinguished from a pure graviton state. (author) [pt

Black holes in higher derivative gravity.

Science.gov (United States)

Lü, H; Perkins, A; Pope, C N; Stelle, K S

2015-05-01

Extensions of Einstein gravity with higher-order derivative terms arise in string theory and other effective theories, as well as being of interest in their own right. In this Letter we study static black-hole solutions in the example of Einstein gravity with additional quadratic curvature terms. A Lichnerowicz-type theorem simplifies the analysis by establishing that they must have vanishing Ricci scalar curvature. By numerical methods we then demonstrate the existence of further black-hole solutions over and above the Schwarzschild solution. We discuss some of their thermodynamic properties, and show that they obey the first law of thermodynamics.

The theories of relativity

International Nuclear Information System (INIS)

Deruelle, N.; Uzan, J.P.

2014-01-01

This book is a quite complete route towards general relativity via special relativity with a start point at Newton's mechanics. The mathematical formulation is based on tensors. All the relativistic aspects of only classical physics - it means no quantum mechanics - are exposed. This book is divided into 3 books and each book represents a consistent knowledge of physics at a certain time in the past: in Newton's time, in the second half of the 19. century and today. The advantage of this presentation is to make the reader feels the changes over time in the concepts of time, space, gravity, cosmology. Each book is divided into 3, 4 and 5 parts which are sub-divided into numerous chapters. Book 1: Space, time and gravity in Newton's theory, with part 1: kinematics, part 2: dynamics and part 3: gravity. Book 2: Special relativity and Maxwell's theory, with part 1: kinematics, part 2: dynamics, part 3: electromagnetism and part 4: electrodynamics. And Book 3: General relativity and gravity, with part 1: curved space-time and gravity, part 2: Schwarzschild solution and black holes, part 3: general relativity and experiments, part 4: Friedman-Lemaitre solutions and cosmology, and part 5: elements or Riemann geometry. The 3. book dedicated to general relativity, tackles topics like the relationships between space-time curvature and gravity, Schwarzschild solutions and black holes, gravitational waves, Friedmann-Lemaitre solutions and cosmology, and Riemann geometry. (A.C.)

Analytical solutions of accreting black holes immersed in a {Lambda}CDM model

Energy Technology Data Exchange (ETDEWEB)

Lima, J.A.S., E-mail: limajas@astro.iag.usp.b [Universidade de Sao Paulo - Instituto de Astronomia, Geofisica e Ciencias Atmosfericas, Rua do Matao, 1226, 05508-090 Cidade Universitaria, Sao Paulo - SP (Brazil); Guariento, Daniel C., E-mail: carrasco@fma.if.usp.b [Universidade de Sao Paulo - Instituto de Fisica, Rua do Matao, Travessa R, 187, 05508-090 Cidade Universitaria, Sao Paulo - SP (Brazil); Horvath, J.E., E-mail: foton@astro.iag.usp.b [Universidade de Sao Paulo - Instituto de Astronomia, Geofisica e Ciencias Atmosfericas, Rua do Matao, 1226, 05508-090 Cidade Universitaria, Sao Paulo - SP (Brazil)

2010-10-04

The evolution of the mass of a black hole embedded in a universe filled with dark energy and cold dark matter is calculated in a closed form within a test fluid model in a Schwarzschild metric, taking into account the cosmological evolution of both fluids. The result describes exactly how accretion asymptotically switches from the matter-dominated to the {Lambda}-dominated regime. For early epochs, the black hole mass increases due to dark matter accretion, and on later epochs the increase in mass stops as dark energy accretion takes over. Thus, the unphysical behaviour of previous analyses is improved in this simple exact model.

Entropy Inequality Violations from Ultraspinning Black Holes.

Science.gov (United States)

Hennigar, Robie A; Mann, Robert B; Kubizňák, David

2015-07-17

We construct a new class of rotating anti-de Sitter (AdS) black hole solutions with noncompact event horizons of finite area in any dimension and study their thermodynamics. In four dimensions these black holes are solutions to gauged supergravity. We find that their entropy exceeds the maximum implied from the conjectured reverse isoperimetric inequality, which states that for a given thermodynamic volume, the black hole entropy is maximized for Schwarzschild-AdS space. We use this result to suggest more stringent conditions under which this conjecture may hold.

Spherically symmetric static spacetimes in vacuum f(T) gravity

International Nuclear Information System (INIS)

Ferraro, Rafael; Fiorini, Franco

2011-01-01

We show that Schwarzschild geometry remains as a vacuum solution for those four-dimensional f(T) gravitational theories behaving as ultraviolet deformations of general relativity. In the gentler context of three-dimensional gravity, we also find that the infrared-deformed f(T) gravities, like the ones used to describe the late cosmic speed up of the Universe, have as the circularly symmetric vacuum solution a Deser-de Sitter or a Banados, Teitelboim and Zanelli-like spacetime with an effective cosmological constant depending on the infrared scale present in the function f(T).

Three types of superpotentials for perturbations in the Einstein-Gauss-Bonnet gravity

International Nuclear Information System (INIS)

Petrov, A N

2009-01-01

Superpotentials (antisymmetric tensor densities) in the Einstein-Gauss-Bonnet (EGB) gravity for arbitrary types of perturbations on arbitrary curved backgrounds are constructed. As a basis, the generalized conservation laws in the framework of an arbitrary D-dimensional metric theory, where conserved currents are expressed through divergences of superpotentials, are used. Such a derivation is exact (perturbations are not infinitesimal) and is approached when a solution (dynamical) is considered as a perturbed system with respect to another solution (background). Three known prescriptions are elaborated: they are the canonical Noether theorem, the Belinfante symmetrization rule and the field-theoretical derivation. All three approaches are presented in a unique way convenient for comparisons and development. Exact expressions for the 01-component of the three types of the superpotentials are derived in the case when an arbitrary static Schwarzschild-like solution in the EGB gravity is considered as a perturbed system with respect to a background of the same type. These formulae are used for calculating the mass of the Schwarzschild-anti-de Sitter black hole in the EGB gravity. As a background, both the anti-de Sitter spacetime in arbitrary dimensions and a 'mass gap' vacuum, which has no maximal set of symmetries, in five dimensions are considered. Problems and perspectives for future development, including the Lovelock gravity, are discussed.

Spatial infinity in higher dimensional spacetimes

International Nuclear Information System (INIS)

Shiromizu, Tetsuya; Tomizawa, Shinya

2004-01-01

Motivated by recent studies on the uniqueness or nonuniqueness of higher dimensional black hole spacetime, we investigate the asymptotic structure of spatial infinity in n-dimensional spacetimes (n≥4). It turns out that the geometry of spatial infinity does not have maximal symmetry due to the nontrivial Weyl tensor (n-1) C abcd in general. We also address static spacetime and its multipole moments P a 1 a 2 ···a s . Contrasting with four dimensions, we stress that the local structure of spacetimes cannot be unique under fixed multipole moments in static vacuum spacetimes. For example, we consider the generalized Schwarzschild spacetimes which are deformed black hole spacetimes with the same multipole moments as spherical Schwarzschild black holes. To specify the local structure of the static vacuum solution we need some additional information, at least the Weyl tensor (n-2) C abcd at spatial infinity

R=0 spacetimes and self-dual Lorentzian wormholes

International Nuclear Information System (INIS)

Dadhich, Naresh; Kar, Sayan; Mukherjee, Sailajananda; Visser, Matt

2002-01-01

A two-parameter family of spherically symmetric, static Lorentzian wormholes is obtained as the general solution of the equation ρ=ρ t =0, where ρ=T ij u i u j , ρ t =(T ij -(1/2)Tg ij )u i u j , and u i u i =-1. This equation characterizes a class of spacetimes which are 'self-dual' (in the sense of electrogravity duality). The class includes the Schwarzschild black hole, a family of naked singularities, and a disjoint family of Lorentzian wormholes, all of which have a vanishing scalar curvature (R=0). The properties of these spacetimes are discussed. Using isotropic coordinates we delineate clearly the domains of parameter space for which wormholes, nakedly singular spacetimes and the Schwarzschild black hole can be obtained. A model for the required 'exotic' stress-energy is discussed, and the notion of traversability for the wormholes is also examined

BOOK REVIEW: Astronomie von Olbers bis Schwarzschild. Nationale Entwicklungen und internationale Beziehungen im 19. Jahrhundert (Acta Historica Astronomiae Vol. 16)

Science.gov (United States)

Sterken, C.; Dick, W. R.; Hamel, J.

2002-12-01

astronomers in his days, when his working place at Altona still belonged to the kingdom of Denmark. This paper is followed by a second one by the same author and deals with the correspondence of H. C. Schumacher and H C. Oersted (1777-1851) and shows how intense and diverse their cooperation was. In a subsequent paper, Wolfgang Kokott describes the role of the Astronomisches Jahrbuch (published from 1776 by the Royal Academy of Sciences at Berlin), a ranking international publication, with Bode's modest Berlin Observatory serving as a clearinghouse of information originating from virtually all European countries. "Karl Schwarzschild and the professionalisation of Astrophysics" is the title of Theodor Schmidt-Kaler's contribution and presents Schwarzschild's contributions to professionalization of astronomy: establishment of course lectures and a permanent astrophysical laboratory, a tight connection between teaching and research, stimulations and suggestions for astronomy at high school and for the formation of high school teachers, international organisation, and the planning of a southern observatory. Peter Habison describes the contribution of Leo de Ball (1853-1916, Director of the Kuffner Observatory in Vienna) to international astronomy. Internationalization in astronomy is also discussed in a following paper by Gudrun Wolfschmidt on the establishment of the Vereinigte Astronomische Gesellschaft, the international Astronomische Gesellschaft in 1863 and finally the International Astronomical Union in 1919. In the second but last paper of the book, Hilmar Duerbeck describes the history of the Chilean National Observatory, beginning with its origins out of Gilliss' US Naval Expedition to the Southern Hemisphere in 1849, over its directors Moesta, Vergara, Obrecht and Ristenpart, to the middle of the 20th century. The paper also includes the astronomical development at the Universidad Catolica and various international expeditions, which aimed at the observations of solar

Conformally-flat, non-singular static metric in infinite derivative gravity

Science.gov (United States)

Buoninfante, Luca; Koshelev, Alexey S.; Lambiase, Gaetano; Marto, João; Mazumdar, Anupam

2018-06-01

In Einstein's theory of general relativity the vacuum solution yields a blackhole with a curvature singularity, where there exists a point-like source with a Dirac delta distribution which is introduced as a boundary condition in the static case. It has been known for a while that ghost-free infinite derivative theory of gravity can ameliorate such a singularity at least at the level of linear perturbation around the Minkowski background. In this paper, we will show that the Schwarzschild metric does not satisfy the boundary condition at the origin within infinite derivative theory of gravity, since a Dirac delta source is smeared out by non-local gravitational interaction. We will also show that the spacetime metric becomes conformally-flat and singularity-free within the non-local region, which can be also made devoid of an event horizon. Furthermore, the scale of non-locality ought to be as large as that of the Schwarzschild radius, in such a way that the gravitational potential in any metric has to be always bounded by one, implying that gravity remains weak from the infrared all the way up to the ultraviolet regime, in concurrence with the results obtained in [arXiv:1707.00273]. The singular Schwarzschild blackhole can now be potentially replaced by a non-singular compact object, whose core is governed by the mass and the effective scale of non-locality.

Scalar field dark matter: behavior around black holes

Energy Technology Data Exchange (ETDEWEB)

Cruz-Osorio, Alejandro; Guzmán, F. Siddhartha; Lora-Clavijo, Fabio D., E-mail: alejandro@ifm.umich.mx, E-mail: guzman@ifm.umich.mx, E-mail: fadulora@ifm.umich.mx [Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Cd. Universitaria, 58040 Morelia, Michoacán (Mexico)

2011-06-01

We present the numerical evolution of a massive test scalar fields around a Schwarzschild space-time. We proceed by using hyperboloidal slices that approach future null infinity, which is the boundary of scalar fields, and also demand the slices to penetrate the event horizon of the black hole. This approach allows the scalar field to be accreted by the black hole and to escape toward future null infinity. We track the evolution of the energy density of the scalar field, which determines the rate at which the scalar field is being diluted. We find polynomial decay of the energy density of the scalar field, and use it to estimate the rate of dilution of the field in time. Our findings imply that the energy density of the scalar field decreases even five orders of magnitude in time scales smaller than a year. This implies that if a supermassive black hole is the Schwarzschild solution, then scalar field dark matter would be diluted extremely fast.

Scalar field dark matter: behavior around black holes

International Nuclear Information System (INIS)

Cruz-Osorio, Alejandro; Guzmán, F. Siddhartha; Lora-Clavijo, Fabio D.

2011-01-01

We present the numerical evolution of a massive test scalar fields around a Schwarzschild space-time. We proceed by using hyperboloidal slices that approach future null infinity, which is the boundary of scalar fields, and also demand the slices to penetrate the event horizon of the black hole. This approach allows the scalar field to be accreted by the black hole and to escape toward future null infinity. We track the evolution of the energy density of the scalar field, which determines the rate at which the scalar field is being diluted. We find polynomial decay of the energy density of the scalar field, and use it to estimate the rate of dilution of the field in time. Our findings imply that the energy density of the scalar field decreases even five orders of magnitude in time scales smaller than a year. This implies that if a supermassive black hole is the Schwarzschild solution, then scalar field dark matter would be diluted extremely fast

General relativity

International Nuclear Information System (INIS)

Gourgoulhon, Eric

2013-01-01

The author proposes a course on general relativity. He first presents a geometrical framework by addressing, presenting and discussion the following notions: the relativistic space-time, the metric tensor, Universe lines, observers, principle of equivalence and geodesics. In the next part, he addresses gravitational fields with spherical symmetry: presentation of the Schwarzschild metrics, radial light geodesics, gravitational spectral shift (Einstein effect), orbitals of material objects, photon trajectories. The next parts address the Einstein equation, black holes, gravitational waves, and cosmological solutions. Appendices propose a discussion of the relationship between relativity and GPS, some problems and their solutions, and Sage codes

The East German Research Landscape in Transition. Part B. Non-University Institutes

Science.gov (United States)

1993-03-02

describe an exception: a land institute of world-wide fame, doing astronomical research. #301: Karl - Schwarzschild Astronomical Observatory Karl ...Prof.Dr.Siegfried A. Marx #301*Q30CT91* {Questionnaire filled in during visits and corrected by letter dated 10 Oct.91): KARL - SCHWARZSCHILD ...OBSERVATORIUM = KARL SCHWARZSCHILD OBSERVATORY) 1. GENERAL SURVEY 1.1. Address, Telephone etc.: {see above) 1.2. Setting, Environment, Access: north of Jena, on

General Relativity During the Great War

Science.gov (United States)

Trimble, Virginia L.

2016-01-01

Einstein's (and Hilbert's) equations saw light of day in the darkness of Berlin 1915, as is well known. Moving from this highlight to less conspicuous topics, we find Karl Schwarzschild's solution of those equations (1916) followed shortly by his death. On the observational and American front, Slipher's assemblage of galaxy radial velocities, begun in 1912 with M31, continued apace. Shapley was busily moving us out of the galactic center. Also at Mt. Wilson, Charles St. John looked for gravitational redshift in the solar spectrum in 1917 without firmly detecting it. Adams demonstrated the very low luminosities of Sirius B and 40 Eri B in 1914 (but his attempt at a redshift for the former came only in 1923). Perhaps least well known is that a handful of additional critical theoretical papers date from the war years and describe the Lense-Thirring effect, the Reissner-Nordstrom solution, and a charged solution with a cosmological constant (due to the even more obscure Friedrich Kottler). Some of these came out of neutral Holland, but Kottler served both at Ypres and on the Galician front. Interesting mixes of military service and relativistic contributions are also associated with the names of Friedmann, Le Lemaître, Weyl (of the tensor), Minkowski, Hubble, Flamm, Droste, and Kretschmann. Astronomers in neutral Denmark, Holland and (until 1917) the USA facilitated transmittal of astronomical observations and other news across the battle lines so that Schwarzschild received an obituary in Nature and Moseley one in Naturwissenschaften.

Embedding Versus Immersion in General Relativity

OpenAIRE

Monte, Edmundo M.

2009-01-01

We briefly discuss the concepts of immersion and embedding of space-times in higher-dimensional spaces. We revisit the classical work by Kasner in which he constructs a model of immersion of the Schwarzschild exterior solution into a six-dimensional pseudo-Euclidean manifold. We show that, from a physical point of view, this model is not entirely satisfactory since the causal structure of the immersed space-time is not preserved by the immersion.

Exact Relativistic `Antigravity' Propulsion

Science.gov (United States)

Felber, Franklin S.

2006-01-01

The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.

A geometrodynamical approach to the MIT confinement scheme

International Nuclear Information System (INIS)

Martellini, M.; Sodano, P.

1978-01-01

Starting from the strong gravity theory of Salam-Isham-Strathdee the M.I.T. bag is identified as a certain region of the global extension of a De Sitter-Schwarzschild solution. As a result the M.I.T. bag radius, a geometrical interpretation of the binding Lagrangian term and a rate of decaying of the ''bag manifold'' into the flat space (which, however, does not lead to observable quark wave functions) are obtained. (author)

The mechanical first law of black hole spacetimes with a cosmological constant and its application to the Schwarzschild-de Sitter spacetime

International Nuclear Information System (INIS)

Urano, Miho; Tomimatsu, Akira; Saida, Hiromi

2009-01-01

The mechanical first law (MFL) of black hole spacetimes is a geometrical relation which relates variations of the mass parameter and horizon area. While it is well known that the MFL of an asymptotic flat black hole is equivalent to its thermodynamical first law, however we do not know the detail of the MFL of black hole spacetimes with a cosmological constant which possess a black hole and cosmological event horizons. This paper aims to formulate an MFL of the two-horizon spacetimes. For this purpose, we try to include the effects of two horizons in the MFL. To do so, we make use of the Iyer-Wald formalism and extend it to regard the mass parameter and the cosmological constant as two independent variables which make it possible to treat the two horizons on the same footing. Our extended Iyer-Wald formalism preserves the existence of the conserved Noether current and its associated Noether charge, and gives an abstract form of the MFL of black hole spacetimes with a cosmological constant. Then, as a representative application of this formalism, we derive the MFL of the Schwarzschild-de Sitter (SdS) spacetime. Our MFL of the SdS spacetime relates the variations of three quantities: the mass parameter, the total area of the two horizons and the volume enclosed by the two horizons. If our MFL is regarded as a thermodynamical first law of the SdS spacetime, it offers a thermodynamically consistent description of the SdS black hole evaporation process: the mass decreases while the volume and the entropy increase. In our suggestion, a generalized second law is not needed to ensure the second law of SdS thermodynamics for its evaporation process.

Wormholes versus black holes: quasinormal ringing at early and late times

Energy Technology Data Exchange (ETDEWEB)

Konoplya, R.A. [Theoretical Astrophysics (TAT), Eberhard-Karls University of Tübingen, Auf der Morgenstelle 10, Tübingen 72076 (Germany); Zhidenko, A., E-mail: roman.konoplya@uni-tuebingen.de, E-mail: olexandr.zhydenko@ufabc.edu.br [Centro de Matemática, Computação e Cognição, Universidade Federal do ABC (UFABC), Rua Abolição, CEP: 09210-180, Santo André, SP (Brazil)

2016-12-01

Recently it has been argued that the phantom thin-shell wormholes matched with the Schwarzschild space-time near the Schwarzschild radius ring like Schwarzschild black holes at early times, but differently at late times [1]. Here we consider perturbations of the wormhole which was constructed without thin-shells: the Bronnikov-Ellis wormhole supported by the phantom matter and electromagnetic field. This wormhole solution is known to be stable under specific equation of state of the phantom matter. We show that if one does not use the above thin-shell matching, the wormhole, depending on the values of its parameters, either rings as the black hole at all times or rings differently also at all times . The wormhole's spectrum, investigated here, posses a number of distinctive features. In the final part we have considered general properties of scattering around arbitrary rotating traversable wormholes. We have found that symmetric and non-symmetric (with respect to the throat) wormholes are qualitatively different in this respect: first, superradiance is allowed only if for those non-symmetric wormholes for which the asymptotic values of the rotation parameters are different on both sides from the throat. Second, the symmetric wormholes cannot mimic effectively the ringing of a black hole at a few various dominant multipoles at the same time, so that the future observations of various events should easily tell the symmetric wormhole from a black hole.

Actual Romanian research in post-newtonian dynamics

Science.gov (United States)

Mioc, V.; Stavinschi, M.

2007-05-01

We survey the recent Romanian results in the study of the two-body problem in post-Newtonian fields. Such a field is characterized, in general, by a potential of the form U(q)=|q|^{-1}+ something (small, but not compulsorily). We distinguish some classes of post-Newtonian models: relativistic (Schwarzschild, Fock, Einstein PN, Reissner-Nordström, Schwarzschild - de Sitter, etc.) and nonrelativistic (Manev, Mücket-Treder, Seeliger, gravito-elastic, etc.). Generalized models (the zonal-satellite problem, quasihomogeneous fields), as well as special cases (anisotropic Manev-type and Schwarzschild-type models, Popovici or Popovici-Manev photogravitational problem), were also tackled. The methods used in such studies are various: analytical (using mainly the theory of perturbations, but also other theories: functions of complex variable, variational calculus, etc.), geometric (qualitative approach of the theory of dynamical systems), and numerical (especially using the Poincaré-section technique). The areas of interest and the general results obtained focus on: exact or approximate analytical solutions; characteristics of local flows (especially at limit situations: collision and escape); quasiperiodic and periodic orbits; equilibria; symmetries; chaoticity; geometric description of the global flow (and physical interpretation of the phase-space structure). We emphasize some special features, which cannot be met within the Newtonian framework: black-hole effect, oscillatory collisions, radial librations, bounded orbits for nonnegative energy, existence of unstable circular motion (or unstable rest), symmetric periodic orbits within anisotropic models, etc.

Null geodesics and red-blue shifts of photons emitted from geodesic particles around a noncommutative black hole space-time

Science.gov (United States)

Kuniyal, Ravi Shankar; Uniyal, Rashmi; Biswas, Anindya; Nandan, Hemwati; Purohit, K. D.

2018-06-01

We investigate the geodesic motion of massless test particles in the background of a noncommutative geometry-inspired Schwarzschild black hole. The behavior of effective potential is analyzed in the equatorial plane and the possible motions of massless particles (i.e. photons) for different values of impact parameter are discussed accordingly. We have also calculated the frequency shift of photons in this space-time. Further, the mass parameter of a noncommutative inspired Schwarzschild black hole is computed in terms of the measurable redshift of photons emitted by massive particles moving along circular geodesics in equatorial plane. The strength of gravitational fields of noncommutative geometry-inspired Schwarzschild black hole and usual Schwarzschild black hole in General Relativity is also compared.

Asymptotically flat black holes in Horndeski theory and beyond

Energy Technology Data Exchange (ETDEWEB)

Babichev, E.; Charmousis, C.; Lehébel, A., E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr, E-mail: antoine.lehebel@th.u-psud.fr [Laboratoire de Physique Théorique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay (France)

2017-04-01

We find spherically symmetric and static black holes in shift-symmetric Horndeski and beyond Horndeski theories. They are asymptotically flat and sourced by a non trivial static scalar field. The first class of solutions is constructed in such a way that the Noether current associated with shift symmetry vanishes, while the scalar field cannot be trivial. This in certain cases leads to hairy black hole solutions (for the quartic Horndeski Lagrangian), and in others to singular solutions (for a Gauss-Bonnet term). Additionally, we find the general spherically symmetric and static solutions for a pure quartic Lagrangian, the metric of which is Schwarzschild. We show that under two requirements on the theory in question, any vacuum GR solution is also solution to the quartic theory. As an example, we show that a Kerr black hole with a non-trivial scalar field is an exact solution to these theories.

Warped solitonic deformations and propagation of black holes in 5D vacuum gravity

International Nuclear Information System (INIS)

Vacaru, Sergiu I; Singleton, D

2002-01-01

In this paper we use the anholonomic frames method to construct exact solutions for vacuum 5D gravity with metrics having off-diagonal components. The solutions are, in general, anisotropic and possess interesting features such as an anisotropic warp factor with respect to the extra dimension, or a gravitational scaling/running of some of the physical parameters associated with the solutions. A certain class of solutions is found to describe Schwarzschild black holes which 'solitonically' propagate in spacetime. The solitonic character of these black-hole solutions arises from the embedding of the sine-Gordon soliton configuration into certain ansatz functions of the 5D metric. These solitonic solutions may either violate or preserve local Lorentz invariance. In addition, there is a connection between these solutions and non-commutative field theory. In addition to the possible physical applications of the solutions presented here, this paper is meant to illustrate the strength of the anholonomic frames method in handling anisotropic solutions of the gravitational field equations

Two-body problem in general relativity: A heuristic guide for the Einstein-Rosen bridge and EPR paradox

OpenAIRE

Weinstein, Galina

2015-01-01

Between 1935 and 1936, Einstein was occupied with the Schwarzschild solution and the singularity within it while working in Princeton on the unified field theory and with his assistant Nathan Rosen, on the theory of the Einstein-Rosen bridges. He was also occupied with quantum theory. He believed that quantum theory was an incomplete representation of real things. Together with Rosen and Boris Podolsky he invented the EPR paradox. I demonstrate that the two-body problem in general relativity ...

Green's function for anti--de Sitter space gravity

International Nuclear Information System (INIS)

Kleppe, G.

1994-01-01

We solve for the retarded Green's function for linearized gravity in a background with a negative cosmological constant, anti--de Sitter space. In this background, it is possible for a signal to reach spatial infinity in a finite time. Therefore the form of the Green's function depends on a choice of boundary condition at spatial infinity. We take as our condition that a signal which reaches infinity should be lost, not reflected back. We calculate the Green's function associated with this condition, and show that it reproduces the correct classical solution for a point mass at the origin, the anti--de Sitter--Schwarzschild solution

ACADEMIC TRAINING LECTURE

CERN Multimedia

Academic Training; Tel. 73127

2001-01-01

26, 27, 28, 29 and 30 March REGULAR LECTURE PROGRAMME From 11:00 hrs - Main Auditorium bldg. 500 Introduction to General Relativity and Black Holes T. Damour / IHES, Bures-sur-Yvette, F. Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.

Self-organizing physical fields and gravity

International Nuclear Information System (INIS)

Pestov, I.B.

2009-01-01

It is shown that the Theory of Self-Organizing Physical Fields provides the adequate and consistent consideration of the gravitational phenomena. The general conclusion lies in the fact that the essence of gravidynamics is the new field concept of time and the general covariant law of energy conservation which in particular means that dark energy is simply the energy of the gravitational field. From the natural geometrical laws of gravidynamics the dynamical equations of the gravitational field are derived. Two exact solutions of these equations are obtained. One of them represents a shock gravitational wave and the other represents the Universe filled up with the gravitational energy only. These solutions are compared with the Schwarzschild and Friedmann solutions in the Einstein general theory of relativity

ADM pseudotensors, conserved quantities and covariant conservation laws in general relativity

International Nuclear Information System (INIS)

Fatibene, L.; Ferraris, M.; Francaviglia, M.; Lusanna, L.

2012-01-01

The ADM formalism is reviewed and techniques for decomposing generic components of metric, connection and curvature are obtained. These techniques will turn out to be enough to decompose not only Einstein equations but also covariant conservation laws. Then a number of independent sets of hypotheses that are sufficient (though not necessary) to obtain standard ADM quantities (and Hamiltonian) from covariant conservation laws are considered. This determines explicitly the range in which standard techniques are equivalent to covariant conserved quantities. The Schwarzschild metric in different coordinates is then considered, showing how the standard ADM quantities fail dramatically in non-Cartesian coordinates or even worse when asymptotically flatness is not manifest; while, in view of their covariance, covariant conservation laws give the correct result in all cases. - Highlights: ► In the paper ADM conserved quantities for GR are obtained from augmented conservation laws. ► Boundary conditions for this to be possible are considered and compared with the literature. ► Some different forms of Schwarzschild solutions are considered as simple examples of different boundary conditions.

Self-Gravitating Stellar Collapse: Explicit Geodesics and Path Integration

Energy Technology Data Exchange (ETDEWEB)

Balakrishna, Jayashree [Department of Mathematics and Natural Sciences, College of Arts and Sciences, Harris-Stowe State University, St. Louis, MO (United States); Bondarescu, Ruxandra [Department of Physics, University of Zurich, Zurich (Switzerland); Moran, Christine C., E-mail: corbett@tapir.caltech.edu [TAPIR, Department of Theoretical Astrophysics, California Institute of Technology, Pasadena, CA (United States)

2016-11-25

We extend the work of Oppenheimer and Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like, and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r = 2M.

Self-Gravitating Stellar Collapse: Explicit Geodesics and Path Integration

International Nuclear Information System (INIS)

Balakrishna, Jayashree; Bondarescu, Ruxandra; Moran, Christine C.

2016-01-01

We extend the work of Oppenheimer and Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like, and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r = 2M.

Gravitational wave emission from a bounded source: A treatment in the full nonlinear regime

International Nuclear Information System (INIS)

Oliveiral, H.P. de; Damiao Soares, I.

2004-03-01

The dynamics of a bounded gravitational collapsing configuration emitting gravitational waves is studied. The exterior spacetime is described by Robinson-Trautman geometries and have the Schwarzschild black hole as its final gravitational configuration, when the gravitational wave emission ceases. The full nonlinear regime is examined by using the Galerkin method that allows us to reduce the equations governing the dynamics to a finite-dimensional dynamical system, after a proper truncation procedure. Gravitational wave emission patterns from given initial configurations are exhibited for several phases of the collapse and the mass-loss ratio that characterizes the amount of mass extracted by the gravitational wave emission is evaluated. We obtain that the smaller initial mass M init of the configuration, the more rapidly the Schwarzschild solution is attained and a larger fraction of M init is lost in the process of gravitational wave emission. Within all our numerical experiments, the distribution of the mass fraction extracted by gravitational wave emission is shown to satisfy the distribution law of nonextensive statistics and this result is independent of the initial configurations considered. (author)

Fluid spheres and R- and T-regions in general relativity

Energy Technology Data Exchange (ETDEWEB)

McVittie, G C; Wiltshire, R J [Kent Univ., Canterbury (UK)

1975-10-01

R- and T-regions of spacetime are first defined in a particular coordinate system and then with the aid of the Schwarzschild vacuum solution are shown to represent the outside and inside of a black hole respectively. A certain class of interior solutions, relating to a perfect fluid, are also considered and it is found that these R- and T-solutions have distinct physical properties. The R-solutions are static, spherically symmetric, permanent, and have a classical analogue, while the corresponding T-solutions, which are wholly time dependent, are cylindrical, temporary, and do not have a classical analogue. It is shown that these T-solutions cannot be generated from their R-region counterparts. Particular T-solutions are also presented in which the corresponding fluid occupies the whole of a T-region. The fluid would under certain circumstances be black body radiation while for other cases the internal pressure is always greater than the density.

Spacetime completeness of non-singular black holes in conformal gravity

Energy Technology Data Exchange (ETDEWEB)

Bambi, Cosimo; Rachwał, Lesław [Center for Field Theory and Particle Physics and Department of Physics, Fudan University, 220 Handan Road, 200433 Shanghai (China); Modesto, Leonardo, E-mail: bambi@fudan.edu.cn, E-mail: lmodesto@sustc.edu.cn, E-mail: grzerach@gmail.com [Department of Physics, Southern University of Science and Technology, 1088 Xueyuan Road, Shenzhen 518055 (China)

2017-05-01

We explicitly prove that the Weyl conformal symmetry solves the black hole singularity problem, otherwise unavoidable in a generally covariant local or non-local gravitational theory. Moreover, we yield explicit examples of local and non-local theories enjoying Weyl and diffeomorphism symmetry (in short co-covariant theories). Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free spherically symmetric and axi-symmetric exact solutions for black hole spacetimes conformally equivalent to the Schwarzschild or the Kerr spacetime. We first check the absence of divergences in the Kretschmann invariant for the rescaled metrics. Afterwords, we show that the new types of black holes are geodesically complete and linked by a Newman-Janis transformation just as in standard general relativity (based on Einstein-Hilbert action). Furthermore, we argue that no massive or massless particles can reach the former Schwarzschild singularity or touch the former Kerr ring singularity in a finite amount of their proper time or of their affine parameter. Finally, we discuss the Raychaudhuri equation in a co-covariant theory and we show that the expansion parameter for congruences of both types of geodesics (for massless and massive particles) never reaches minus infinity. Actually, the null geodesics become parallel at the r =0 point in the Schwarzschild spacetime (the origin) and the focusing of geodesics is avoided. The arguments of regularity of curvature invariants, geodesic completeness, and finiteness of geodesics' expansion parameter ensure us that we are dealing with singularity-free and geodesically-complete black hole spacetimes.

Light deflection and Gauss-Bonnet theorem: definition of total deflection angle and its applications

Science.gov (United States)

Arakida, Hideyoshi

2018-05-01

In this paper, we re-examine the light deflection in the Schwarzschild and the Schwarzschild-de Sitter spacetime. First, supposing a static and spherically symmetric spacetime, we propose the definition of the total deflection angle α of the light ray by constructing a quadrilateral Σ^4 on the optical reference geometry M^opt determined by the optical metric \\bar{g}_{ij}. On the basis of the definition of the total deflection angle α and the Gauss-Bonnet theorem, we derive two formulas to calculate the total deflection angle α ; (1) the angular formula that uses four angles determined on the optical reference geometry M^opt or the curved (r, φ ) subspace M^sub being a slice of constant time t and (2) the integral formula on the optical reference geometry M^opt which is the areal integral of the Gaussian curvature K in the area of a quadrilateral Σ ^4 and the line integral of the geodesic curvature κ _g along the curve C_{Γ}. As the curve C_{Γ}, we introduce the unperturbed reference line that is the null geodesic Γ on the background spacetime such as the Minkowski or the de Sitter spacetime, and is obtained by projecting Γ vertically onto the curved (r, φ ) subspace M^sub. We demonstrate that the two formulas give the same total deflection angle α for the Schwarzschild and the Schwarzschild-de Sitter spacetime. In particular, in the Schwarzschild case, the result coincides with Epstein-Shapiro's formula when the source S and the receiver R of the light ray are located at infinity. In addition, in the Schwarzschild-de Sitter case, there appear order O(Lambda;m) terms in addition to the Schwarzschild-like part, while order O(Λ) terms disappear.

Doppler frequency in interplanetary radar and general relativity

Science.gov (United States)

Mcvittie, G. C.

1972-01-01

The change of frequency of an interplanetary radar signal sent from the earth to another planet or to a space probe is worked out according to general relativity. The Schwarzschild spacetime is employed and its null geodesics control the motion of the signals. Exact Doppler frequency formulas are derived for one-way and two-way radar in terms of an arbitrary Schwarzschild radial coordinate. A reduction to the special relativity case is used to interpret the formulas in terms of the relative radial velocity of emitter and target. The general relativity corrections are worked out approximately for each of three possible Schwarzschild radial coordinates, and a numerical example is given. The amount of the correction is different according as one or the other of the Schwarzschild coordinates is identified with the radius vector deduced from classical celestial mechanics. The identification problem is discussed.

Stellar configurations in f(R) theories of gravity

International Nuclear Information System (INIS)

Henttunen, K.; Multamaeki, T.; Vilja, I.

2008-01-01

We study stellar configurations and the space-time around them in metric f(R) theories of gravity. In particular, we focus on the polytropic model of the Sun in two specific cases: the f(R)=R-μ 4 /R model and a model with a stabilizing higher order term f(R)=R-μ 4 /R+βR 3 /(3μ 4 ). We show how the stellar configuration in the f(R) theory can, by appropriate initial conditions, be selected to be equal to that described by the Lane-Emden equation and how a simple scaling relation exists between the solutions. We also derive the correct solution analytically near the center of the star in f(R) theory. Previous analytical and numerical results are confirmed, indicating that the space-time around the Sun is incompatible with solar system constraints in the f(R)=R-μ 4 /R model. Numerical work shows that stellar configurations, with a regular metric at the center, lead to γ PPN ≅1/2 outside the star for both models, i.e., the Schwarzschild-de Sitter space-time is not the correct vacuum solution for such configurations. This shows that even when one fine-tunes the initial conditions inside a star such that the mass of the effective scalar in the equivalent scalar-tensor theory is large, γ PPN is still 1/2 outside the star. Conversely, by selecting the Schwarzschild-de Sitter metric as the outside solution, or equivalently setting the mass of the effective scalar to be large outside the star, we find that the stellar configuration is unchanged but the metric is irregular at the center. The possibility of constructing a f(R) theory compatible with the solar system experiments and possible new constraints arising from the radius-mass relation of stellar objects is discussed

Introduction to general relativity

CERN Document Server

Parthasarthy, R

2016-01-01

INTRODUCTION TO GENERAL RELATIVITY begins with a description of the geometry of curved space, explaining geodesics, parallel transport, covariant differentiation, geodesic deviation and spacetime symmetry by killing vectors. It then introduces Einstein's theory of gravitation followed by Schwarzschild solution with its relevance to Positive Mass theorem. The three tests for Einstein's gravity are explained. Other exact solutions such as Vaidya, Kerr and Reisner - Nordstrom metric are included. In the Chapter on cosmological solutions, a detailed description of Godel metric is provided. It then introduces five dimensional spacetime of Kaluza showing the unification of gravity with electromagnetism. This is extended to include non-Abelian gauge theory by invoking compact extra dimensions. Explicit expressions in this case for Christoffel connections and ricci tensor are derived and the higher dimensional gravity action is shown to compactification are given.

Complexity on dwarf galaxy scales : A bimodal distributionfFunction in sculptor

NARCIS (Netherlands)

Breddels, Maarten A.; Helmi, Amina

2014-01-01

In our previous work, we presented Schwarzschild models of the Sculptor dwarf spheroidal galaxy demonstrating that this system could be embedded in dark matter halos that are either cusped or cored. Here, we show that the non-parametric distribution function recovered through Schwarzschild's method

Self-gravitating black hole scalar wigs

Science.gov (United States)

Barranco, Juan; Bernal, Argelia; Degollado, Juan Carlos; Diez-Tejedor, Alberto; Megevand, Miguel; Núñez, Darío; Sarbach, Olivier

2017-07-01

It has long been known that no static, spherically symmetric, asymptotically flat Klein-Gordon scalar field configuration surrounding a nonrotating black hole can exist in general relativity. In a series of previous papers, we proved that, at the effective level, this no-hair theorem can be circumvented by relaxing the staticity assumption: for appropriate model parameters, there are quasibound scalar field configurations living on a fixed Schwarzschild background which, although not being strictly static, have a larger lifetime than the age of the universe. This situation arises when the mass of the scalar field distribution is much smaller than the black hole mass, and following the analogies with the hair in the literature we dubbed these long-lived field configurations wigs. Here we extend our previous work to include the gravitational backreaction produced by the scalar wigs. We derive new approximate solutions of the spherically symmetric Einstein-Klein-Gordon system which represent self-gravitating scalar wigs surrounding black holes. These configurations interpolate between boson star configurations and Schwarzschild black holes dressed with the long-lived scalar test field distributions discussed in previous papers. Nonlinear numerical evolutions of initial data sets extracted from our approximate solutions support the validity of our approach. Arbitrarily large lifetimes are still possible, although for the parameter space that we analyze in this paper they seem to decay faster than the quasibound states. Finally, we speculate about the possibility that these configurations could describe the innermost regions of dark matter halos.

MAGNETIC ENERGY BUILDUP FOR RELATIVISTIC MAGNETAR GIANT FLARES

International Nuclear Information System (INIS)

Yu Cong

2011-01-01

Motivated by coronal mass ejection studies, we construct general relativistic models of a magnetar magnetosphere endowed with strong magnetic fields. The equilibrium states of the stationary, axisymmetric magnetic fields in the magnetar magnetosphere are obtained as solutions of the Grad-Shafranov equation in a Schwarzschild spacetime. To understand the magnetic energy buildup in the magnetar magnetosphere, a generalized magnetic virial theorem in the Schwarzschild metric is newly derived. We carefully address the question whether the magnetar magnetospheric magnetic field can build up sufficient magnetic energy to account for the work required to open up the magnetic field during magnetar giant flares. We point out the importance of the Aly-Sturrock constraint, which has been widely studied in solar corona mass ejections, as a reference state in understanding magnetar energy storage processes. We examine how the magnetic field can possess enough energy to overcome the Aly-Sturrock energy constraint and open up. In particular, general relativistic (GR) effects on the Aly-Sturrock energy constraint in the Schwarzschild spacetime are carefully investigated. It is found that, for magnetar outbursts, the Aly-Sturrock constraint is more stringent, i.e., the Aly-Sturrock energy threshold is enhanced due to the GR effects. In addition, neutron stars with greater mass have a higher Aly-Sturrock energy threshold and are more difficult to erupt. This indicates that magnetars are probably not neutron stars with extreme mass. For a typical neutron star with mass of 1-2 M sun , we further explore the cross-field current effects, caused by the mass loading, on the possibility of stored magnetic field energy exceeding the Aly-Sturrock threshold.

Binary black hole initial data from matched asymptotic expansions

International Nuclear Information System (INIS)

Yunes, Nicolas; Owen, Benjamin J.; Tichy, Wolfgang; Bruegmann, Bernd

2006-01-01

We present an approximate metric for a binary black-hole spacetime to construct initial data for numerical relativity. This metric is obtained by asymptotically matching a post-Newtonian metric for a binary system to a perturbed Schwarzschild metric for each hole. In the inner zone near each hole, the metric is given by the Schwarzschild solution plus a quadrupolar perturbation corresponding to an external tidal gravitational field. In the near zone, well outside each black hole but less than a reduced wavelength from the center of mass of the binary, the metric is given by a post-Newtonian expansion including the lowest-order deviations from flat spacetime. When the near zone overlaps each inner zone in a buffer zone, the post-Newtonian and perturbed Schwarzschild metrics can be asymptotically matched to each other. By demanding matching (over a 4-volume in the buffer zone) rather than patching (choosing a particular 2-surface in the buffer zone), we guarantee that the errors are small in all zones. The resulting piecewise metric is made formally C ∞ with smooth transition functions so as to obtain the finite extrinsic curvature of a 3-slice. In addition to the metric and extrinsic curvature, we present explicit results for the lapse and the shift, which can be used as initial data for numerical simulations. This initial data is not accurate all the way to the asymptotically flat ends inside each hole, and therefore must be used with evolution codes which employ black hole excision rather than puncture methods. This paper lays the foundations of a method that can be straightforwardly iterated to obtain initial data to higher perturbative order

Siemens IT solutions for power sector. PROFIT solutions

International Nuclear Information System (INIS)

Lunter, P.

2004-01-01

The cost reduction, flexibility and revenue increase, potential exploitation, productivity increase, and business opportunities exploitation - that is all what can be required in the races for the promonent positioning on the electricity power market. These requirements can be realized by the sophisticated IT solutions hand-tailored to the special requirements of the electric power producers and tradesmen. This approach makes it possible to achieve greater profit. Our solutions 'PROFIT Solutions', that are symbiosis of the most progressive information technologies and the power plant techniques of the company Siemens, satisfy submitted specifications in substantial measure. The system solutions 'PROFIT Solutions' comprise three solution groups: process, operation a business. The solutions of the group 'IT Process Solutions' increase flexibility and manoeuvrability of equipment, improve the efficiency and contribute to more economical operation of the power generation. Solutions 'IT Process Solutions' simplify and shorten the period of power cycles and conduce to higher labour productivity. Solutions group 'IT Process Solutions' approaches equipment to the market - supports the profit strategies, helps quickly and expertly to determine and predict hazards. The extension PROFIT Cockpit means the nuance to the solutions world 'PROFIT Solutions'. The survey about the whole installation is within reach at the simple touch of a button. It is possible to compile the total system part by part from single solutions 'PROFIT Solutions'. As a matter of fact all single parts can be interconnected with already existing solutions. Routines 'PROFIT Solutions' cooperate with all modern control systems. (author)

Basic relativity

CERN Document Server

Mould, Richard A

1994-01-01

This comprehensive textbook develops in a logical and coherent way both the formalism and the physical ideas of special and general relativity. Part one focuses on the special theory and begins with the study of relativistic kinematics from three points of view. Part two begins with a chapter introducing differential geometry. Subsequent chapters cover: rotation, the electromagnetic field, and material media. A second chapter on differential geometry provides the background for Einstein's gravitational-field equation and Schwarzschild's solution. The book is aimed at advanced undergraduates and beginning graduate students in physics or astrophysics.

Kerr metric in the deSitter background

International Nuclear Information System (INIS)

Vaidya, P.C.

1984-01-01

In addition to the Kerr metric with cosmological constant Λ several other metrics are presented giving a Kerr-like solution of Einstein's equations in the background of deSitter universe. A new metric of what may be termed as rotating deSitter space-time devoid of matter but containing null fluid with twisting null rays, has been presented. This metric reduces to the standard deSitter metric when the twist in the rays vanishes. Kerr metric in this background is the immediate generalization of Schwarzschild's exterior metric with cosmological constant. (author)

Black holes in multi-fractional and Lorentz-violating models

Energy Technology Data Exchange (ETDEWEB)

Calcagni, Gianluca [CSIC, Instituto de Estructura de la Materia, Madrid (Spain); Rodriguez Fernandez, David [Universidad de Oviedo, Department of Physics, Oviedo (Spain); Ronco, Michele [Universita di Roma ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); INFN, Rome (Italy)

2017-05-15

We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length l{sub *}. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to l{sub *}. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models. (orig.)

Black holes in multi-fractional and Lorentz-violating models

International Nuclear Information System (INIS)

Calcagni, Gianluca; Rodriguez Fernandez, David; Ronco, Michele

2017-01-01

We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length l_*. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to l_*. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models. (orig.)

Black holes in multi-fractional and Lorentz-violating models.

Science.gov (United States)

Calcagni, Gianluca; Rodríguez Fernández, David; Ronco, Michele

2017-01-01

We study static and radially symmetric black holes in the multi-fractional theories of gravity with q -derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length [Formula: see text]. In the q -derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to [Formula: see text]. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q -derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models.

Nonlinear Thermal Instability in Compressible Viscous Flows Without Heat Conductivity

Science.gov (United States)

Jiang, Fei

2018-04-01

We investigate the thermal instability of a smooth equilibrium state, in which the density function satisfies Schwarzschild's (instability) condition, to a compressible heat-conducting viscous flow without heat conductivity in the presence of a uniform gravitational field in a three-dimensional bounded domain. We show that the equilibrium state is linearly unstable by a modified variational method. Then, based on the constructed linearly unstable solutions and a local well-posedness result of classical solutions to the original nonlinear problem, we further construct the initial data of linearly unstable solutions to be the one of the original nonlinear problem, and establish an appropriate energy estimate of Gronwall-type. With the help of the established energy estimate, we finally show that the equilibrium state is nonlinearly unstable in the sense of Hadamard by a careful bootstrap instability argument.

One-loop quantum gravity repulsion in the early Universe.

Science.gov (United States)

Broda, Bogusław

2011-03-11

Perturbative quantum gravity formalism is applied to compute the lowest order corrections to the classical spatially flat cosmological Friedmann-Lemaître-Robertson-Walker solution (for the radiation). The presented approach is analogous to the approach applied to compute quantum corrections to the Coulomb potential in electrodynamics, or rather to the approach applied to compute quantum corrections to the Schwarzschild solution in gravity. In the framework of the standard perturbative quantum gravity, it is shown that the corrections to the classical deceleration, coming from the one-loop graviton vacuum polarization (self-energy), have (UV cutoff free) opposite to the classical repulsive properties which are not negligible in the very early Universe. The repulsive "quantum forces" resemble those known from loop quantum cosmology.

Relativistic gravitation from massless systems of scalar and vector fields

International Nuclear Information System (INIS)

Fonseca Teixeira, A.F. da.

1979-01-01

Under the laws of Einstein's gravitational theory, a massless system consisting of the diffuse sources of two fields is discussed. One fields is scalar, of long range, the other is a vector field of short range. A proportionality between the sources is assumed. Both fields are minimally coupled to gravitation, and contribute positive definitely to the time component of the energy momentum tensor. A class of static, spherically symmetric solutions of the equations is obtained, in the weak field limit. The solutions are regular everywhere, stable, and can represent large or small physical systems. The gravitational field presents a Schwarzschild-type asymptotic behavior. The dependence of the energy on the various parameters characterizing the system is discussed in some detail. (Author) [pt

Astronomical Observations by Speckle Interferometry.

Science.gov (United States)

1986-06-12

commonly -been noted [Heintz (101)] that it was Karl *, Schwarzchild who iui 1895 [ Schwarzschild (190)] made the first measure- ments of binary stars...J. Lett 163. Michelson, A A, Pease. F. G. 1921. Ap. 280: L23 J. 53: 249 190. Schwarzschild . K. 1896. Astron. Nadir. 164. Morgan. B. L., lieddoes. 1

Scalar geons in Born-Infeld gravity

Energy Technology Data Exchange (ETDEWEB)

Afonso, V.I. [Unidade Acadêmica de Física, Universidade Federal de Campina Grande, 58109-970 Campina Grande, PB (Brazil); Olmo, Gonzalo J. [Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia—CSIC, Universidad de Valencia, Burjassot-46100, Valencia (Spain); Rubiera-Garcia, D., E-mail: viafonso@df.ufcg.edu.br, E-mail: gonzalo.olmo@uv.es, E-mail: drgarcia@fc.ul.pt [Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa, Edifício C8, Campo Grande, P-1749-016 Lisbon (Portugal)

2017-08-01

The existence of static, spherically symmetric, self-gravitating scalar field solutions in the context of Born-Infeld gravity is explored. Upon a combination of analytical approximations and numerical methods, the equations for a free scalar field (without a potential term) are solved, verifying that the solutions recover the predictions of General Relativity far from the center but finding important new effects in the central regions. We find two classes of objects depending on the ratio between the Schwarzschild radius and a length scale associated to the Born-Infeld theory: massive solutions have a wormhole structure, with their throat at r ≈ 2 M , while for the lighter configurations the topology is Euclidean. The total energy density of these solutions exhibits a solitonic profile with a maximum peaked away from the center, and located at the throat whenever a wormhole exists. The geodesic structure and curvature invariants are analyzed for the various configurations considered.

Schwarzschild, Karl (1873-1916)

Science.gov (United States)

Murdin, P.

2000-11-01

Mathematical physicist, born in Frankfurt am Main, Germany, at first worked on celestial mechanics, including POINCARÉ's theory of rotating bodies, the tidal deformation of moons and LAPLACE's origin of the solar system. He became professor at Göttingen and Potsdam. He wrote on relativity and quantum theory. He early on proposed that space was non-Euclidean, giving a lower limit for the radius of...

Null geodesics and shadow of a rotating black hole in extended Chern-Simons modified gravity

International Nuclear Information System (INIS)

Amarilla, Leonardo; Eiroa, Ernesto F.; Giribet, Gaston

2010-01-01

The Chern-Simons modification to general relativity in four dimensions consists of adding to the Einstein-Hilbert term a scalar field that couples to the first-class Pontryagin density. In this theory, which has attracted considerable attention recently, the Schwarzschild metric persists as an exact solution, and this is why this model resists several observational constraints. In contrast, the spinning black hole solution of the theory is not given by the Kerr metric but by a modification of it, so far only known for slow rotation and small coupling constant. In the present paper, we show that, in this approximation, the null geodesic equation can be integrated, and this allows us to investigate the shadow cast by a black hole. We discuss how, in addition to the angular momentum of the solution, the coupling to the Chern-Simons term deforms the shape of the shadow.

INFLUENCE OF THE HIGHER ORDER DERIVATIVES ON THE PLANET PERIHELION PRECESSION IN THE EINSTEIN FIELD EQUATIONS FOR VACUUM CONDITION

Directory of Open Access Journals (Sweden)

Teguh Budi Prayitno

2011-04-01

Full Text Available This paper studies the effect of higher order derivative tensor in the Einstein field equations for vacuum condition on the planet perihelion precession. This tensor was initially proposed as the space-time curvature tensor by Deser and Tekin on discussions about the energy effects caused by this tensor. However, they include this tensor to Einstein field equations as a new model in general relativity theory. This is very interesting since there are some questions in cosmology and astrophysics that have no answers. Thus, they hoped this model could solve those problems by finding analytical or perturbative solution and interpreting it. In this case, the perturbative solution was used to find the Schwarzschild solution and it was also applied to consider the planetary motion in the solar gravitational field. Furthermore, it was proven that the tensor is divergence-free in order to keep the Einstein field equations remain valid.

On the localisation of four-dimensional brane-world black holes: II. The general case

International Nuclear Information System (INIS)

Kanti, P; Pappas, T; Pappas, N

2016-01-01

We perform a comprehensive analysis of a number of scalar field theories in an attempt to find analytically five-dimensional, localised-on-the-brane, black-hole solutions. Extending a previous analysis, we assume a generalised Vaidya ansatz for the five-dimensional metric tensor that allows for a time-dependent, non-trivial profile of the mass function in terms of the bulk coordinate and a deviation from the over-restricting Schwarzschild-type solution on the brane. In order to support such a solution, we study a variety of theories including single or multiple scalar fields, with canonical or non-canonical kinetic terms, minimally or non-minimally coupled to gravity. We demonstrate that for such a metric ansatz and for a carefully chosen energy-momentum tensor which is non-isotropic in five dimensions, solutions that have the form of a Schwarzschild–(anti)de Sitter or Reissner–Nordstrom type of solution do emerge. However, the resulting profile of the mass function along the bulk coordinate, when allowed, is not the correct one for eliminating bulk singularities. (paper)

Holographic dark energy from fluid/gravity duality constraint by cosmological observations

Science.gov (United States)

Pourhassan, Behnam; Bonilla, Alexander; Faizal, Mir; Abreu, Everton M. C.

2018-06-01

In this paper, we obtain a holographic model of dark energy using the fluid/gravity duality. This model will be dual to a higher dimensional Schwarzschild black hole, and we would use fluid/gravity duality to relate to the parameters of this black hole to such a cosmological model. We will also analyze the thermodynamics of such a solution, and discuss the stability model. Finally, we use cosmological data to constraint the parametric space of this dark energy model. Thus, we will use observational data to perform cosmography for this holographic model based on fluid/gravity duality.

Stability of the graviton Bose–Einstein condensate in the brane-world

Energy Technology Data Exchange (ETDEWEB)

Casadio, Roberto, E-mail: casadio@bo.infn.it [Dipartimento di Fisica e Astronomia, Università di Bologna, via Irnerio 46, 40126 Bologna (Italy); INFN, Sezione di Bologna, viale B. Pichat 6, 40127 Bologna (Italy); Rocha, Roldão da, E-mail: roldao.rocha@ufabc.edu.br [CMCC, Universidade Federal do ABC, 09210-580, Santo André, SP (Brazil)

2016-12-10

We consider a solution of the effective four-dimensional Einstein equations, obtained from the general relativistic Schwarzschild metric through the principle of Minimal Geometric Deformation (MGD). Since the brane tension can, in general, introduce new singularities on a relativistic Eötvös brane model in the MGD framework, we require the absence of observed singularities, in order to constrain the brane tension. We then study the corresponding Bose–Einstein condensate (BEC) gravitational system and determine the critical stability region of BEC MGD stellar configurations. Finally, the critical stellar densities are shown to be related with critical points of the information entropy.

A quantum analogy to the classical gravitomagnetic clock effect

Science.gov (United States)

Faruque, S. B.

2018-06-01

We present an approximation to the solution of Dirac equation in Schwarzschild field found through the use of Foldy-Wouthuysen Hamiltonian. We solve the equation for the positive energy states and found the frequencies by which the states oscillate. Difference of the periods of oscillation of the two states with two different total angular momentum quantum number j has an analogical form of the classical clock effect found in general relativity. But unlike the term that appears as clock effect in classical physics, here the term is quantized. Thus, we find a quantum analogue of the classical gravitomagnetic clock effect.

Holographic Aspects of a Relativistic Nonconformal Theory

Directory of Open Access Journals (Sweden)

Chanyong Park

2013-01-01

Full Text Available We study a general D-dimensional Schwarzschild-type black brane solution of the Einstein-dilaton theory and derive, by using the holographic renormalization, its thermodynamics consistent with the geometric results. Using the membrane paradigm, we calculate the several hydrodynamic transport coefficients and compare them with the results obtained by the Kubo formula, which shows the self-consistency of the gauge/gravity duality in the relativistic nonconformal theory. In order to understand more about the relativistic non-conformal theory, we further investigate the binding energy, drag force, and holographic entanglement entropy of the relativistic non-conformal theory.

Regge calculus and observations. II. Further applications.

Science.gov (United States)

Williams, Ruth M.; Ellis, G. F. R.

1984-11-01

The method, developed in an earlier paper, for tracing geodesies of particles and light rays through Regge calculus space-times, is applied to a number of problems in the Schwarzschild geometry. It is possible to obtain accurate predictions of light bending by taking sufficiently small Regge blocks. Calculations of perihelion precession, Thomas precession, and the distortion of a ball of fluid moving on a geodesic can also show good agreement with the analytic solution. However difficulties arise in obtaining accurate predictions for general orbits in these space-times. Applications to other problems in general relativity are discussed briefly.

Noncommutative black holes

Energy Technology Data Exchange (ETDEWEB)

Lopez-DomInguez, J C [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico); Obregon, O [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico); RamIrez, C [Facultad de Ciencias FIsico Matematicas, Universidad Autonoma de Puebla, PO Box 1364, 72000 Puebla (Mexico); Sabido, M [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico)

2007-11-15

We study noncommutative black holes, by using a diffeomorphism between the Schwarzschild black hole and the Kantowski-Sachs cosmological model, which is generalized to noncommutative minisuperspace. Through the use of the Feynman-Hibbs procedure we are able to study the thermodynamics of the black hole, in particular, we calculate Hawking's temperature and entropy for the 'noncommutative' Schwarzschild black hole.

Rational Solutions and Lump Solutions of the Potential YTSF Equation

Science.gov (United States)

Sun, Hong-Qian; Chen, Ai-Hua

2017-07-01

By using of the bilinear form, rational solutions and lump solutions of the potential Yu-Toda-Sasa-Fukuyama (YTSF) equation are derived. Dynamics of the fundamental lump solution, n1-order lump solutions, and N-lump solutions are studied for some special cases. We also find some interaction behaviours of solitary waves and one lump of rational solutions.

Image formation in weak gravitational lensing by tidal charged black holes

International Nuclear Information System (INIS)

Horvath, Zsolt; Gergely, Laszlo Arpad; Hobill, David

2010-01-01

We derive a generic weak lensing equation and apply it for the study of images produced by tidal charged brane black holes. We discuss the similarities and point out the differences with respect to the Schwarzschild black hole weak lensing, to both first- and second-order accuracy, when either the mass or the tidal charge dominates. In the case of mass-dominated weak lensing, we analyze the position of the images, the magnification factors and the flux ratio, as compared to the Schwarzschild lensing. The most striking modification appears in the flux ratio. When the tidal charge represents the dominating lensing effect, the number and orientation of the images with respect to the optical axis resembles the lensing properties of a Schwarzschild geometry, where the sign associated with the mass is opposite to that for the tidal charge. Finally it is found that the ratio of the brightness of the images as a function of image separation in the case of tidal charged black holes obeys a power-law relation significantly different from that of Schwarzschild black holes. This might provide a means for determining the underlying spacetime structure.

25 Jahre - Institut fuer Geodaesie, Teil 1: Wissenschaftliche Beitraege und Berichte (25 Years - Institute of Geodesy, Part 1: Scientific Contributions and Reports)

Science.gov (United States)

2000-01-01

Analyse der Bahnbewegung des Mondes (E. W. BROWN, 1896) Polschwankung (SETH CARLO CHANDLER, 1885; KARL FRIEDRICH KOJSTNER, 1890; SIMON NEWCOMB, 1891, 1892...Photographic Zenith Tubes) wurden erstmals urn die Jahr- hundertwende von STOLZE (1893), RuNGE (1893), SCHNAUDER (1900) und SCHWARZSCHILD (1903) vor...Geburtstag, Eugen Kuntz zurn 70. Geburtstag, Herman MAilzer zumn 70. Geburtstag, Verbff Geod Inst U Karlsruhe, 23 5-241 SCHWARZSCHILD , K., 1903

Solution preparation

International Nuclear Information System (INIS)

Seitz, M.G.

1982-01-01

Reviewed in this statement are methods of preparing solutions to be used in laboratory experiments to examine technical issues related to the safe disposal of nuclear waste from power generation. Each approach currently used to prepare solutions has advantages and any one approach may be preferred over the others in particular situations, depending upon the goals of the experimental program. These advantages are highlighted herein for three approaches to solution preparation that are currently used most in studies of nuclear waste disposal. Discussion of the disadvantages of each approach is presented to help a user select a preparation method for his particular studies. Also presented in this statement are general observations regarding solution preparation. These observations are used as examples of the types of concerns that need to be addressed regarding solution preparation. As shown by these examples, prior to experimentation or chemical analyses, laboratory techniques based on scientific knowledge of solutions can be applied to solutions, often resulting in great improvement in the usefulness of results

Black holes in vector-tensor theories

Energy Technology Data Exchange (ETDEWEB)

Heisenberg, Lavinia [Institute for Theoretical Studies, ETH Zurich, Clausiusstrasse 47, 8092 Zurich (Switzerland); Kase, Ryotaro; Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Minamitsuji, Masato, E-mail: lavinia.heisenberg@eth-its.ethz.ch, E-mail: r.kase@rs.tus.ac.jp, E-mail: masato.minamitsuji@tecnico.ulisboa.pt, E-mail: shinji@rs.kagu.tus.ac.jp [Centro Multidisciplinar de Astrofisica—CENTRA, Departamento de Fisica, Instituto Superior Tecnico—IST, Universidade de Lisboa—UL, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)

2017-08-01

We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic and quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.

Equation of Motion of a Mass Point in Gravitational Field and Classical Tests of Gauge Theory of Gravity

International Nuclear Information System (INIS)

Wu Ning; Zhang Dahua

2007-01-01

A systematic method is developed to study the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton's second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.

Gravitational field of massive point particle in general relativity

International Nuclear Information System (INIS)

Fiziev, P.P.

2003-10-01

Using various gauges of the radial coordinate we give a description of the static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist infinitely many such solutions to the Einstein equations which are physically different and only some of them describe the gravitational field of a single massive point particle. In particular, we show that the widespread Hilbert's form of Schwarzschild solution does not solve the Einstein equations with a massive point particle's stress-energy tensor. Novel normal coordinates for the field and a new physical class of gauges are proposed, in this way achieving a correct description of a point mass source in GR. We also introduce a gravitational mass defect of a point particle and determine the dependence of the solutions on this mass defect. In addition we give invariant characteristics of the physically and geometrically different classes of spherically symmetric static space-times created by one point mass. (author)

Insight solutions are correct more often than analytic solutions

Science.gov (United States)

Salvi, Carola; Bricolo, Emanuela; Kounios, John; Bowden, Edward; Beeman, Mark

2016-01-01

How accurate are insights compared to analytical solutions? In four experiments, we investigated how participants’ solving strategies influenced their solution accuracies across different types of problems, including one that was linguistic, one that was visual and two that were mixed visual-linguistic. In each experiment, participants’ self-judged insight solutions were, on average, more accurate than their analytic ones. We hypothesised that insight solutions have superior accuracy because they emerge into consciousness in an all-or-nothing fashion when the unconscious solving process is complete, whereas analytic solutions can be guesses based on conscious, prematurely terminated, processing. This hypothesis is supported by the finding that participants’ analytic solutions included relatively more incorrect responses (i.e., errors of commission) than timeouts (i.e., errors of omission) compared to their insight responses. PMID:27667960

Solar Observations on Magneto-Convection

Science.gov (United States)

1989-05-31

Technical Library National Solar Observatory Sunspot, NM 88349 Karl - Schwarzschild -Strasse 1 8046 Garching bei Mundhen Solar Observations On Magneto...Schmidt, Hermann-Ulrich Schmidt, Hans-Christoph Thomas (eds.) Max-Planck-Institut fir Physik und Astrophysik Institut fiur Astrophysik Karl ... Schwarzschild -St-. 1 D-8046 Garching, FklG 14TIS CRiA.&l DTIC TA. U~Jar,iou8:ed B ......... ... Distribution I -- Availability COcý----- Avail and or Dist special

How far away is far enough for extracting numerical waveforms, and how much do they depend on the extraction method?

International Nuclear Information System (INIS)

Pazos, Enrique; Dorband, Ernst Nils; Nagar, Alessandro; Palenzuela, Carlos; Schnetter, Erik; Tiglio, Manuel

2007-01-01

We present a method for extracting gravitational waves from numerical spacetimes which generalizes and refines one of the standard methods based on the Regge-Wheeler-Zerilli perturbation formalism. At the analytical level, this generalization allows a much more general class of slicing conditions for the background geometry, and is thus not restricted to Schwarzschild-like coordinates. At the numerical level, our approach uses high-order multi-block methods, which improve both the accuracy of our simulations and of our extraction procedure. In particular, the latter is simplified since there is no need for interpolation, and we can afford to extract accurate waves at large radii with only little additional computational effort. We then present fully nonlinear three-dimensional numerical evolutions of a distorted Schwarzschild black hole in Kerr-Schild coordinates with an odd parity perturbation and analyse the improvement that we gain from our generalized wave extraction, comparing our new method to the standard one. In particular, we analyse in detail the quasinormal frequencies of the extracted waves, using both methods. We do so by comparing the extracted waves with one-dimensional high resolution solutions of the corresponding generalized Regge-Wheeler equation. We explicitly see that the errors in the waveforms extracted with the standard method at fixed, finite extraction radii do not converge to zero with increasing resolution. We find that even with observers as far out as R = 80M-which is larger than what is commonly used in state-of-the-art simulations-the assumption in the standard method that the background is close to having Schwarzschild-like coordinates increases the error in the extracted waves considerably. Furthermore, those errors are dominated by the extraction method itself and not by the accuracy of our simulations. For extraction radii between 20M and 80M and for the resolutions that we use in this paper, our new method decreases the errors

How far away is far enough for extracting numerical waveforms, and how much do they depend on the extraction method?

Energy Technology Data Exchange (ETDEWEB)

Pazos, Enrique [Department of Physics and Astronomy, 202 Nicholson Hall, Louisiana State University, Baton Rouge, LA 70803 (United States); Dorband, Ernst Nils [Department of Physics and Astronomy, 202 Nicholson Hall, Louisiana State University, Baton Rouge, LA 70803 (United States); Nagar, Alessandro [Dipartimento di Fisica, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129 Torino (Italy); Palenzuela, Carlos [Department of Physics and Astronomy, 202 Nicholson Hall, Louisiana State University, Baton Rouge, LA 70803 (United States); Schnetter, Erik [Center for Computation and Technology, 216 Johnston Hall, Louisiana State University, Baton Rouge, LA 70803 (United States); Tiglio, Manuel [Department of Physics and Astronomy, 202 Nicholson Hall, Louisiana State University, Baton Rouge, LA 70803 (United States)

2007-06-21

We present a method for extracting gravitational waves from numerical spacetimes which generalizes and refines one of the standard methods based on the Regge-Wheeler-Zerilli perturbation formalism. At the analytical level, this generalization allows a much more general class of slicing conditions for the background geometry, and is thus not restricted to Schwarzschild-like coordinates. At the numerical level, our approach uses high-order multi-block methods, which improve both the accuracy of our simulations and of our extraction procedure. In particular, the latter is simplified since there is no need for interpolation, and we can afford to extract accurate waves at large radii with only little additional computational effort. We then present fully nonlinear three-dimensional numerical evolutions of a distorted Schwarzschild black hole in Kerr-Schild coordinates with an odd parity perturbation and analyse the improvement that we gain from our generalized wave extraction, comparing our new method to the standard one. In particular, we analyse in detail the quasinormal frequencies of the extracted waves, using both methods. We do so by comparing the extracted waves with one-dimensional high resolution solutions of the corresponding generalized Regge-Wheeler equation. We explicitly see that the errors in the waveforms extracted with the standard method at fixed, finite extraction radii do not converge to zero with increasing resolution. We find that even with observers as far out as R = 80M-which is larger than what is commonly used in state-of-the-art simulations-the assumption in the standard method that the background is close to having Schwarzschild-like coordinates increases the error in the extracted waves considerably. Furthermore, those errors are dominated by the extraction method itself and not by the accuracy of our simulations. For extraction radii between 20M and 80M and for the resolutions that we use in this paper, our new method decreases the errors

Relativistic stars in degenerate higher-order scalar-tensor theories after GW170817

Science.gov (United States)

Kobayashi, Tsutomu; Hiramatsu, Takashi

2018-05-01

We study relativistic stars in degenerate higher-order scalar-tensor theories that evade the constraint on the speed of gravitational waves imposed by GW170817. It is shown that the exterior metric is given by the usual Schwarzschild solution if the lower order Horndeski terms are ignored in the Lagrangian and a shift symmetry is assumed. However, this class of theories exhibits partial breaking of Vainshtein screening in the stellar interior and thus modifies the structure of a star. Employing a simple concrete model, we show that for high-density stars the mass-radius relation is altered significantly even if the parameters are chosen so that only a tiny correction is expected in the Newtonian regime. We also find that, depending on the parameters, there is a maximum central density above which solutions cease to exist.

Diffusion of aqueous solutions of ionic, zwitterionic, and polar solutes

Science.gov (United States)

Teng, Xiaojing; Huang, Qi; Dharmawardhana, Chamila Chathuranga; Ichiye, Toshiko

2018-06-01

The properties of aqueous solutions of ionic, zwitterionic, and polar solutes are of interest to many fields. For instance, one of the many anomalous properties of aqueous solutions is the behavior of water diffusion in different monovalent salt solutions. In addition, solutes can affect the stabilities of macromolecules such as proteins in aqueous solution. Here, the diffusivities of aqueous solutions of sodium chloride, potassium chloride, tri-methylamine oxide (TMAO), urea, and TMAO-urea are examined in molecular dynamics simulations. The decrease in the diffusivity of water with the concentration of simple ions and urea can be described by a simple model in which the water molecules hydrogen bonded to the solutes are considered to diffuse at the same rate as the solutes, while the remainder of the water molecules are considered to be bulk and diffuse at almost the same rate as pure water. On the other hand, the decrease in the diffusivity of water with the concentration of TMAO is apparently affected by a decrease in the diffusion rate of the bulk water molecules in addition to the decrease due to the water molecules hydrogen bonded to TMAO. In other words, TMAO enhances the viscosity of water, while urea barely affects it. Overall, this separation of water molecules into those that are hydrogen bonded to solute and those that are bulk can provide a useful means of understanding the short- and long-range effects of solutes on water.

Noether's stars in f (R) gravity

Science.gov (United States)

De Laurentis, Mariafelicia

2018-05-01

The Noether Symmetry Approach can be used to construct spherically symmetric solutions in f (R) gravity. Specifically, the Noether conserved quantity is related to the gravitational mass and a gravitational radius that reduces to the Schwarzschild radius in the limit f (R) → R. We show that it is possible to construct the M- R relation for neutron stars depending on the Noether conserved quantity and the associated gravitational radius. This approach enables the recovery of extreme massive stars that could not be stable in the standard Tolman-Oppenheimer-Volkoff based on General Relativity. Examples are given for some power law f (R) gravity models.

Entropy Spectrum of Black Holes of Heterotic String Theory via Adiabatic Invariance

Institute of Scientific and Technical Information of China (English)

Alexis Larra？ aga; Luis Cabarique; Manuel Londo？ o

2012-01-01

Using adiabatic invariance and the Bohr-Sommerfeld quantization rule we investigate the entropy spectroscopy of two black holes of heterotic string theory,the charged GMGHS and the rotating Sen solutions.It is shown that the entropy spectrum is equally spaced in both cases,identically to the spectrum obtained before for Schwarzschild,Reissner-Nordstr?m and Kerr black holes.Since the adiabatic invariance method does not use quasinormal mode analysis,there is no need to impose the small charge or small angular momentum limits and there is no confusion on whether the real part or the imaginary part of the modes is responsible for the entropy spectrum.

Thermodynamic phase transition of a black hole in rainbow gravity

Directory of Open Access Journals (Sweden)

Zhong-Wen Feng

2017-09-01

Full Text Available In this letter, using the rainbow functions that were proposed by Magueijo and Smolin, we investigate the thermodynamics and the phase transition of rainbow Schwarzschild black hole. First, we calculate the rainbow gravity corrected Hawking temperature. From this modification, we then derive the local temperature, free energy, and other thermodynamic quantities in an isothermal cavity. Finally, we analyze the critical behavior, thermodynamic stability, and phase transition of the rainbow Schwarzschild black hole. The results show that the rainbow gravity can stop the Hawking radiation in the final stages of black holes' evolution and lead to the remnants of black holes. Furthermore, one can observe that the rainbow Schwarzschild black hole has one first-order phase transition, two second-order phase transitions, and three Hawking–Page-type phase transitions in the framework of rainbow gravity theory.

International Conference on Hyperbolic Problems Theory, Numerics, Applications Held in Stony Brook, New York on 13-17 June 1994

Science.gov (United States)

1994-07-25

Astrophysik are investigated numerically. These collisions do not seem to Karl - Schwarzschild -str., 1, D-85470 Garching, Germany be elastic. On the other hand...Astrophysak, Departamento de Matemdtsca Aplscada y Astronomia Karl -Schwaarzschild-Str. i Universadad de Valencia 85740 Garching bes Munchen. Germany "E...the R-W metric to the empty space Schwarzschild metric, and since in this cae mass and momentum cannot cross the interface, (which in this case models

Radiochromic liquid solution

International Nuclear Information System (INIS)

Noakes, J.E.; Culp, R.A.

1983-01-01

A radiochromic solution which is sensitive to small dosages of ionizing and ultraviolet radiation is described. It consists of a solution of a leucocyanide dye in a clear polar solvent with enough organic acid added to make the solution at least slightly acidic and responds to radiation by permanently changing color. Up to one half of the solution by weight can be replaced by a second solution of an aromatic solvent and an organic fluor. Another modification of the invention is a solution of a leucocyanide dye in a clear polar solvent having an aromatic group, an organic fluor, and enough organic acid to make the solution at least slightly acidic. (author)

Compacton solutions and multiple compacton solutions for a continuum Toda lattice model

International Nuclear Information System (INIS)

Fan Xinghua; Tian Lixin

2006-01-01

Some special solutions of the Toda lattice model with a transversal degree of freedom are obtained. With the aid of Mathematica and Wu elimination method, more explicit solitary wave solutions, including compacton solutions, multiple compacton solutions, peakon solutions, as well as periodic solutions are found in this paper

Plugging solution

Energy Technology Data Exchange (ETDEWEB)

Sharipov, A U; Yangirov, I Z

1982-01-01

A clay-powder, cement, and water-base plugging solution is proposed having reduced solution viscosity characteristics while maintaining tensile strength in cement stone. This solution utilizes silver graphite and its ingredients, by mass weight, are as follows: cement 51.2-54.3%; claypowder 6.06-9.1%; silver graphite 0.24-0.33%; with water making up the remainder.

Solid-soluted content of cerium in solid solution of sphene

International Nuclear Information System (INIS)

Zhao Wei; Teng Yuancheng; Li Yuxiang; Ren Xuetan; Huang Junjun

2010-01-01

The sphene solid solution was synthesized by solid-state method,with calcium carbonate, silica, titanium dioxide, cerium oxalate and alumina as raw materials. The solid-soluted content of cerium in sphene was researched by means of X-ray diffraction (XRD), backscattering scanning electron microscopy (BSE), energy dispersive spectroscopy (EDS) and so on. The influence of A l3+ ion introduction to sphene on the solid-soluted content of cerium in sphene solid solution was studied. The results indicate that when introducing Al 3+ to sphene as electrovalence compensation, Ce 4+ could be well solidified to Ca 1-x Ce x Ti 1-2x A l2x SiO 5 , and the solid-soluted content is approximately 12.61%. With no electrovalence compensation, Ce 4+ could be solidified to Ca 1-2x Ce x TiSiO 5 , and the solid-soluted content is approximately 10.98%. The appropriate synthesis temperature of sphene solid solution is 1 260 degree C.(authors)

Solute-solute interactions in intermetallic compounds

Energy Technology Data Exchange (ETDEWEB)

Banerjee, Debashis; Murray, Ryan; Collins, Gary S., E-mail: collins@wsu.edu [Washington State University, Department of Physics and Astronomy (United States); Zacate, Matthew O. [Northern Kentucky University, Department of Physics and Geology (United States)

2017-11-15

Experiments were carried out on highly ordered GdAl{sub 2} samples containing extremely dilute mole fractions of{sup 111}In/Cd probe-atom solutes (about 10{sup −11}), intrinsic antisite atoms Al{sub Gd} having mole fractions of order 0-10{sup −2}, and doped with Ag solutes at mole fractions of order 10{sup −2}. Three types of defect interactions were investigated. (1) Quadrupole interactions caused by Ag-solute atoms neighboring{sup 111}In/Cd solute probe atoms were detected using the method of perturbed angular correlation of gamma rays (PAC). Three complexes of pairs of In-probes and Ag-solutes occupying neighboring positions on Gd- and Al-sublattices were identified by comparing site fractions in Gd-poor and Gd-rich GdAl{sub 2}(Ag) samples and from the symmetry of the quadrupole interactions. Interaction enthalpies between solute-atom pairs were determined from temperature dependences of observed site fractions. Repulsive interactions were observed for close-neighbor complexes In{sub Gd}+Ag{sub Gd} and In{sub Gd}+Ag{sub Al} pairs, whereas a slightly attractive interaction was observed for In{sub Al}+Ag{sub Al}. Interaction enthalpies were all small, in the range ±0.15 eV. (2) Quadrupole interactions caused by intrinsic antisite atoms Al{sub Gd} neighboring In{sub Gd} probes were also detected and site fractions measured as a function of temperature, as in previous work on samples not doped with Ag-solutes [Temperature- and composition-driven changes in site occupation of solutes in Gd{sub 1+3x}Al{sub 2−3x}, Zacate and Collins (Phys. Rev. B69, 174202 (1))]. However, the effective binding enthalpy between In{sub Gd} probe and Al{sub Gd} antisite was found to change sign from -0.12 eV (attractive interaction) in undoped samples to + 0.24 eV (repulsive) in Ag-doped samples. This may be attributed to an attractive interaction between Al{sub Gd} antisite atoms and Ag-dopants that competes with the attractive interaction between In{sub Gd} and Al{sub Gd

Liquid scintillation solutions

International Nuclear Information System (INIS)

Long, E.C.

1976-01-01

The liquid scintillation solution described includes a mixture of: a liquid scintillation solvent, a primary scintillation solute, a secondary scintillation solute, a variety of appreciably different surfactants, and a dissolving and transparency agent. The dissolving and transparency agent is tetrahydrofuran, a cyclic ether. The scintillation solvent is toluene. The primary scintillation solute is PPO, and the secondary scintillation solute is dimethyl POPOP. The variety of appreciably different surfactants is composed of isooctylphenol-polyethoxyethanol and sodium dihexyl sulphosuccinate [fr

Hairy black holes in N=2 gauged supergravity

Energy Technology Data Exchange (ETDEWEB)

Faedo, Federico [Dipartimento di Fisica, Università di Milano, Via Celoria 16, 20133 Milano (Italy); Klemm, Dietmar; Nozawa, Masato [Dipartimento di Fisica, Università di Milano, Via Celoria 16, 20133 Milano (Italy); INFN, Sezione di Milano, Via Celoria 16, 20133 Milano (Italy)

2015-11-06

We construct black holes with scalar hair in a wide class of four-dimensional N=2 Fayet-Iliopoulos gauged supergravity theories that are characterized by a prepotential containing one free parameter. Considering the truncated model in which only a single real scalar survives, the theory is reduced to an Einstein-scalar system with a potential, which admits at most two AdS critical points and is expressed in terms of a real superpotential. Our solution is static, admits maximally symmetric horizons, asymptotically tends to AdS space corresponding to an extremum of the superpotential, but is disconnected from the Schwarzschild-AdS family. The condition under which the spacetime admits an event horizon is addressed for each horizon topology. It turns out that for hyperbolic horizons the black holes can be extremal. In this case, the near-horizon geometry is AdS{sub 2}×H{sup 2}, where the scalar goes to the other, non-supersymmetric, critical point of the potential. Our solution displays fall-off behaviours different from the standard one, due to the fact that the mass parameter m{sup 2}=−2ℓ{sup −2} at the supersymmetric vacuum lies in a characteristic range m{sub BF}{sup 2}≤m{sup 2}solution shows qualitatively the same thermodynamic behaviour as the Schwarzschild-AdS black hole, but the entropy is always smaller for a given mass and AdS curvature radius. We also find that our spherical black holes are unstable against radial perturbations.

Accelerating particles in general relativity (stationary C-metric)

International Nuclear Information System (INIS)

Farhoosh, H.

1979-01-01

The purpose of this thesis is to study the physical and geometrical properties of uniformly accelerating particles in the general theory of relativity and it consists of four main parts. In the first part the structure of the Killing horizons in the static vacuum C-metric which represents the gravitational field of a uniformly accelerating Schwarzschild like particle (non-rotating and spherically symmetric) is studied. In the second part these results are generalized to include the effects of the rotation of the source. For small acceleration and small rotation this solution reveals the existance of three Killing horizons. Two the these horizons are the Schwarzschild and the Rindler surfaces which are mainly due to the mass and the acceleration of the particle, respectively. In part three the radial geodesic and non-geodesic motions in the static vacuum C-metric (non-rotating case) are investigated. The effect of the dragging of the inertial frame is also shown in this part. In part four the radiative behavior of the stationary charged C-metric representing the electro-gravitational field of a uniformly accelerating and rotating charged particle with magnetic monopole and the NUT-parameter are investigated. The physical quantities - the news function, mass loss, mass, charge and the multipole moments - are calculated. It is also shown in this part that the magnetic monopole in the presence of rotation and acceleration affects the electric charge

Editor's note: Reviews in Modern Astronomy 27

Science.gov (United States)

Berlepsch, Regina v.

2015-06-01

In order to make the scientific events of the meetings of the Astronomische Gese llschaft (AG) more international and bring them to the attention of the worldwide astronomical community, it was decided to devote the Reviews in Modern Astronomy} to the outcomes of the large annual fall meetings of the AG. In particular, it emphasized the Karl Schwarzschild Lectures, the Ludwig Biermann Award Lectures, the invited reviews, and the highlight contributions on recent progress and achievements from leading scientists. The most prestigious of them, the Karl Schwarzschild Lectures, constitutes a special series of reviews by outstanding scientists who have been awarded the Karl Schwarzschild Medal during the fall meeting of the AG. At the same time, excellent young astronomers are honored by the Ludwig Biermann Award. In 2010 the ``Doctoral Thesis Award'' was established to honor the most outstanding Doctoral Thesis of the past year.

Proteins in solution: Fractal surfaces in solutions

Directory of Open Access Journals (Sweden)

R. Tscheliessnig

2016-02-01

Full Text Available The concept of the surface of a protein in solution, as well of the interface between protein and 'bulk solution', is introduced. The experimental technique of small angle X-ray and neutron scattering is introduced and described briefly. Molecular dynamics simulation, as an appropriate computational tool for studying the hydration shell of proteins, is also discussed. The concept of protein surfaces with fractal dimensions is elaborated. We finish by exposing an experimental (using small angle X-ray scattering and a computer simulation case study, which are meant as demonstrations of the possibilities we have at hand for investigating the delicate interfaces that connect (and divide protein molecules and the neighboring electrolyte solution.

Solvent wash solution

International Nuclear Information System (INIS)

Neace, J.C.

1986-01-01

This patent describes a process for removing diluent degradation products from a solvent extraction solution comprising an admixture of an organic extractant for uranium and plutonium and a non-polar organic liquid diluent, which has been used to recover uranium and plutonium from spent nuclear fuel. Comprising combining a wash solution consisting of: (a) water; and (b) a positive amount up to about, an including, 50 volume percent of at least one highly-polar water-miscible organic solvent, based on the total volume of the water and the highly-polar organic solvent, with the solvent extraction solution after uranium and plutonium values have been stripped from the solvent extraction solution, the diluent degradation products dissolving in the highly-polar organic solvent and the extractant and diluent of the extraction solution not dissolving in the highly-polar organic solvent, and separating the highly-polar organic solvent and the extraction solution to obtain a purified extraction solution

Solution mining process

International Nuclear Information System (INIS)

Showalter, W.E.

1984-01-01

A solution mining process which may be used for uranium, thorium, vanadium, copper, nickel, molybdenum, rhenium, and selenium is claimed. During a first injection-and-production phase of between 6 months and 5 years, a leaching solution is injected through at least one well into the formation to solubilize the mineral values and form a pregnant liquor. This liquor is recovered through another well. The leaching solution contains sulfuric acid, nitric acid, hydrochloric acid, carbonic acid, an alkali metal carbonate, an alkali metal bicarbonate, ammonium carbonate or ammonium bicarbonate. Subsequently during a first production-only phase of between about 2 weeks and one year, injection of the leaching solution is suspended but pregnant liquor is still recovered. This stage is followed by a second injection-and-production phase of between 6 months and 5 years and a second production-only phase. The mineral values are separated from the pregnant liquor to form a barren liquor. The leaching agent is introduced into this liquor, and the solution is recycled. In a second claim for the solution mining of uranium, dilute carbonic acid is used as the leaching solution. The solution has a pH less than 7 and a bicarbonate ion concentration between about 380 ppm and 1000 ppm. The injection-and-production phase lasts between one and two years and the production only phase takes between one and four months. Carbon dioxide is introduced into the barren liquor to form a dilute carbonic acid solution and the solution is recycled

The double copy: Bremsstrahlung and accelerating black holes

CERN Document Server

Luna, Andres; Nicholson, Isobel; O'Connell, Donal; White, Chris D

2016-01-01

Advances in our understanding of perturbation theory suggest the existence of a correspondence between classical general relativity and Yang-Mills theory. A concrete example of this correspondence, which is known as the double copy, was recently introduced for the case of stationary Kerr-Schild spacetimes. Building on this foundation, we examine the simple time-dependent case of an accelerating, radiating point source. The gravitational solution, which generalises the Schwarzschild solution, includes a non-trivial stress-energy tensor. This stress-energy tensor corresponds to a gauge theoretic current in the double copy. We interpret both of these sources as representing the radiative part of the field. Furthermore, in the simple example of Bremsstrahlung, we determine a scattering amplitude describing the radiation, maintaining the double copy throughout. Our results provide the strongest evidence yet that the classical double copy is directly related to the BCJ double copy for scattering amplitudes.

Gravastars with higher dimensional spacetimes

Science.gov (United States)

Ghosh, Shounak; Ray, Saibal; Rahaman, Farook; Guha, B. K.

2018-07-01

We present a new model of gravastar in the higher dimensional Einsteinian spacetime including Einstein's cosmological constant Λ. Following Mazur and Mottola (2001, 2004) we design the star with three specific regions, as follows: (I) Interior region, (II) Intermediate thin spherical shell and (III) Exterior region. The pressure within the interior region is equal to the negative matter density which provides a repulsive force over the shell. This thin shell is formed by ultra relativistic plasma, where the pressure is directly proportional to the matter-energy density which does counter balance the repulsive force from the interior whereas the exterior region is completely vacuum assumed to be de Sitter spacetime which can be described by the generalized Schwarzschild solution. With this specification we find out a set of exact non-singular and stable solutions of the gravastar which seems physically very interesting and reasonable.

Elementary general relativity

International Nuclear Information System (INIS)

Clarke, C.

1979-01-01

The plan of the book is as follows: Chapter 1 develops special relativity in a setting and notation that can immediately be transferred to general relativity. Most of the fundamental geometrical ideas are established here. Chapter 2 gives a more conventional account of some selected applications of special relativity. Chapter 3 is the heart of the book. A geometrical model of space-time is progressively built up, motivated by physical arguments stemming from the equivalence principle, leading to Einstein's field equations. Chapter 4 deals very quickly with the simplest form of weak-field theory with application to gravitational radiation. Chapter 5 concludes the book with a fairly detailed analysis of the Schwarzschild solution, plane fronted gravitational waves, and the Robertson-Walker cosmological solutions. Exercises at the end of each chapter extend the general theory into particular applications, giving a broader picture of the scope of the subject. (author)

The inverse spatial Laplacian of spherically symmetric spacetimes

International Nuclear Information System (INIS)

Fernandes, Karan; Lahiri, Amitabha

2017-01-01

We derive the inverse spatial Laplacian for static, spherically symmetric backgrounds by solving Poisson’s equation for a point source. This is different from the electrostatic Green function, which is defined on the four dimensional static spacetime, while the equation we consider is defined on the spatial hypersurface of such spacetimes. This Green function is relevant in the Hamiltonian dynamics of theories defined on spherically symmetric backgrounds, and closed form expressions for the solutions we find are absent in the literature. We derive an expression in terms of elementary functions for the Schwarzschild spacetime, and comment on the relation of this solution with the known Green function of the spacetime Laplacian operator. We also find an expression for the Green function on the static pure de-Sitter space in terms of hypergeometric functions. We conclude with a discussion of the constraints of the electromagnetic field. (paper)

Ernst Equation and Riemann Surfaces: Analytical and Numerical Methods

International Nuclear Information System (INIS)

Ernst, Frederick J

2007-01-01

Shortly after Einstein published his general theory of relativity, the spherically symmetric solution of the vacuum field equations was discovered by Karl Schwarzschild, while Hermann Weyl showed that from any axisymmetric solution ψ of the Laplace equation ∇ 2 ψ = 0 (satisfying appropriate boundary conditions) the metric tensor of a static axisymmetric vacuum spacetime can be constructed. In particular, the Schwarzschild solution corresponds to a rather trivial solution of Laplace's equation expressed in terms of prolate spheroidal coordinates. It took about 45 years before Roy Kerr discovered what he called the 'rotating Schwarzschild solution', and an additional five years before I established that from any complex axisymmetric solution E of the nonlinear equation E∇ 2 E = ∇E·∇E (satisfying appropriate boundary conditions) the metric tensor of a stationary axisymmetric vacuum spacetime can be constructed. In particular, the Kerr solution corresponds to an extremely simple solution of this equation expressed in terms of prolate spheroidal coordinates. Ever more complicated solutions of this equation (using prolate spheroidal coordinates) were discovered by Tomimatsu and Sato, but for none of the associated spacetimes has a reasonable material source been suggested. What the present book describes are some of the heroic efforts that have been undertaken to construct physically significant spacetimes by solving the vacuum Ernst equation. Unfortunately, thus far, no one has made much progress extending the Ernst equation approach to facilitate the investigation of spacetime within a stationary axisymmetric material source, where, for example, the stress-energy tensor is that of a perfect fluid. However, in 1994, Meinel and Neugebauer had the novel idea of focusing attention upon global solutions such as the spacetime geometry associated with a rotating infinitely thin disk of dust, where the material source can be represented by discontinuities in the

PFP solution stabilization

International Nuclear Information System (INIS)

Aftanas, B.L.

1996-01-01

This Functional Design Criteria (FDC) addresses remediation of the plutonium-bearing solutions currently in inventory at the Plutonium Finishing Plant (PFP). The recommendation from the Environmental Impact Statement (EIS) is that the solutions be treated thermally and stabilized as a solid for long term storage. For solutions which are not discardable, the baseline plan is to utilize a denitration process to stabilize the solutions prior to packaging for storage

Proceedings of the Antiproton Science and Technology Workshop Held in Santa Monica, California on 6-9 October 1987

Science.gov (United States)

1988-07-01

34 pp. 221-232, Positron Studies of Solids, Surfaces, and Atoms, Allen P. Mills, Jr., William S. Crane, and Karl F. Canter, Eds., Proceedings Symposium...quoted for antimatter in the Walgate article of 133 MS/mg was based on the wrong /p ratio; it should be 15 M$/mg.] B. Schwarzschild , "Laser Beam Focus...particles.") B. Schwarzschild , "Now They’re Even Trapping Antiprotons," Physics Today 39, No. 9, 19 (Sept 1986). Arthur L. Robinson, "Antiprotons Captured

Einstein, the exponential metric, and a proposed gravitational Michelson-Morley experiment

International Nuclear Information System (INIS)

Yilmaz, H.

1979-01-01

An early but potentially important remark of Einstein on the exponential nature of time-dilation is discussed. Using the same argument for the length-contraction, plus two alternative kinematical assumptions, the Schwarzschild and exponential metrics are derived. A gravitational Michelson-Morley experiment with one arm directed along the vertical is proposed to test the metrics. The experiment may be considered as a laboratory test of the Schwarzschild field and possibly a test of the black-hole interpretation of collapsed matter

Periodic Solutions and S-Asymptotically Periodic Solutions to Fractional Evolution Equations

Directory of Open Access Journals (Sweden)

Jia Mu

2017-01-01

Full Text Available This paper deals with the existence and uniqueness of periodic solutions, S-asymptotically periodic solutions, and other types of bounded solutions for some fractional evolution equations with the Weyl-Liouville fractional derivative defined for periodic functions. Applying Fourier transform we give reasonable definitions of mild solutions. Then we accurately estimate the spectral radius of resolvent operator and obtain some existence and uniqueness results.

A Dual Egalitarian Solution

NARCIS (Netherlands)

Klijn, F.; Slikker, M.; Tijs, S.H.

2000-01-01

In this note we introduce an egalitarian solution, called the dual egalitarian solution, that is the natural counterpart of the egalitarian solution of Dutta and Ray (1989).We prove, among others, that for a convex game the egalitarian solution coincides with the dual egalitarian solution for its

Solitons and action propagation according to general relativity (Part one)

International Nuclear Information System (INIS)

Stavroulakis, N.

1987-01-01

The current exposition of General Relativity involves two contradictory statements: at first it is asserted that every change in the distribution of matter brings about gravitational waves. Then it is asserted that, specifically, no gravitational effect is produced by the pulsations of a spherical source. By analysing the second statement, we conclude that it arises from a vicious circle tied up with mathematical errors which led to the Schwarzschild solution and the theory of black holes. In order to obtain the correct formulation of the problem, we establish rigorously the general form of the θ(4)-invariant space-time metrics on R x R 3 and bring out the principles allowing to associate gravitational effects with oscillating masses [fr

Perturbations and quasi-normal modes of black holes in Einstein-Aether theory

International Nuclear Information System (INIS)

Konoplya, R.A.; Zhidenko, A.

2007-01-01

We develop a new method for calculation of quasi-normal modes of black holes, when the effective potential, which governs black hole perturbations, is known only numerically in some region near the black hole. This method can be applied to perturbations of a wide class of numerical black hole solutions. We apply it to the black holes in the Einstein-Aether theory, a theory where general relativity is coupled to a unit time-like vector field, in order to observe local Lorentz symmetry violation. We found that in the non-reduced Einstein-Aether theory, real oscillation frequency and damping rate of quasi-normal modes are larger than those of Schwarzschild black holes in the Einstein theory

Does the mass of a black hole decrease due to the accretion of phantom energy?

International Nuclear Information System (INIS)

Gao Changjun; Chen Xuelei; Faraoni, Valerio; Shen Yougen

2008-01-01

According to Babichev et al., the accretion of a phantom test fluid onto a Schwarzschild black hole will induce the mass of the black hole to decrease, however the backreaction was ignored in their calculation. Using new exact solutions describing black holes in a background Friedmann-Robertson-Walker universe, we find that the physical black hole mass may instead increase due to the accretion of phantom energy. If this is the case, and the future universe is dominated by phantom dark energy, the black hole apparent horizon and the cosmic apparent horizon will eventually coincide and, after that, the black hole singularity will become naked in finite comoving time before the big rip occurs, violating the cosmic censorship conjecture.

Quasi-normal modes from non-commutative matrix dynamics

Science.gov (United States)

Aprile, Francesco; Sanfilippo, Francesco

2017-09-01

We explore similarities between the process of relaxation in the BMN matrix model and the physics of black holes in AdS/CFT. Focusing on Dyson-fluid solutions of the matrix model, we perform numerical simulations of the real time dynamics of the system. By quenching the equilibrium distribution we study quasi-normal oscillations of scalar single trace observables, we isolate the lowest quasi-normal mode, and we determine its frequencies as function of the energy. Considering the BMN matrix model as a truncation of N=4 SYM, we also compute the frequencies of the quasi-normal modes of the dual scalar fields in the AdS5-Schwarzschild background. We compare the results, and we finda surprising similarity.

Neutrino's helicity in a gravitational field

International Nuclear Information System (INIS)

Pansart, J.P.

1996-01-01

By using approximated solutions of Dirac's equation, we show that there is no helicity reversal for light neutrinos in the Schwarzschild metric nor in an expanding universe. The actual coupling between a particle spin and the angular momentum of a heavy rotating body induces a possible helicity reversal but with an unobservable probability proportional to m 2 p / E 2 , where m p is the particle mass and E its energy. In these calculations, the helicity is defined through the spin orientation with respect to the current and not with respect to the linear momentum. This definition gives simple expressions and is equal to the usual definition in the case of a flat space. (N.T.)

Negative-mass lagging cores of the big bang

International Nuclear Information System (INIS)

Miller, B.D.

1976-01-01

Examples are given of spherically symmetric cosmological models containing space-sections with the following properties: at large values of the geometrically defined coordinate R, the mass is positive, while at small values of R, the mass is negative. The negative-mass region of spacetime has local properties similar to those of the negative-mass Schwarzschild solution. The big bang in these models is partially spacelike and partially timelike, so the spacetimes do not obey the strong form of the cosmic censorship hypothesis. The timelike, negative-mass segments of the big bang are unlimited sources of electromagnetic and gravitational radiation, and as such may be attractive as ''lagging core'' models of highly energetic astrophysical phenomena

Negative-mass lagging cores of the big bang

Energy Technology Data Exchange (ETDEWEB)

Miller, B.D.

1976-09-01

Examples are given of spherically symmetric cosmological models containing space-sections with the following properties: at large values of the geometrically defined coordinate R, the mass is positive, while at small values of R, the mass is negative. The negative-mass region of spacetime has local properties similar to those of the negative-mass Schwarzschild solution. The big bang in these models is partially spacelike and partially timelike, so the spacetimes do not obey the strong form of the cosmic censorship hypothesis. The timelike, negative-mass segments of the big bang are unlimited sources of electromagnetic and gravitational radiation, and as such may be attractive as ''lagging core'' models of highly energetic astrophysical phenomena. (AIP)

Transition between vortex rings and MAP solutions for electrically charged magnetic solutions

Energy Technology Data Exchange (ETDEWEB)

Wong, Khai-Ming; Soltanian, Amin; Teh, Rosy [School of Physics, Universiti Sains Malaysia, 11800 USM, Penang (Malaysia)

2014-03-05

We consider the bifurcation and transition of axially symmetric monopole-antimonopole pair (MAP) and vortex ring solutions in the presence of electric charge for the SU(2) Yang-Mills-Higgs field theory. Here we investigate the properties of MAP/vortex ring solutions with n = 3,η = 0.65, for different Higgs field strength λ. For λ < 4.93, there is only one fundamental branch of vortex ring solution, but at the critical value of λ{sub b} = 4.93, branching happens and 2 sets of new solutions appeared. The new branch with less energy is a full MAP solution while the branch with higher energy contains MAP at the beginning and separation between poles of MAP on the z-axis reduces gradually and at another critical value of λ{sub t} = 14.852, they merge together at z = 0. Beyond this point the solutions change to the vortex ring solutions and a transitions between MAP and vortex ring solutions happens at this branch.

Obstruction of black hole singularity by quantum field theory effects

Energy Technology Data Exchange (ETDEWEB)

Abedi, Jahed; Arfaei, Hessamaddin [Department of Physics, Sharif University of Technology,P.O. Box 11155-9161, Tehran, Irany (Iran, Islamic Republic of); School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)

2016-03-21

We consider the back reaction of the energy due to quantum fluctuation of the background fields considering the trace anomaly for Schwarzschild black hole. It is shown that it will result in modification of the horizon and also formation of an inner horizon. We show that the process of collapse of a thin shell stops before formation of the singularity at a radius slightly smaller than the inner horizon at the order of (c{sub A}(M/(M{sub p}))){sup 1/3}l{sub p}. After the collapse stops the reverse process takes place. Thus we demonstrate that without turning on quantum gravity and just through the effects the coupling of field to gravity as trace anomaly of quantum fluctuations the formation of the singularity through collapse is obstructed. An important consequence of our work is existence of an extremal solution with zero temperature and a mass which is lower bound for the Schwazschild solution. This solution is also the asymptotic final stable state after Hawking radiation.

Theoretical physics 3. Classical field theory. On electrodynamics, non-Abelian gauge theories, and gravitation. 3. ed.

International Nuclear Information System (INIS)

Scheck, Florian

2010-01-01

Stringent presentation of field theory, mediates the connection from the classicalelectrodynamics up to modern gauge theories. The compact presentation is ideal for the bachelor study. New chapter on general relativity theory. Deepens the learned by numerous application from laser physic, metamaterials and different more. Theoretical physics 3. Classical field theory. On electrodynamics, non-Abelian, and gravitation is the third of five volumes on theoretical physics by professor Scheck. The cycle theoretical physics comprehends: Volume 1: Mechanics. From Newtons law to the deterministic chaos. Volume 2: Nonrelativistic quantum theory. From the hydrogen atom to the many-particle systems. Volume 3: Classical field theory. From the electrodynamics to the gauge theories. Volume 5: From the laws of thermodynamics to the quantum statistics. This textbook mediates modern theoretical physics in string presentation illustrated by many examples. It contains numerous problems with solution hints ore exemplary, complete solutions. The third edition was revised in many single topics, especially the chapter on general relativity theory was supplemented by an extensive analysis of the Schwarzschild solution. [de

AdS Black Hole with Phantom Scalar Field

Directory of Open Access Journals (Sweden)

Limei Zhang

2017-01-01

Full Text Available We present an AdS black hole solution with Ricci flat horizon in Einstein-phantom scalar theory. The phantom scalar fields just depend on the transverse coordinates x and y, which are parameterized by the parameter α. We study the thermodynamics of the AdS phantom black hole. Although its horizon is a Ricci flat Euclidean space, we find that the thermodynamical properties of the black hole solution are qualitatively the same as those of AdS Schwarzschild black hole. Namely, there exists a minimal temperature and the large black hole is thermodynamically stable, while the smaller one is unstable, so there is a so-called Hawking-Page phase transition between the large black hole and the thermal gas solution in the AdS space-time in Poincare coordinates. We also calculate the entanglement entropy for a strip geometry dual to the AdS phantom black holes and find that the behavior of the entanglement entropy is qualitatively the same as that of the black hole thermodynamical entropy.

Bolting multicenter solutions

Energy Technology Data Exchange (ETDEWEB)

Bena, Iosif [Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS, 91191 Gif-sur-Yvette Cedex (France); Bossard, Guillaume [Centre de Physique Théorique, Ecole Polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau Cedex (France); Katmadas, Stefanos; Turton, David [Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS, 91191 Gif-sur-Yvette Cedex (France)

2017-01-30

We introduce a solvable system of equations that describes non-extremal multicenter solutions to six-dimensional ungauged supergravity coupled to tensor multiplets. The system involves a set of functions on a three-dimensional base metric. We obtain a family of non-extremal axisymmetric solutions that generalize the known multicenter extremal solutions, using a particular base metric that introduces a bolt. We analyze the conditions for regularity, and in doing so we show that this family does not include solutions that contain an extremal black hole and a smooth bolt. We determine the constraints that are necessary to obtain smooth horizonless solutions involving a bolt and an arbitrary number of Gibbons-Hawking centers.

Thick brane solutions

International Nuclear Information System (INIS)

Dzhunushaliev, Vladimir; Minamitsuji, Masato; Folomeev, Vladimir

2010-01-01

This paper gives a comprehensive review on thick brane solutions and related topics. Such models have attracted much attention from many aspects since the birth of the brane world scenario. In many works, it has been usually assumed that a brane is an infinitely thin object; however, in more general situations, one can no longer assume this. It is also widely considered that more fundamental theories such as string theory would have a minimal length scale. Many multidimensional field theories coupled to gravitation have exact solutions of gravitating topological defects, which can represent our brane world. The inclusion of brane thickness can realize a variety of possible brane world models. Given our understanding, the known solutions can be classified into topologically non-trivial solutions and trivial ones. The former class contains solutions of a single scalar (domain walls), multi-scalar, gauge-Higgs (vortices), Weyl gravity and so on. As an example of the latter class, we consider solutions of two interacting scalar fields. Approaches to obtain cosmological equations in the thick brane world are reviewed. Solutions with spatially extended branes (S-branes) and those with an extra time-like direction are also discussed.

Wormholes supported by phantom energy from Shan-Chen cosmological fluids

Energy Technology Data Exchange (ETDEWEB)

Wang, Deng [Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Meng, Xin-He [Nankai University, Department of Physics, Tianjin (China); Institute of Theoretical Physics, CAS, State key Lab of Theoretical Physics, Beijing (China)

2016-03-15

In the present paper, the exact solutions of spherically symmetrical Einstein field equations describing wormholes supported by phantom energy that violates the null energy condition from Shan-Chen background fluid are obtained. We have considered the important case of the model parameter ψ ∼ 1, which corresponds to the ''saturation effect'', and this regime corresponds to an effective form of ''asymptotic freedom'' for the fluids, but occurring at cosmological rather than subnuclear scales. Then we investigate the allowed range for the values of the model parameters g and ω when the spacetime metrics describe wormholes and discuss the possible singularities of the solutions, finding that the obtained spacetimes are geodesically complete. Furthermore, we construct two traversable wormholes through matching our obtained interior solutions to the exterior Schwarzschild solutions and analyze the traversabilities of the wormholes. Finally, we consider the case of anisotropic pressure and discover that the transverse pressure also crosses the phantom divide -1 with the growth of the wormhole dimension, and it tends to be the same as the radial pressure with the growth of the wormhole radius. (orig.)

Wormholes minimally violating the null energy condition

Energy Technology Data Exchange (ETDEWEB)

Bouhmadi-López, Mariam [Departamento de Física, Universidade da Beira Interior, 6200 Covilhã (Portugal); Lobo, Francisco S N; Martín-Moruno, Prado, E-mail: mariam.bouhmadi@ehu.es, E-mail: fslobo@fc.ul.pt, E-mail: pmmoruno@fc.ul.pt [Centro de Astronomia e Astrofísica da Universidade de Lisboa, Campo Grande, Edifício C8, 1749-016 Lisboa (Portugal)

2014-11-01

We consider novel wormhole solutions supported by a matter content that minimally violates the null energy condition. More specifically, we consider an equation of state in which the sum of the energy density and radial pressure is proportional to a constant with a value smaller than that of the inverse area characterising the system, i.e., the area of the wormhole mouth. This approach is motivated by a recently proposed cosmological event, denoted {sup t}he little sibling of the big rip{sup ,} where the Hubble rate and the scale factor blow up but the cosmic derivative of the Hubble rate does not [1]. By using the cut-and-paste approach, we match interior spherically symmetric wormhole solutions to an exterior Schwarzschild geometry, and analyse the stability of the thin-shell to linearized spherically symmetric perturbations around static solutions, by choosing suitable properties for the exotic material residing on the junction interface radius. Furthermore, we also consider an inhomogeneous generalization of the equation of state considered above and analyse the respective stability regions. In particular, we obtain a specific wormhole solution with an asymptotic behaviour corresponding to a global monopole.

A boring solution

Energy Technology Data Exchange (ETDEWEB)

Radiuk, M I; Iushkova, N E; Kozubovskii, A I

1979-10-25

A boring solution is being patented for boring for oil and gas, which can be used in wells, where the temperature of the circulating liquid reaches 100/sup 0/. Polyvinyl acetate emulsion (PVE) is added for the purpose of decreasing viscosity of the solution at a temperature of agression into the boring solution containing clay, water, carboxymethylcellulose (CBC), a chloride from the number of sodium, potassium, or magnesium chlorides. The solution has the following composition in %: clay, 10 to 20; CBC, 1.5 to 2.0; chloride, 5 to 20; PVE, 0.5 to 2; water, up to 100. In accordance to GOST 1000-62 for the accepted PVE, the compound has the following composition, in %: monomer, 0.8; dry residue, greater than or equal to 50; plasticizer (tributyl phthalate), 5 to 15. The boring solution is processed according to the following method. The original solution, containing clay, water, salts, receives 1.5 to 2% CBC and afterwards it is processed with 0.5 to 2% PVE.

Crystal Nucleation of Tolbutamide in Solution: Relationship to Solvent, Solute Conformation, and Solution Structure.

Science.gov (United States)

Zeglinski, Jacek; Kuhs, Manuel; Khamar, Dikshitkumar; Hegarty, Avril C; Devi, Renuka K; Rasmuson, Åke C

2018-04-03

The influence of the solvent in nucleation of tolbutamide, a medium-sized, flexible and polymorphic organic molecule, has been explored by measuring nucleation induction times, estimating solvent-solute interaction enthalpies using molecular modelling and calorimetric data, probing interactions and clustering with spectroscopy, and modelling solvent-dependence of molecular conformation in solution. The nucleation driving force required to reach the same induction time is strongly solvent-dependent, increasing in the order: acetonitrilenucleation difficulty is a function of the strength of solvent-solute interaction, with emphasis on the interaction with specific H-bonding polar sites of importance in the crystal structure. A clear exception from this rule is the most difficult nucleation in toluene despite the weakest solvent-solute interactions. However molecular dynamics modelling predicts that tolbutamide assumes an intramolecularly H-bonded conformation in toluene, substantially different from and more stable than the conformation in the crystal structure, and thus presenting an additional barrier to nucleation. This explains why nucleation in toluene is the most difficult and why the relatively higher propensity for aggregation of tolbutamide molecules in toluene solution, as observed with FTIR spectroscopy, does not translate into easier nucleation. Thus, our combined experimental and molecular modelling study suggests that the solvent can influence on the nucleation not only via differences in the desolvation but also through the influence on molecular conformation. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

''Splendeurs et miseres'' of Hawking's effect

Energy Technology Data Exchange (ETDEWEB)

Hijicek, P

1977-01-01

The Hawking effect, the result that a Schwarzschild black hole will emit particles as if it were a hot body with a given temperature depending upon the mass of the hole and the sun, the Planck, Newton, and Boltzmann constants, and the light velocity, is considered. Restriction is made to the Schwarzschild space-time, in order to suppress the geometrical, purely general relativistic aspects as far as possible. The treatment includes quantum field theory in curved space--times, and spherically symmetric collapse. 23 references. (JFP)

Liquid scintillation solution

International Nuclear Information System (INIS)

Long, E.C.

1977-01-01

A liquid scintillation solution is described which includes (1) a scintillation solvent (toluene and xylene), (2) a primary scintillation solute (PPO and Butyl PBD), (3) a secondary scintillation solute (POPOP and Dimethyl POPOP), (4) a plurality of substantially different surfactants and (5) a filter dissolving and/or transparentizing agent. 8 claims

New compacton solutions and solitary wave solutions of fully nonlinear generalized Camassa-Holm equations

International Nuclear Information System (INIS)

Tian Lixin; Yin Jiuli

2004-01-01

In this paper, we introduce the fully nonlinear generalized Camassa-Holm equation C(m,n,p) and by using four direct ansatzs, we obtain abundant solutions: compactons (solutions with the absence of infinite wings), solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions and obtain kink compacton solutions and nonsymmetry compacton solutions. We also study other forms of fully nonlinear generalized Camassa-Holm equation, and their compacton solutions are governed by linear equations

Solute-matrix and Solute-Solute Interactions during Supercritical Fluid Extraction of Sea Buckthorn Leaves

Czech Academy of Sciences Publication Activity Database

Sajfrtová, Marie; Sovová, Helena

2012-01-01

Roč. 42, SI (2012), s. 1682-1691 E-ISSN 1877-7058. [International Congress of Chemical and Process Engineering CHISA 2012 and 15th Conference PRES 2012 /20./. Prague, 25.08.2012-29.08.2012] R&D Projects: GA TA ČR TA01010578 Institutional support: RVO:67985858 Keywords : supercritical fluid extraction * sea buckthom leaves * solute-solute interaction Subject RIV: CI - Industrial Chemistry, Chemical Engineering

Analytic Solutions and Resonant Solutions of Hyperbolic Partial Differential Equations

Science.gov (United States)

Wagenmaker, Timothy Roger

This dissertation contains two main subject areas. The first deals with solutions to the wave equation Du/Dt + a Du/Dx = 0, where D/Dt and D/Dx represent partial derivatives and a(t,x) is real valued. The question I studied, which arises in control theory, is whether solutions which are real analytic with respect to the time variable are dense in the space of all solutions. If a is real analytic in t and x, the Cauchy-Kovalevsky Theorem implies that the solutions real analytic in t and x are dense, since it suffices to approximate the initial data by polynomials. The same positive result is valid when a is continuously differentiable and independent of t. This is proved by regularization in time. The hypothesis that a is independent of t cannot be replaced by the weaker assumption that a is real analytic in t, even when it is infinitely smooth. I construct a(t,x) for which the solutions which are analytic in time are automatically periodic in time. In particular these solutions are not dense in the space of all solutions. The second area concerns the resonant interaction of oscillatory waves propagating in a compressible inviscid fluid. An asymptotic description given by Andrew Majda, Rodolfo Rosales, and Maria Schonbek (MRS) involves the genuinely nonlinear quasilinear hyperbolic system Du/Dt + D(uu/2)/Dt + v = 0, Dv/Dt - D(vv/2)/Dt - u = 0. They performed many numerical simulations which indicated that small amplitude solutions of this system tend to evade shock formation, and conjectured that "smooth initial data with a sufficiently small amplitude never develop shocks throughout a long time interval of integration.". I proved that for smooth periodic U(x), V(x) and initial data u(0,x) = epsilonU(x), v(0,x) = epsilonV(x), the solution is smooth for time at least constant times | ln epsilon| /epsilon. This is longer than the lifetime order 1/ epsilon of the solution to the decoupled Burgers equations. The decoupled equation describes nonresonant interaction of

A Finite-Difference Solution of Solute Transport through a Membrane Bioreactor

Directory of Open Access Journals (Sweden)

B. Godongwana

2015-01-01

Full Text Available The current paper presents a theoretical analysis of the transport of solutes through a fixed-film membrane bioreactor (MBR, immobilised with an active biocatalyst. The dimensionless convection-diffusion equation with variable coefficients was solved analytically and numerically for concentration profiles of the solutes through the MBR. The analytical solution makes use of regular perturbation and accounts for radial convective flow as well as axial diffusion of the substrate species. The Michaelis-Menten (or Monod rate equation was assumed for the sink term, and the perturbation was extended up to second-order. In the analytical solution only the first-order limit of the Michaelis-Menten equation was considered; hence the linearized equation was solved. In the numerical solution, however, this restriction was lifted. The solution of the nonlinear, elliptic, partial differential equation was based on an implicit finite-difference method (FDM. An upwind scheme was employed for numerical stability. The resulting algebraic equations were solved simultaneously using the multivariate Newton-Raphson iteration method. The solution allows for the evaluation of the effect on the concentration profiles of (i the radial and axial convective velocity, (ii the convective mass transfer rates, (iii the reaction rates, (iv the fraction retentate, and (v the aspect ratio.

Black holes in higher dimensional gravity theory with corrections quadratic in curvature

International Nuclear Information System (INIS)

Frolov, Valeri P.; Shapiro, Ilya L.

2009-01-01

Static spherically symmetric black holes are discussed in the framework of higher dimensional gravity with quadratic in curvature terms. Such terms naturally arise as a result of quantum corrections induced by quantum fields propagating in the gravitational background. We focus our attention on the correction of the form C 2 =C αβγδ C αβγδ . The Gauss-Bonnet equation in four-dimensional spacetime enables one to reduce this term in the action to the terms quadratic in the Ricci tensor and scalar curvature. As a result the Schwarzschild solution which is Ricci flat will be also a solution of the theory with the Weyl scalar C 2 correction. An important new feature of the spaces with dimension D>4 is that in the presence of the Weyl curvature-squared term a necessary solution differs from the corresponding 'classical' vacuum Tangherlini metric. This difference is related to the presence of secondary or induced hair. We explore how the Tangherlini solution is modified by 'quantum corrections', assuming that the gravitational radius r 0 is much larger than the scale of the quantum corrections. We also demonstrated that finding a general solution beyond the perturbation method can be reduced to solving a single third order ordinary differential equation (master equation).

Liquid scintillation solution

International Nuclear Information System (INIS)

Long, E.C.

1976-01-01

The invention deals with a liquid scintillation solution which contains 1) a scintillation solvent (toluol), 2) a primary scintillation solute (PPO), 3) a secondary scintillation solute (dimethyl POPOP), 4) several surfactants (iso-octyl-phenol polyethoxy-ethanol and sodium di-hexyl sulfosuccinate) essentially different from one another and 5) a filter resolution and/or transparent-making agent (cyclic ether, especially tetrahydrofuran). (HP) [de

Particle energy and Hawking temperature

International Nuclear Information System (INIS)

Ding Chikun; Wang Mengjie; Jing Jiliang

2009-01-01

Some authors have recently found that the tunneling approach gives a different Hawking temperature for a Schwarzschild black hole in a different coordinate system. In this Letter, we find that to work out the Hawking temperature in a different coordinate system by the tunneling approach, we must use the correct definition of the energy of the radiating particles. By using a new definition of the particle energy, we obtain the correct Hawking temperature for a Schwarzschild black hole in two dynamic coordinate systems, the Kruskal-Szekers and dynamic Lemaitre coordinate systems.

Temporal and spatial foliations of spacetimes.

Science.gov (United States)

Herold, H.

For the solution of initial-value problems in numerical relativity usually the (3+1) splitting of Einstein's equations is employed. An important part of this splitting is the choice of the temporal gauge condition. In order to estimate the quality of time-evolution schemes, different time slicings of given well-known spherically symmetric spacetimes have been studied. Besides the maximal slicing condition the harmonic slicing prescription has been used to calculate temporal foliations of the Schwarzschild and the Oppenheimer-Snyder spacetime. Additionally, the author has studied a recently proposed, geometrically motivated spatial gauge condition, which is defined by considering the foliations of the three-dimensional space-like hypersurfaces by 2-surfaces of constant mean extrinsic curvature. Apart from the equations for the shift vector, which can be derived for this gauge condition, he has investigated such spatial foliations for well-known stationary axially symmetric spacetimes, namely for the Kerr metric and for numerically determined solutions for rapidly rotating neutron stars.

Brane-antibrane democracy

International Nuclear Information System (INIS)

Kallosh, R.; Rajaraman, A.

1996-01-01

We suggest a duality-invariant formula for the entropy and temperature of nonextreme black holes in supersymmetric string theory. The entropy is given in terms of the duality-invariant parameter of the deviation from extremality and 56 SU(8) covariant central charges. It interpolates between the entropies of Schwarzschild solution and extremal solutions with various amount of unbroken supersymmetries, and therefore, serves for classification of black holes in supersymmetric string theories. We introduce the second auxiliary 56 via an E(7) symmetric constraint. The symmetric and antisymmetric combinations of these two multiplets are related via moduli to the corresponding two fundamental representations of E(7): brane and antibrane open-quote open-quote numbers.close-quote close-quote Using the CPT as well as C symmetry of the entropy formula and duality one can explain the mysterious simplicity of the nonextreme black hole area formula in terms of branes and antibranes. copyright 1996 The American Physical Society

Determination of the activity of a molecular solute in saturated solution

International Nuclear Information System (INIS)

Nordstroem, Fredrik L.; Rasmuson, Ake C.

2008-01-01

Prediction of the solubility of a solid molecular compound in a solvent, as well as, estimation of the solution activity coefficient from experimental solubility data both require estimation of the activity of the solute in the saturated solution. The activity of the solute in the saturated solution is often defined using the pure melt at the same temperature as the thermodynamic reference. In chemical engineering literature also the activity of the solid is usually defined on the same reference state. However, far below the melting temperature, the properties of this reference state cannot be determined experimentally, and different simplifications and approximations are normally adopted. In the present work, a novel method is presented to determine the activity of the solute in the saturated solution (=ideal solubility) and the heat capacity difference between the pure supercooled melt and solid. The approach is based on rigorous thermodynamics, using standard experimental thermodynamic data at the melting temperature of the pure compound and solubility measurements in different solvents at various temperatures. The method is illustrated using data for ortho-, meta-, and para-hydroxybenzoic acid, salicylamide and paracetamol. The results show that complete neglect of the heat capacity terms may lead to estimations of the activity that are incorrect by a factor of 12. Other commonly used simplifications may lead to estimations that are only one-third of the correct value

Determination of the activity of a molecular solute in saturated solution

Energy Technology Data Exchange (ETDEWEB)

Nordstroem, Fredrik L. [Department of Chemical Engineering and Technology, Royal Institute of Technology, 100 44 Stockholm (Sweden); Rasmuson, Ake C. [Department of Chemical Engineering and Technology, Royal Institute of Technology, 100 44 Stockholm (Sweden)], E-mail: rasmuson@ket.kth.se

2008-12-15

Prediction of the solubility of a solid molecular compound in a solvent, as well as, estimation of the solution activity coefficient from experimental solubility data both require estimation of the activity of the solute in the saturated solution. The activity of the solute in the saturated solution is often defined using the pure melt at the same temperature as the thermodynamic reference. In chemical engineering literature also the activity of the solid is usually defined on the same reference state. However, far below the melting temperature, the properties of this reference state cannot be determined experimentally, and different simplifications and approximations are normally adopted. In the present work, a novel method is presented to determine the activity of the solute in the saturated solution (=ideal solubility) and the heat capacity difference between the pure supercooled melt and solid. The approach is based on rigorous thermodynamics, using standard experimental thermodynamic data at the melting temperature of the pure compound and solubility measurements in different solvents at various temperatures. The method is illustrated using data for ortho-, meta-, and para-hydroxybenzoic acid, salicylamide and paracetamol. The results show that complete neglect of the heat capacity terms may lead to estimations of the activity that are incorrect by a factor of 12. Other commonly used simplifications may lead to estimations that are only one-third of the correct value.

Selling value with the business solutions : Konica Minolta Business Solutions Finland Ltd.

OpenAIRE

Piira, Antti

2013-01-01

Abstract Konica Minolta aims to develop its sales from product sales to solution sales. This is a challenging transition that requires resources and new ideas from the company and its people. The thesis attempted to explore the current situation of solution sales at Konica Minolta Business Solutions Finland and to produce ideas on how to develop and support solution sales. In addition motivation factors and the utilization of customer references in sales was examinated. The triangulat...

Density of nitric acid solutions of plutonium; Densite des solutions nitriques de plutonium

Energy Technology Data Exchange (ETDEWEB)

Guibergia, J P [Commissariat a l' Energie Atomique, Saclay (France).Centre d' Etudes Nucleaires

1960-07-01

The report is intended to furnish an expression making it possible to determine the density of a nitric acid solution of plutonium. Under certain defined experimental conditions, the equation found makes it possible to deduce, for a solution whose concentration, free acidity and temperature are known, the corresponding value of the density of that solution. (author) [French] L'expose a pour but de donner une formule permettant la determination de la densite d'une solution nitrique de plutonium. Suivant certaines conditions experimentales precisees, l'equation trouvee permet, pour une solution dont la concentration, l'acidite libre nitrique et la temperature sont donnees, de deduire la valeur correspondant de la densite de cette solution. (auteur)

Analytical Solution of Multicompartment Solute Kinetics for Hemodialysis

Directory of Open Access Journals (Sweden)

Przemysław Korohoda

2013-01-01

Full Text Available Objective. To provide an exact solution for variable-volume multicompartment kinetic models with linear volume change, and to apply this solution to a 4-compartment diffusion-adjusted regional blood flow model for both urea and creatinine kinetics in hemodialysis. Methods. A matrix-based approach applicable to linear models encompassing any number of compartments is presented. The procedure requires the inversion of a square matrix and the computation of its eigenvalues λ, assuming they are all distinct. This novel approach bypasses the evaluation of the definite integral to solve the inhomogeneous ordinary differential equation. Results. For urea two out of four eigenvalues describing the changes of concentrations in time are about 105 times larger than the other eigenvalues indicating that the 4-compartment model essentially reduces to the 2-compartment regional blood flow model. In case of creatinine, however, the distribution of eigenvalues is more balanced (a factor of 102 between the largest and the smallest eigenvalue indicating that all four compartments contribute to creatinine kinetics in hemodialysis. Interpretation. Apart from providing an exact analytic solution for practical applications such as the identification of relevant model and treatment parameters, the matrix-based approach reveals characteristic details on model symmetry and complexity for different solutes.

In Vivo Remineralization of Artificial Carious Lesions using Calcifying Solution and Fluoride Solution

Directory of Open Access Journals (Sweden)

Els Sunarsih Budipramana

2015-10-01

Full Text Available The remineralization potential of fluoride and calcifying solution was studiedas in situ model. Matched enamel discs of artifically demineralized human enamel were attached to an acrylic mandibular removable appliance of 6 adult volunteers who rinsed their mouth with a solution containing either 50 ppm F-, 200 ppm F- in amine fluoride, calcifying solution (formula BR21 or placebo as a control. The volunteers were asked to rinse 3 times a day for 3 minutes with 15 ml of the solution for 6 days (18 times. On the 7th day enamel discs were taken out from the partial denture. Three kinds of measurements were done: enamel permeability testing, depth lesion testing and fluoride retention testing. New demineralized enamel discs were attached to the partial dentures and the volunteers were asked to start rinsing with other solutions using the same protocols. The purpose of this study was to answer the question why the calcifying solutions were no more used as a remineralizing solution. The data ws analyzed using SPSS/PC for two factors Anova and one way Anova for enamel permeability and Kruskal Wallis for studying enamel depth lesion and fluoride retention. There was no significant difference after rinsing with calcifying solution and placebo in enamel permeability, depth lesions, and fluoride retention when compared to fluoride solution. To get a better result in remineralizing carious teeth fluoride contents in solution must be higher than 50 ppm F-.

One Monopole-Antimonopole Pair Solutions

International Nuclear Information System (INIS)

Teh, Rosy; Wong, K.-M.

2009-01-01

We present new classical generalized one monopole-antimonopole pair solutions of the SU(2) Yang-Mills-Higgs theory with the Higgs field in the adjoint representation. We show that in general the one monopole-antimonopole solution need not be solved by imposing mθ-winding number to be integer greater than one. We also show that this solution can be solved when m = 1 by transforming the large distance asymptotic solutions to general solutions that depend on a parameter p. Secondly we show that these large distance asymptotic solutions can be further generalized to the Jacobi elliptic functions. We focus our numerical calculation on the Jacobi elliptic functions solution when the nφ-winding number is one and show that this generalized Jacobi elliptic 1-MAP solution possesses lower energy. All these solutions are numerical finite energy non-BPS solutions of the Yang-Mills-Higgs field theory.

Business-to-business electronic commerce systems and services. Smart EC solution; Kigyoka nrenkei system solution system. Smart EC solution

Energy Technology Data Exchange (ETDEWEB)

Setoguchi, T.; Manchu, Y.; Katsumata, M. [Toshiba Corp., Tokyo (Japan)

2000-04-01

Toshiba provides a range of information technology (IT) solutions called SmartEC Solution, which includes business-to-business electronic commerce systems and services based on international standards and industrial know-how, especially our electronic data interchange (EDI) know-how as a manufacturer. These IT solutions are supplied as services covering strategy planning, system integration, and application service provider based on five types of business-to-business electronic commerce. (author)

Equatorial Geodesics Around the Magnetars

Science.gov (United States)

Alfradique, Viviane A. P.; Troconis, Orlenys N.; Negreiros, Rodrigo P.

Neutron stars manifest themselves as different classes of astrophysical sources that are associated to distinct phenomenology. Here we focus our attention on magnetars (or strongly magnetized neutron stars) that are associated to Soft Gamma Repeaters and Anomalous X-ray Pulsars. The magnetic field on surface of these objects, reaches values greater than 1015 G. Under intense magnetic fields, relativistic effects begin to be decisive for the definition of the structure and evolution of these objects. We are tempted to question ourselves to how strengths fields affect the structure of neutron star. In this work, our objective is study and compare two solutions of Einstein-Maxwell equations: the Bonnor solution, which is an analytical solution that describe the exterior spacetime for a massive compact object which has a magnetic field that is characterize as a dipole field and a complete solution that describe the interior and exterior spacetime for the same source found by numerical methods). For this, we describe the geodesic equations generated by such solutions. Our results show that the orbits generated by the Bonnor solution are the same as described by numerical solution. Also, show that the inclusion of magnetic fields with values up to 1017G in the center of the star does not modify sharply the particle orbits described around this star, so the use of Schwarzschild solution for the description of these orbits is a reasonable approximation.

Neutrino`s helicity in a gravitational field; Helicite des neutrinos dans un champ gravitationnel

Energy Technology Data Exchange (ETDEWEB)

Pansart, J.P.

1996-12-31

By using approximated solutions of Dirac`s equation, we show that there is no helicity reversal for light neutrinos in the Schwarzschild metric nor in an expanding universe. The actual coupling between a particle spin and the angular momentum of a heavy rotating body induces a possible helicity reversal but with an unobservable probability proportional to m{sup 2}{sub p} / E{sup 2}, where m{sub p} is the particle mass and E its energy. In these calculations, the helicity is defined through the spin orientation with respect to the current and not with respect to the linear momentum. This definition gives simple expressions and is equal to the usual definition in the case of a flat space. (N.T.). 10 refs.

A note on the Deser-Tekin charges

International Nuclear Information System (INIS)

Petrov, A N

2005-01-01

Perturbed equations for an arbitrary metric theory of gravity in D dimensions are constructed in the vacuum of this theory. The nonlinear part together with matter fields are a source for the linear part and are treated as a total energy-momentum tensor. A generalized family of conserved currents expressed through divergences of anti-symmetrical tensor densities (superpotentials) linear in perturbations is constructed. The new family generalizes the Deser and Tekin currents and superpotentials in quadratic curvature gravity theories generating Killing charges in dS and AdS vacua. As an example, the mass of a D-dimensional Schwarzschild black hole in an effective AdS spacetime (a solution in the Einstein-Gauss-Bonnet theory) is examined. (letter to the editor)

Inside oscillatons

International Nuclear Information System (INIS)

Urena-Lopez, L Arturo; Matos, Tonatiuh; Becerril, Ricardo

2002-01-01

Non-singular self-gravitating objects can be found by solving the coupled Einstein-Klein-Gordon (EKG) equations for a real scalar field. Such objects are generically known as oscillatons, in which the scalar field and the metric are fully time-dependent. In this paper, we describe a numerical procedure to minimize the nonlinearities present in the EKG equations, in the case of spherical symmetry, which permits us to find accurate numerical solutions. In order to gain physical insight of relativistic oscillatons, we study oscillatons in flat space, in the weak field limit, the so-called Newtonian oscillatons, using a fixed Schwarzschild background. This last case may be related to the ejected scalar field during a gravitational collapse of scalar field configurations

The algebraic-hyperbolic approach to the linearized gravitational constraints on a Minkowski background

International Nuclear Information System (INIS)

Winicour, Jeffrey

2017-01-01

An algebraic-hyperbolic method for solving the Hamiltonian and momentum constraints has recently been shown to be well posed for general nonlinear perturbations of the initial data for a Schwarzschild black hole. This is a new approach to solving the constraints of Einstein’s equations which does not involve elliptic equations and has potential importance for the construction of binary black hole data. In order to shed light on the underpinnings of this approach, we consider its application to obtain solutions of the constraints for linearized perturbations of Minkowski space. In that case, we find the surprising result that there are no suitable Cauchy hypersurfaces in Minkowski space for which the linearized algebraic-hyperbolic constraint problem is well posed. (note)

Charges in gravitational fields: From Fermi, via Hanni-Ruffini-Wheeler, to the 'electric Meissner effect'

Science.gov (United States)

Ruffini, R.

2004-07-01

Recent developments in obtaining a detailed model for gamma-ray bursts have shown the need for a deeper understanding of phenomena described by solutions of the Einstein-Maxwell equations, reviving interest in the behavior of charges close to a black hole. In particular a drastic difference has been found between the lines of force of a charged test particle in the fields of Schwarzschild and Reissner-Nordström black holes. This difference characterizes a general relativistic effect for the electric field of a charged test particle around a (charged) Reissner-Nordström black hole similar to the “Meissner effect” for a magnetic field around a superconductor. These new results are related to earlier work by Fermi and Hanni-Ruffini-Wheeler.

Remarks on a five-dimensional Kaluza-Klein theory of the massive Dirac monopole

International Nuclear Information System (INIS)

Cotaescu, Ion I.

2005-01-01

The Gross-Perry-Sorkin spacetime, formed by the Euclidean Taub-Newman-Unti-Tamburino space with the time trivially added, is the appropriate background of the Dirac magnetic monopole without an explicit mass term. We show that there exists a very simple five-dimensional metric of spacetimes carrying massive magnetic monopoles that is an exact solution of the vacuum Einstein equations. Moreover, the same isometry properties as the original Euclidean Taub-Newman-Unti-Tamburino space are preserved. This leads to an Abelian Kaluza-Klein theory whose metric appears as a combination between the Gross-Perry-Sorkin and Schwarzschild ones. The asymptotic motion of the scalar charged test particles is discussed, now by accounting for the mixing between the gravitational and magnetic effects

Solute-vacancy binding in aluminum

International Nuclear Information System (INIS)

Wolverton, C.

2007-01-01

Previous efforts to understand solute-vacancy binding in aluminum alloys have been hampered by a scarcity of reliable, quantitative experimental measurements. Here, we report a large database of solute-vacancy binding energies determined from first-principles density functional calculations. The calculated binding energies agree well with accurate measurements where available, and provide an accurate predictor of solute-vacancy binding in other systems. We find: (i) some common solutes in commercial Al alloys (e.g., Cu and Mg) possess either very weak (Cu), or even repulsive (Mg), binding energies. Hence, we assert that some previously reported large binding energies for these solutes are erroneous. (ii) Large binding energies are found for Sn, Cd and In, confirming the proposed mechanism for the reduced natural aging in Al-Cu alloys containing microalloying additions of these solutes. (iii) In addition, we predict that similar reduction in natural aging should occur with additions of Si, Ge and Au. (iv) Even larger binding energies are found for other solutes (e.g., Pb, Bi, Sr, Ba), but these solutes possess essentially no solubility in Al. (v) We have explored the physical effects controlling solute-vacancy binding in Al. We find that there is a strong correlation between binding energy and solute size, with larger solute atoms possessing a stronger binding with vacancies. (vi) Most transition-metal 3d solutes do not bind strongly with vacancies, and some are even energetically strongly repelled from vacancies, particularly for the early 3d solutes, Ti and V

Application of solution-mineral equilibrium chemistry to solution mining of uranium ores

International Nuclear Information System (INIS)

Riese, A.C.; Propp, C.J.

1980-01-01

Modern methods of uranium solution mining are typically accompanied by gains and losses of mass through reagent consumption by rock-forming minerals, with subsequent formation of clay minerals, gypsum, carbonates, and iron oxyhydroxides. A systematic approach to alleviate such problems involves the application of leach solutions that are in equilibrium with the host-rock minerals but in disequilibrium with the ore-forming minerals. This partial equilibrium can be approximated by solution-composition adjustments within the systems K 2 O-Al 2 O 3 SiO 2 -H 2 O and Na 2 O 3 -Al 2 O 3 SiO 2 -H 2 O. Uranium ore containing 0.15 percent U 3 O 8 from the Gulf Mineral Resources Corporation's Mariano Lake mine, the Smith Lake district of the Grants mineral belt, was collected for investigation. Presented are a theoretical evaluation of leachate data and an experimental treatment of the ore, which contained mainly K-feldspar, plagioclase feldspar, and quartz (with lesser amounts of micas, clay minerals, and organic carbonaceous material). Small-scale (less than or equal to 1 kg) column-leaching experiments were conducted to model the results of conventional leaching operations and to provide leachate solutions that could be compared with solutions calculated to be in equilibrium with the matrix minerals. Leach solutions employed include: 1) sulfuric acid, 2) sodium bicarbonate, and 3) sulfuric acid with 1.0 molal potassium chloride. The uranium concentrations in the sodium-bicarbonate leach solution and the acid-leach solution were about a gram per liter at the termination of the tests. However, the permeability of the ore in the acid leach was greatly reduced, owing to the formation of clay minerals. Uranium solubility in the leach column stabilized with the potassium-chloride solution was calculated from leachate compositions to be limited by the solubility of carnotite

Performance Evaluation of Absorbent Solution for Draw Solute Recovery in Forward Osmosis Desalination Process

International Nuclear Information System (INIS)

Kim, Young; Lee, Jong Hoon; Lee, Kong Hoon; Kim, Yu-Chang; Oh, Dong Wook; Lee, Jungho

2013-01-01

Although forward osmosis desalination technology has drawn substantial attention as a next-generation desalination method, the energy efficiency of its draw solution treatment process should be improved for its commercialization. When ammonium bicarbonate is used as the draw solute, the system consists of forward-osmosis membrane modules, draw solution separation and recovery processes. Mixed gases of ammonia and carbon dioxide generated during the draws solution separation, need to be recovered to re-concentrate ammonium bicarbonate solution, for continuous operation as well as for the economic feasibility. The diluted ammonium bicarbonate solution has been proposed as the absorbent for the draw solution regeneration. In this study, experiments are conducted to investigate performance and features of the absorption corresponding to absorbent concentration. It is concluded that ammonium bicarbonate solution can be used to recover the generated ammonia and carbon dioxide. The results will be applied to design and operation of pilot-scale forward-osmosis desalination system

Performance Evaluation of Absorbent Solution for Draw Solute Recovery in Forward Osmosis Desalination Process

Energy Technology Data Exchange (ETDEWEB)

Kim, Young; Lee, Jong Hoon; Lee, Kong Hoon; Kim, Yu-Chang; Oh, Dong Wook; Lee, Jungho [Korea Institute of Machinery Materials, Daejeon (Korea, Republic of)

2013-04-15

Although forward osmosis desalination technology has drawn substantial attention as a next-generation desalination method, the energy efficiency of its draw solution treatment process should be improved for its commercialization. When ammonium bicarbonate is used as the draw solute, the system consists of forward-osmosis membrane modules, draw solution separation and recovery processes. Mixed gases of ammonia and carbon dioxide generated during the draws solution separation, need to be recovered to re-concentrate ammonium bicarbonate solution, for continuous operation as well as for the economic feasibility. The diluted ammonium bicarbonate solution has been proposed as the absorbent for the draw solution regeneration. In this study, experiments are conducted to investigate performance and features of the absorption corresponding to absorbent concentration. It is concluded that ammonium bicarbonate solution can be used to recover the generated ammonia and carbon dioxide. The results will be applied to design and operation of pilot-scale forward-osmosis desalination system.

Whole analogy between Daniel Bernoulli solution and direct kinematics solution

Directory of Open Access Journals (Sweden)

Filipović Mirjana

2010-01-01

Full Text Available In this paper, the relationship between the original Euler-Bernoulli's rod equation and contemporary knowledge is established. The solution which Daniel Bernoulli defined for the simplest conditions is essentially the solution of 'direct kinematics'. For this reason, special attention is devoted to dynamics and kinematics of elastic mechanisms configuration. The Euler-Bernoulli equation and its solution (used in literature for a long time should be expanded according to the requirements of the mechanisms motion complexity. The elastic deformation is a dynamic value that depends on the total mechanism movements dynamics. Mathematical model of the actuators comprises also elasticity forces.

Gesammelte Werke / Collected Works

Science.gov (United States)

Schwarzschild, Karl; Voigt, Hans-Heinrich

Der bekannte Astronom Karl Schwarzschild (1873-1916) gilt als der Begründer der Astrophysik und als hervorragender Forscher mit einer erstaunlichen Bandbreite seiner Interessen. Arbeiten zur Himmelsmechanik, Elektrodynamik und Relativitätstheorie weisen ihn als vorzüglichen Mathematiker und Physiker auf der Höhe seiner Zeit aus. Untersuchungen zur Photographischen Photometrie, Optik und Spektroskopie zeigen den versierten Beobachter, der sein Meßinstrumentarium beherrscht, und schließlich arbeitete Schwarzschild als Astrophysiker an Sternatmosphären, Kometen, Struktur und Dynamik von Sternsystemen. Die in seinem kurzen Leben entstandene Fülle an wissenschaftlichen Arbeiten ist in drei Bänden der Gesamtausgabe gesammelt, ergänzt durch biographisches Material, Annotationen von Fachleuten und einen Essay des Nobelpreisträgers S. Chandrasekhar. The well-known astronomer Karl Schwarzschild (1873-1916) is regarded as the founder of astrophysics and as an exceptionally talented researcher whose interests spanned a remarkably broad spectrum. His work on celestial mechanics, electrodynamics, and relativity theory demonstrates his great abilities as a mathematician and physicist who significantly influenced the science of his times. His investigations of photographic photometry, optics, and spectroscopy display his strengths as an observer who knew his instruments. But above all Schwarzschild pursued questions of astrophysics, addressing in particular stellar atmospheres, comets, and the structure and dynamics of stellar systems. The host of scientific works that he authored in his short life is now collected in the form of this three-volume complete works; it is supplemented by biographical material, notes from some of todays experts, and an essay by the Nobel Laureate S. Chandrasekhar.

Voltage quality: solutions of desensitization; Qualite de la tension: les solutions de desensibilisation

Energy Technology Data Exchange (ETDEWEB)

Anon.

1999-10-01

The occurrence of voltage drops and cuts can lead to major malfunctions in electrical installations with sometimes important economical impacts. Thus, the use of solutions of desensitization are needed to avoid such disturbances. This technical paper gives a summary of the basic solutions elaborated by Electricite de France (EdF) with the participation of electrical engineering associations in order to solve the problems encountered in existing installations and to provide specifications for the newly designed installations: the desensitization process (origin of voltage drops, solutions, costs), the diagnosis of industrial installations (identification, quantitative analysis and recording of disturbances, complementary informations, causes, economical impact, solutions, costs, remedial action), the general and specific solutions of desensitization (instrumentation and control systems, switches, relays, motors, speed regulators and variators), specific solutions for computerized and electronic systems, and the role of batteries. (J.S.)

Application of solution-mineral equilibrium chemistry to solution mining of uranium ores

International Nuclear Information System (INIS)

Riese, A.C.; Popp, C.J.

1979-01-01

The tests described were undertaken to determine the extent to leach solution-rock interactions with uranium-bearing ore obtained from the Mariano Lake mine. Leach solutions of an acidic (H/sub 2/O/sub 4/-sulfuric acid) and basic (NaHCO/sub 3/-sodium bicarbonate) nature were tested, in addition to a leach solution containing potassium chloride and sulfuric acid (KCl/H/sub 2/SO/sub 4/). The latter solution was chosen in an attempt to equilibrate the aqueous phase with the rock-forming silicate minerals and minimize adverse effects such as clay formation, porosity loss, and lixiviant loss. 29 refs

Homogenization Theory for the Prediction of Obstructed Solute Diffusivity in Macromolecular Solutions.

Science.gov (United States)

Donovan, Preston; Chehreghanianzabi, Yasaman; Rathinam, Muruhan; Zustiak, Silviya Petrova

2016-01-01

The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models include parameters that are not readily measurable, are specific to the polymer-solute-solvent system, or are fitted and do not have a physical meaning. Here, for the first time, we develop a homogenization theory framework for the prediction of effective solute diffusivity in macromolecular environments based on physical parameters that are easily measurable and not specific to the macromolecule-solute-solvent system. Homogenization theory is useful for situations where knowledge of fine-scale parameters is used to predict bulk system behavior. As a first approximation, we focus on a model where the solute is subjected to obstructed diffusion via stationary spherical obstacles. We find that the homogenization theory results agree well with computationally more expensive Monte Carlo simulations. Moreover, the homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy. Lastly, we provide a mathematical formula for the effective diffusivity in terms of a non-dimensional and easily measurable geometric system parameter.

Homogenization Theory for the Prediction of Obstructed Solute Diffusivity in Macromolecular Solutions.

Directory of Open Access Journals (Sweden)

Preston Donovan

Full Text Available The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models include parameters that are not readily measurable, are specific to the polymer-solute-solvent system, or are fitted and do not have a physical meaning. Here, for the first time, we develop a homogenization theory framework for the prediction of effective solute diffusivity in macromolecular environments based on physical parameters that are easily measurable and not specific to the macromolecule-solute-solvent system. Homogenization theory is useful for situations where knowledge of fine-scale parameters is used to predict bulk system behavior. As a first approximation, we focus on a model where the solute is subjected to obstructed diffusion via stationary spherical obstacles. We find that the homogenization theory results agree well with computationally more expensive Monte Carlo simulations. Moreover, the homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy. Lastly, we provide a mathematical formula for the effective diffusivity in terms of a non-dimensional and easily measurable geometric system parameter.

Solutions for the food processing industry; Shokuhin seizogyo solution

Energy Technology Data Exchange (ETDEWEB)

Toda, T; Iwami, N [Fuji Electric Co. Ltd., Tokyo (Japan)

1999-09-10

To improve quality control and maintain stable operation, the food processing industry requires problem solutions in total, including not only processing and operation control divisions but also quality control, design and production technology, and maintenance divisions. This paper describes solutions for HACCP (hazard analysis critical control point) support, quality control, and maintenance, in order to improve the quality level, ensure traceability and realize stable processing operations. (author)

Influence of the cosmological constant on gravitational lensing in small systems

International Nuclear Information System (INIS)

Sereno, Mauro

2008-01-01

The cosmological constant Λ affects gravitational lensing phenomena. The contribution of Λ to the observable angular positions of multiple images and to their amplification and time delay is here computed through a study of the weak deflection limit of the equations of motion in the Schwarzschild-de Sitter metric. Because of Λ the unresolved images are slightly demagnified, the radius of the Einstein ring decreases, and the time delay increases. The effect is however negligible for near lenses. In the case of a null cosmological constant, we provide some updated results on lensing by a Schwarzschild black hole

Geodesics of black holes with dark energy

Science.gov (United States)

Ghaderi, K.

2017-12-01

Dark energy is the most popular hypothesis to explain recent observations suggesting that the world will increasingly expand. One of the models of dark energy is quintessence which is highly plausible. In this paper, we investigate the effect of dark energy on the null geodesics of Schwarzschild, Reissner-Nordström, Schwarzschild-de Sitter and Bardeen black holes. Using the definition of effective potential, the radius of the circular orbits, the period, the instability of the circular orbits, the force exerted on the photons and the deviation angle of light in quintessence field are calculated and the results are analyzed and discussed.

Passive House Solutions

Energy Technology Data Exchange (ETDEWEB)

Strom, I.; Joosten, L.; Boonstra, C. [DHV Sustainability Consultants, Eindhoiven (Netherlands)

2006-05-15

PEP stands for 'Promotion of European Passive Houses' and is a consortium of European partners, supported by the European Commission, Directorate General for Energy and Transport. In this working paper an overview is given of Passive House solutions. An inventory has been made of Passive House solutions for new build residences applied in each country. Based on this, the most common basic solutions have been identified and described in further detail, including the extent to which solutions are applied in common and best practice and expected barriers for the implementation in each country. An inventory per country is included in the appendix. The analysis of Passive House solutions in partner countries shows high priority with regard to the performance of the thermal envelope, such as high insulation of walls, roofs, floors and windows/ doors, thermal bridge-free construction and air tightness. Due to the required air tightness, special attention must be paid to indoor air quality through proper ventilation. Finally, efficient ((semi-)solar) heating systems for combined space and DHW heating still require a significant amount of attention in most partner countries. Other basic Passive House solutions show a smaller discrepancy with common practice and fewer barriers have been encountered in partner countries. In the next section, the general barriers in partner countries have been inventoried. For each type of barrier a suggested approach has been given. Most frequently encountered barriers in partner countries are: limited know-how; limited contractor skills; and acceptation of Passive Houses in the market. Based on the suggested approaches to overcoming barriers, this means that a great deal of attention must be paid to providing practical information and solutions to building professionals, providing practical training to installers and contractors and communication about the Passive House concept to the market.

Influence of container structures and content solutions on dispensing time of ophthalmic solutions

Directory of Open Access Journals (Sweden)

Keiji Yoshikawa

2010-05-01

Full Text Available Keiji Yoshikawa1, Hiroshi Yamada21Yoshikawa Eye Clinic, Tokyo, Japan; 2Santen Pharmaceutical Co., Ltd., Osaka, JapanPurpose: To investigate the influence of container structures and content solutions on the time of dispensing from eye dropper bottles.Methods: Eye dropper bottle models, solution models (filtrate water/surfactant solution and a dispensing time measuring apparatus were prepared to measure the dispensing time.Results: With filtrate water and pressure thrust load of 0.3 MPa, the dispensing time significantly increased from 1.1 ± 0.5 seconds to 4.6 ± 1.1 seconds depending on the decrease of inner aperture diameters from 0.4 mm to 0.2 mm (P < 0.0001. When using the bottle models with inner aperture diameters of 0.4 mm or larger, the dispensing time became constant. The dispensing time using surfactant solution showed the same tendency as above. When pressure thrust load was large (0.07 MPa, the solution flew out continuously with inner aperture diameters of 0.4 mm or larger and the dispensing time could not be measured. The inner aperture diameter most strongly explained the variation of the dispensing time in both the content solutions in the multiple linear regression analysis (filtrate water: 46%, R2 = 0.462, surfactant solution: 56%, R2 = 0.563.Conclusions: Among content solutions and container structures, the dispensing time was mostly influenced by the diameter of the inner aperture of bottles.Keywords: dispensing time, model eye dropper bottle, model ophthalmic solution, nozzle internal space volume, nozzle inner aperture diameter

Professional Hadoop solutions

CERN Document Server

Lublinsky, Boris; Yakubovich, Alexey

2013-01-01

The go-to guidebook for deploying Big Data solutions with Hadoop Today's enterprise architects need to understand how the Hadoop frameworks and APIs fit together, and how they can be integrated to deliver real-world solutions. This book is a practical, detailed guide to building and implementing those solutions, with code-level instruction in the popular Wrox tradition. It covers storing data with HDFS and Hbase, processing data with MapReduce, and automating data processing with Oozie. Hadoop security, running Hadoop with Amazon Web Services, best practices, and automating Hadoop processes i

Enhanced safeguards via solution monitoring

International Nuclear Information System (INIS)

Burr, T.; Wangen, L.

1996-09-01

Solution monitoring is defined as the essentially continuous monitoring of solution level, density, and temperature in all tanks in the process that contain, or could contain, safeguards-significant quantities of nuclear material. This report describes some of the enhancements that solution monitoring could make to international safeguards. The focus is on the quantifiable benefits of solution monitoring, but qualitatively, solution monitoring can be viewed as a form of surveillance. Quantitatively, solution monitoring can in some cases improve diversion detection probability. For example, the authors show that under certain assumptions, solution monitoring can be used to reduce the standard deviation of the annual material balance, σ MB , from approximately 17 kg to approximately 4 kg. Such reduction in σ MB will not always be possible, as they discuss. However, in all cases, solution monitoring would provide assurance that the measurement error models are adequate so that one has confidence in his estimate of σ MB . Some of the results in this report were generated using data that were simulated with prototype solution monitoring software that they are developing. An accompanying document describes that software

Siemens IT solutions for power sector

International Nuclear Information System (INIS)

Lunter, P.

2004-01-01

The cost reduction, flexibility and revenue increase, potential exploitation, productivity increase, and business opportunities exploitation - that is all what can be required in the races for the promonent positioning on the electricity power market. These requirements can be realized by the sophisticated IT solutions hand-tailored to the special requirements of the electric power producers and tradesmen. This approach makes it possible to achieve greater profit. Our solutions 'PROFIT Solutions', that are symbiosis of the most progressive information technologies and the power plant techniques of the company Siemens, satisfy submitted specifications in substantial measure. The system solutions 'PROFIT Solutions' comprise three solution groups: process, operation a business. The solutions of the group 'IT Process Solutions' increase flexibility and manoeuvrability of equipment, improve the efficiency and contribute to more economical operation of the power generation. Solutions 'IT Process Solutions' simplify and shorten the period of power cycles and conduce to higher labour productivity. Solutions group 'IT Process Solutions' approaches equipment to the market - supports the profit strategies, helps quickly and expertly to determine and predict hazards. The extension PROFIT Cockpit means the nuance to the solutions world 'PROFIT Solutions'. The survey about the whole installation is within reach at the simple touch of a button. It is possible to compile the total system part by part from single solutions 'PROFIT Solutions'. As a matter of fact all single parts can be interconnected with already existing solutions. Routines 'PROFIT Solutions' cooperate with all modern control systems. (author)

Classical solutions and extended supergravity

International Nuclear Information System (INIS)

de Alfaro, V.; Fubini, S.; Furlan, G.

1980-03-01

The existence and properties of classical solutions for gravity coupled to matter fields have been investigated previously with the limitation to conformally flat solutions. In the search for a guiding criterion to determine the form of the coupling among the fields, one is led to consider supersymmetric theories, and the question arises whether classical solutions persist in these models. It is found that a discrepancy persists between supergravity and standard meron solutions. Owing to the appearance of the scalar field, a new set of meron solutions exists for particular Lagrangian models. In conclusion, the form of solutions in Minkowski space is discussed

A class of black holes in dRGT massive gravity and their thermodynamical properties

Energy Technology Data Exchange (ETDEWEB)

Ghosh, Suchant G. [Jamia Millia Islamia, Centre of Theoretical Physics, New Delhi (India); University of Kwazulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, Private Bag 54001, Durban (South Africa); Tannukij, Lunchakorn [Mahidol University, Department of Physics, Faculty of Science, Bangkok (Thailand); Wongjun, Pitayuth [Naresuan University, The Institute for Fundamental Study, Phitsanulok (Thailand); Ministry of Education, Thailand Center of Excellence in Physics, Bangkok (Thailand)

2016-03-15

We present an exact spherical black hole solution in de Rham, Gabadadze, and Tolley (dRGT) massive gravity for a generic choice of the parameters in the theory, and also discuss the thermodynamical and phase structure of the black hole in both the grand canonical and the canonical ensembles (for the charged case). It turns out that the dRGT black hole solution includes other known solutions to the Einstein field equations, such as the monopole-de Sitter-Schwarzschild solution with the coefficients of the third and fourth terms in the potential and the graviton mass in massive gravity naturally generates the cosmological constant and the global monopole term. Furthermore, we compute the mass, temperature and entropy of the dRGT black hole, and also perform thermodynamical stability analysis. It turns out that the presence of the graviton mass completely changes the black hole thermodynamics, and it can provide the Hawking-Page phase transition which also occurs for the charged black holes. Interestingly, the entropy of a black hole is barely affected and still obeys the standard area law. In particular, our results, in the limit m{sub g} → 0, reduced exactly to the results of general relativity. (orig.)

Pitfall in quantum mechanical/molecular mechanical molecular dynamics simulation of small solutes in solution.

Science.gov (United States)

Hu, Hao; Liu, Haiyan

2013-05-30

Developments in computing hardware and algorithms have made direct molecular dynamics simulation with the combined quantum mechanical/molecular mechanical methods affordable for small solute molecules in solution, in which much improved accuracy can be obtained via the quantum mechanical treatment of the solute molecule and even sometimes water molecules in the first solvation shell. However, unlike the conventional molecular mechanical simulations of large molecules, e.g., proteins, in solutions, special care must be taken in the technical details of the simulation, including the thermostat of the solute/solvent system, so that the conformational space of the solute molecules can be properly sampled. We show here that the common setup for classical molecular mechanical molecular dynamics simulations, such as the Berendsen or single Nose-Hoover thermostat, and/or rigid water models could lead to pathological sampling of the solutes' conformation. In the extreme example of a methanol molecule in aqueous solution, improper and sluggish setups could generate two peaks in the distribution of the O-H bond length. We discuss the factors responsible for this somewhat unexpected result and evoke a simple and ancient technical fix-up to resolve this problem.

Semianalytical Solutions of Radioactive or Reactive Transport in Variably-Fractured Layered Media: 1. Solutes

International Nuclear Information System (INIS)

George J. Moridis

2001-01-01

In this paper, semianalytical solutions are developed for the problem of transport of radioactive or reactive solute tracers through a layered system of heterogeneous fractured media with misaligned fractures. The tracer transport equations in the non-flowing matrix account for (a) diffusion, (b) surface diffusion, (c) mass transfer between the mobile and immobile water fractions, (d) linear kinetic or equilibrium physical, chemical, or combined solute sorption or colloid filtration, and (e) radioactive decay or first-order chemical reactions. The tracer-transport equations in the fractures account for the same processes, in addition to advection and hydrodynamic dispersion. Any number of radioactive decay daughter products (or products of a linear, first-order reaction chain) can be tracked. The solutions, which are analytical in the Laplace space, are numerically inverted to provide the solution in time and can accommodate any number of fractured and/or porous layers. The solutions are verified using analytical solutions for limiting cases of solute and colloid transport through fractured and porous media. The effect of important parameters on the transport of 3 H, 237 Np and 239 Pu (and its daughters) is investigated in several test problems involving layered geological systems of varying complexity

Solution chemistry and separation of metal ions in leached solution

International Nuclear Information System (INIS)

Shibata, J.

1991-01-01

The method to presume a dissolved state of metal ions in an aqueous solution and the technology to separate and concentrate metal ions in a leached solution are described in this paper. It is very important for the separation of metal ions to know the dissolved state of metal ions. If we know the composition of an aqueous solution and the stability constants of metal-ligand complexes, we can calculate and estimate the concentration of each species in the solution. Then, we can decide the policy to separate and concentrate metal ions. There are several methods for separation and purification; hydroxide precipitation method, sulfide precipitation method, solvent extraction method and ion exchange resin method. Solvent extraction has been used in purification processes of copper refinery, uranium refinery, platinum metal refinery and rare earth metal refinery. Fundamental process of solvent extraction, a kind of commercial extractants, a way of determining a suitable extractant and an equipment are discussed. Finally, it will be emphasized how the separation of rare earths is improved in solvent extraction. (author) 21 figs., 8 tabs., 8 refs

Stationary black holes: large D analysis

International Nuclear Information System (INIS)

Suzuki, Ryotaku; Tanabe, Kentaro

2015-01-01

We consider the effective theory of large D stationary black holes. By solving the Einstein equations with a cosmological constant using the 1/D expansion in near zone of the black hole we obtain the effective equation for the stationary black hole. The effective equation describes the Myers-Perry black hole, bumpy black holes and, possibly, the black ring solution as its solutions. In this effective theory the black hole is represented as an embedded membrane in the background, e.g., Minkowski or Anti-de Sitter spacetime and its mean curvature is given by the surface gravity redshifted by the background gravitational field and the local Lorentz boost. The local Lorentz boost property of the effective equation is observed also in the metric itself. In fact we show that the leading order metric of the Einstein equation in the 1/D expansion is generically regarded as a Lorentz boosted Schwarzschild black hole. We apply this Lorentz boost property of the stationary black hole solution to solve perturbation equations. As a result we obtain an analytic formula for quasinormal modes of the singly rotating Myers-Perry black hole in the 1/D expansion.

Extended DBI massive gravity with generalized fiducial metric

Science.gov (United States)

Chullaphan, Tossaporn; Tannukij, Lunchakorn; Wongjun, Pitayuth

2015-06-01

We consider an extended model of DBI massive gravity by generalizing the fiducial metric to be an induced metric on the brane corresponding to a domain wall moving in five-dimensional Schwarzschild-Anti-de Sitter spacetime. The model admits all solutions of FLRW metric including flat, closed and open geometries while the original one does not. The background solutions can be divided into two branches namely self-accelerating branch and normal branch. For the self-accelerating branch, the graviton mass plays the role of cosmological constant to drive the late-time acceleration of the universe. It is found that the number degrees of freedom of gravitational sector is not correct similar to the original DBI massive gravity. There are only two propagating degrees of freedom from tensor modes. For normal branch, we restrict our attention to a particular class of the solutions which provides an accelerated expansion of the universe. It is found that the number of degrees of freedom in the model is correct. However, at least one of them is ghost degree of freedom which always present at small scale implying that the theory is not stable.

Extended DBI massive gravity with generalized fiducial metric

International Nuclear Information System (INIS)

Chullaphan, Tossaporn; Tannukij, Lunchakorn; Wongjun, Pitayuth

2015-01-01

We consider an extended model of DBI massive gravity by generalizing the fiducial metric to be an induced metric on the brane corresponding to a domain wall moving in five-dimensional Schwarzschild-Anti-de Sitter spacetime. The model admits all solutions of FLRW metric including flat, closed and open geometries while the original one does not. The background solutions can be divided into two branches namely self-accelerating branch and normal branch. For the self-accelerating branch, the graviton mass plays the role of cosmological constant to drive the late-time acceleration of the universe. It is found that the number degrees of freedom of gravitational sector is not correct similar to the original DBI massive gravity. There are only two propagating degrees of freedom from tensor modes. For normal branch, we restrict our attention to a particular class of the solutions which provides an accelerated expansion of the universe. It is found that the number of degrees of freedom in the model is correct. However, at least one of them is ghost degree of freedom which always present at small scale implying that the theory is not stable.

Some new radiating Kerr-Newman solutions

International Nuclear Information System (INIS)

Patel, L.K.; Singh, Tajinder; Koppar, S.S.

1991-01-01

Three exact non-static solutions of Einstein-Maxwell equations corresponding to a field of flowing null radiation plus an electromagnetic field are presented. These solutions are non-static generalizations of the well known Kerr-Newman solution. The current vector is null in all the three solutions. These solutions are the electromagnetic generalizations of the three generalized radiating Kerr solutions discussed by Vaidya and Patel. The solutions discussed here describe the exterior gravitational fields of rotating radiating charged bodies. Many known solutions are derived as particular cases. (author). 12 refs

Technetium recovery from high alkaline solution

Energy Technology Data Exchange (ETDEWEB)

Nash, Charles A.

2016-07-12

Disclosed are methods for recovering technetium from a highly alkaline solution. The highly alkaline solution can be a liquid waste solution from a nuclear waste processing system. Methods can include combining the solution with a reductant capable of reducing technetium at the high pH of the solution and adding to or forming in the solution an adsorbent capable of adsorbing the precipitated technetium at the high pH of the solution.

Existence of Periodic Solutions and Stability of Zero Solution of a Mathematical Model of Schistosomiasis

Directory of Open Access Journals (Sweden)

Lin Li

2014-01-01

Full Text Available A mathematical model on schistosomiasis governed by periodic differential equations with a time delay was studied. By discussing boundedness of the solutions of this model and construction of a monotonic sequence, the existence of positive periodic solution was shown. The conditions under which the model admits a periodic solution and the conditions under which the zero solution is globally stable are given, respectively. Some numerical analyses show the conditional coexistence of locally stable zero solution and periodic solutions and that it is an effective treatment by simply reducing the population of snails and enlarging the death ratio of snails for the control of schistosomiasis.

Prediction of thermodynamic properties of solute elements in Si solutions using first-principles calculations

International Nuclear Information System (INIS)

Iwata, K.; Matsumiya, T.; Sawada, H.; Kawakami, K.

2003-01-01

The method is presented to predict the activity coefficients and the interaction parameters of the solute elements in infinite dilute Si solutions by the use of first-principles calculations based on density functional theory. In this method, the regular solution model is assumed. The calculated activity coefficients in solid Si are converted to those in molten Si by the use of the solid-liquid partition coefficients. Furthermore, the interaction parameters in solid Si solutions are calculated and compared with reported experimental values of those in liquid Si solutions. The results show that the calculated activity coefficients and interaction parameters of Al, Fe, Ti and Pb in Si solutions are in good agreement with the tendency of the experiments. However, the calculations have some quantitative discrepancy from the experiments. It is expected that consideration of the excess entropy would reduce this discrepancy

PERVASIVE BUSINESS INTELLIGENCE SOLUTIONS

Directory of Open Access Journals (Sweden)

Rocsana Tonis (Bucea-Manea

2011-03-01

Full Text Available The utility of BI solutions is accepted all over the world in the modern organizations. However, the BI solutions do not offer a constant feedback in line with the organizational activities. In this context, there have been developed pervasive BI solutions which are present at different levels of the organization, so that employees can observe only what is most relevant to their day-to-day tasks. They are organized in vertical silos, with clearly identified performance and expectations. The paper emphasizes the role of pervasive BI solutions in reaching the key performance indicators of the modern organizations, more important in the context of crisis.

Electrical Conductivity and Chemical Composition of Soil Solution: Comparison of Solution Samplers in Tropical Soils

Directory of Open Access Journals (Sweden)

Davi Lopes do Carmo

2016-01-01

Full Text Available ABSTRACT Soil solution samplers may have the same working principle, but they differ in relation to chemical and physical characteristics, cost and handling, and these aspects exert influence on the chemical composition of the soil solution obtained. This study was carried out to evaluate, over time, the chemical composition of solutions extracted by Suolo Acqua, with the hydrophilic membrane (HM as a standard, using soils with contrasting characteristics, and to determine the relationship between electrical conductivity (EC and concentration of ions and pH of soil solution samples. This study was carried out under laboratory conditions, using three soils samples with different clay and organic matter (OM contents. Soil solution contents of F−, Cl−, NO−3, Br−, SO42−, Na+, NH4+, K+, Mg2+, Ca2+, were analyzed, as well as inorganic, organic, and total C contents, pH, and EC, in four successive sampling times. Soil solution chemical composition extracted by the Suolo Acqua sampler is similar to that collected by the HM, but the Suolo Acqua extracted more Na+ and soluble organic C than the HM solution. Solution EC, cation and anion concentrations, and soluble C levels are higher in the soil with greater clay and OM contents (Latossolo and Cambissolo in this case. Soil solution composition varied over time, with considerable changes in pH, EC, and nutrient concentrations, especially associated with soil OM. Thus, single and isolated sampling of the soil solution must be avoided, otherwise composition of the soil solution may not be correctly evaluated. Soil solution EC was regulated by pH, as well as the sum of cation and anion concentrations, and the C contents determined in the soil liquid phase.

Weak solutions of magma equations

International Nuclear Information System (INIS)

Krishnan, E.V.

1999-01-01

Periodic solutions in terms of Jacobian cosine elliptic functions have been obtained for a set of values of two physical parameters for the magma equation which do not reduce to solitary-wave solutions. It was also obtained solitary-wave solutions for another set of these parameters as an infinite period limit of periodic solutions in terms of Weierstrass and Jacobian elliptic functions

AdS solutions through transgression

International Nuclear Information System (INIS)

Donos, Aristomenis; Gauntlett, Jerome P.; Kim, Nakwoo

2008-01-01

We present new classes of explicit supersymmetric AdS 3 solutions of type IIB supergravity with non-vanishing five-form flux and AdS 2 solutions of D = 11 supergravity with electric four-form flux. The former are dual to two-dimensional SCFTs with (0,2) supersymmetry and the latter to supersymmetric quantum mechanics with two supercharges. We also investigate more general classes of AdS 3 solutions of type IIB supergravity and AdS 2 solutions of D = 11 supergravity which in addition have non-vanishing three-form flux and magnetic four-form flux, respectively. The construction of these more general solutions makes essential use of the Chern-Simons or 'transgression' terms in the Bianchi identity or the equation of motion of the field strengths in the supergravity theories. We construct infinite new classes of explicit examples and for some of the type IIB solutions determine the central charge of the dual SCFTs. The type IIB solutions with non-vanishing three-form flux that we construct include a two-torus, and after two T-dualities and an S-duality, we obtain new AdS 3 solutions with only the NS fields being non-trivial.

Logical gaps in the approximate solutions of the social learning game and an exact solution.

Science.gov (United States)

Dai, Wenjie; Wang, Xin; Di, Zengru; Wu, Jinshan

2014-01-01

After the social learning models were proposed, finding solutions to the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built either upon an ad-hoc argument or a twisted Bayesian analysis of the games. Here, we present logical gaps in those solutions and offer an exact solution of our own. We also introduce a minor extension to the original game so that not only logical differences but also differences in action outcomes among those solutions become visible.

Effects of solution volume on hydrogen production by pulsed spark discharge in ethanol solution

Energy Technology Data Exchange (ETDEWEB)

Xin, Y. B.; Sun, B., E-mail: sunb88@dlmu.edu.cn; Zhu, X. M.; Yan, Z. Y.; Liu, H.; Liu, Y. J. [College of Environmental Science and Engineering, Dalian Maritime University, Dalian 116026 (China)

2016-07-15

Hydrogen production from ethanol solution (ethanol/water) by pulsed spark discharge was optimized by varying the volume of ethanol solution (liquid volume). Hydrogen yield was initially increased and then decreased with the increase in solution volume, which achieved 1.5 l/min with a solution volume of 500 ml. The characteristics of pulsed spark discharge were studied in this work; the results showed that the intensity of peak current, the rate of current rise, and energy efficiency of hydrogen production can be changed by varying the volume of ethanol solution. Meanwhile, the mechanism analysis of hydrogen production was accomplished by monitoring the process of hydrogen production and the state of free radicals. The analysis showed that decreasing the retention time of gas production and properly increasing the volume of ethanol solution can enhance the hydrogen yield. Through this research, a high-yield and large-scale method of hydrogen production can be achieved, which is more suitable for industrial application.

On the generation of magnetostatic solutions from gravitational two-soliton solutions of a stationary mass

Energy Technology Data Exchange (ETDEWEB)

Chaudhuri, A. [B.K.C. College, Department of Physics, Kolkata (India); Chaudhuri, S. [University of Burdwan, Department of Physics, Burdwan (India)

2017-11-15

In the paper, magnetostatic solutions of the Einstein-Maxwell field equations are generated from the gravitational two-soliton solutions of a stationary mass. Using the soliton technique of Belinskii and Zakharov (Sov Phys JETP 48:985, 1978, Sov Phys JETP 50:1, 1979), we construct diagonal two-soliton solutions of Einstein's gravitational field equations for an axially symmetric stationary space-time and investigate some properties of the generated stationary gravitational metric. Magnetostatic solutions corresponding to the generated stationary gravitational solutions are then constructed using the transformation technique of Das and Chaudhuri (Pramana J Phys 40:277, 1993). The mass and the dipole moment of the source are evaluated. In our analysis we make use of a second transformation (Chaudhuri in Pramana J Phys 58:449, 2002), probably for the first time in the literature, to generate magnetostatic solutions from the stationary gravitational two-soliton solutions which give us simple and straightforward expressions for the mass and the magnetic dipole moment. (orig.)

Karl Schwarzschild Lecture: The Ups and Downs of the Hubble Constant (With 12 Figures)

Science.gov (United States)

Tammann, G. Andreas

2006-01-01

A brief history of the determination of the Hubble constant H_0 is given. Early attempts following Lemaitre (1927) gave much too high values due to errors of the magnitude scale, Malmquist bias and calibration problems. By 1962 most authors agreed that 75< H_0 <130. After 1975 a dichotomy arose with values near 100 and others around 55. The former came from apparent-magnitude-limited samples and were affected by Malmquist bias. New distance indicators were introduced; they were sometimes claimed to yield high values of H_0, but the most recent data lead to H_0 in the 60's, yet with remaining difficulties as to the zero-point of the respective distance indicators. SNe Ia with their large range and very small luminosity dispersion (avoiding Malmquist bias) offer a unique opportunity to determine the large-scale value of H_0. Their maximum luminosity can be well calibrated from 10 SNe Ia in local parent galaxies whose Cepheids have been observed with HST. An unforeseen difficulty - affecting all Cepheid distances - is that their P-L relation varies from galaxy to galaxy, presumably in function of metallicity. A proposed solution is summarized here. The conclusion is that H_0 = 63.2 +/- 1.3 (random) +/- 5.3 (systematic) on all scales. The expansion age becomes then (with Omega_m=0.3, Omega_Lambda=0.7) 15.1 Gyr.

Isolated effects of external bath osmolality, solute concentration, and electrical charge on solute transport across articular cartilage.

Science.gov (United States)

Pouran, Behdad; Arbabi, Vahid; Zadpoor, Amir A; Weinans, Harrie

2016-12-01

The metabolic function of cartilage primarily depends on transport of solutes through diffusion mechanism. In the current study, we use contrast enhanced micro-computed tomography to determine equilibrium concentration of solutes through different cartilage zones and solute flux in the cartilage, using osteochondral plugs from equine femoral condyles. Diffusion experiments were performed with two solutes of different charge and approximately equal molecular weight, namely iodixanol (neutral) and ioxaglate (charge=-1) in order to isolate the effects of solute's charge on diffusion. Furthermore, solute concentrations as well as bath osmolality were changed to isolate the effects of steric hindrance on diffusion. Bath concentration and bath osmolality only had minor effects on the diffusion of the neutral solute through cartilage at the surface, middle and deep zones, indicating that the diffusion of the neutral solute was mainly Fickian. The negatively charged solute diffused considerably slower through cartilage than the neutral solute, indicating a large non-Fickian contribution in the diffusion of charged molecules. The numerical models determined maximum solute flux in the superficial zone up to a factor of 2.5 lower for the negatively charged solutes (charge=-1) as compared to the neutral solutes confirming the importance of charge-matrix interaction in diffusion of molecules across cartilage. Copyright © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

Solution behavior of metoclopramide in aqueous-alcoholic solutions at 30°C

Science.gov (United States)

Deosarkar, S. D.; Sawale, R. T.; Tawde, P. D.; Kalyankar, T. M.

2016-07-01

Densities (ρ) and refractive indices ( n D) of solutions of antiemetic drug metoclopramide (4-amino-5-chloro- N-(2-(diethylamino)ethyl)-2-methoxybenzamide hydrochloride hydrate) in methanolwater and ethanol-water mixtures of different compositions were measured at 30°C. Apparent molar volume (φv) of the drug was calculated from density data and partial molar volumes (φ v 0 ) were determined from Massons relation. Concentration dependence of nD has been studied to determine refractive indices of solution at infinite dilution ( n D 0 ). Results have been interpreted in terms of solute-solvent interactions.

Gauge unification of basic forces particularly of gravitation with strong interactions

International Nuclear Information System (INIS)

Salam, A.

1977-01-01

Corresponding to the two known types of gauge theories, Yang-Mills with spin-one mediating particles and Einstein Weyl with spin-two mediating particles, it is speculated that two distinct gauge unifications of the basic forces appear to be taking place. One is the familiar Yang-Mills unification of weak and electromagnetic forces with the strong. The second is the less familiar gauge unification of gravitation with spin-two tensor-dominated aspects of strong interactions. It is proposed that there are strongly interacting spin-two strong gravitons obeying Einstein's equations, and their existence gives a clue to an understanding of the (partial) confinement of quarks, as well as of the concept of hadronic temperature, through the use of Schwarzschild de-Sitter-like partially confining solitonic solutions of the strong gravity Einstein equation

Evaluation of the optical cross talk level in the SiPMs adopted in ASTRI SST-2M Cherenkov Camera using EASIROC front-end electronics

International Nuclear Information System (INIS)

Impiombato, D; Giarrusso, S; Mineo, T; Agnetta, G; Biondo, B; Catalano, O; Gargano, C; Rosa, G La; Russo, F; Sottile, G; Belluso, M; Billotta, S; Bonanno, G; Garozzo, S; Marano, D; Romeo, G

2014-01-01

ASTRI (Astrofisica con Specchi a Tecnologia Replicante Italiana), is a flagship project of the Italian Ministry of Education, University and Research whose main goal is the design and construction of an end-to-end prototype of the Small Size of Telescopes of the Cherenkov Telescope Array. The prototype, named ASTRI SST-2M, will adopt a wide field dual mirror optical system in a Schwarzschild-Couder configuration to explore the VHE range of the electromagnetic spectrum. The camera at the focal plane is based on Silicon Photo-Multipliers detectors which is an innovative solution for the detection astronomical Cherenkov light. This contribution reports some preliminary results on the evaluation of the optical cross talk level among the SiPM pixels foreseen for the ASTRI SST-2M camera

Aplicação do cálculo tensorial em problemas fundamentais da gravitação

Directory of Open Access Journals (Sweden)

Paola Terezinha Seidel

2015-12-01

Full Text Available By the nineteenth century various scientists shared the view that the description of the universe was already completed. However, Einstein's Gravitation Theory showed that future truths of physics go beyond the decimal places of already established truths. In a not too distant past Einstein's theory contradicted the imaginative level of most scientists, however, is now present even in the calibration of Global Positioning Systems (GPS. The mathematical tools that supported Einstein’s study were tensors, these objects allowed to settle the relationship between geometry and matter described by Einstein's tensor. Building the tensors that composes Einstein's tensor is possible to obtain the solution for the black hole Schwarzschild type. Therefore, it is valid to use the software Maple and GRTensorII package to compare the analytical and computational results.

Einstein in matrix form exact derivation of the theory of special and general relativity without tensors

CERN Document Server

Ludyk, Günter

2013-01-01

This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einsteins theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the "Black Hole" phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.

Osmotic potential calculations of inorganic and organic aqueous solutions over wide solute concentration levels and temperatures

Energy Technology Data Exchange (ETDEWEB)

Cochrane, T. T., E-mail: agteca@hotmail.com [AGTECA S.A., 230 Oceanbeach Road, Mount Maunganui, Tauranga 3116 (New Zealand); Cochrane, T. A., E-mail: tom.cochrane@canterbury.ac.nz [Department of Civil and Natural Resources Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140 (New Zealand)

2016-01-15

Purpose: To demonstrate that the authors’ new “aqueous solution vs pure water” equation to calculate osmotic potential may be used to calculate the osmotic potentials of inorganic and organic aqueous solutions over wide ranges of solute concentrations and temperatures. Currently, the osmotic potentials of solutions used for medical purposes are calculated from equations based on the thermodynamics of the gas laws which are only accurate at low temperature and solute concentration levels. Some solutions used in medicine may need their osmotic potentials calculated more accurately to take into account solute concentrations and temperatures. Methods: The authors experimented with their new equation for calculating the osmotic potentials of inorganic and organic aqueous solutions up to and beyond body temperatures by adjusting three of its factors; (a) the volume property of pure water, (b) the number of “free” water molecules per unit volume of solution, “N{sub f},” and (c) the “t” factor expressing the cooperative structural relaxation time of pure water at given temperatures. Adequate information on the volume property of pure water at different temperatures is available in the literature. However, as little information on the relative densities of inorganic and organic solutions, respectively, at varying temperatures needed to calculate N{sub f} was available, provisional equations were formulated to approximate values. Those values together with tentative t values for different temperatures chosen from values calculated by different workers were substituted into the authors’ equation to demonstrate how osmotic potentials could be estimated over temperatures up to and beyond bodily temperatures. Results: The provisional equations formulated to calculate N{sub f}, the number of free water molecules per unit volume of inorganic and organic solute solutions, respectively, over wide concentration ranges compared well with the calculations of N{sub f

Osmotic potential calculations of inorganic and organic aqueous solutions over wide solute concentration levels and temperatures

International Nuclear Information System (INIS)

Cochrane, T. T.; Cochrane, T. A.

2016-01-01

Purpose: To demonstrate that the authors’ new “aqueous solution vs pure water” equation to calculate osmotic potential may be used to calculate the osmotic potentials of inorganic and organic aqueous solutions over wide ranges of solute concentrations and temperatures. Currently, the osmotic potentials of solutions used for medical purposes are calculated from equations based on the thermodynamics of the gas laws which are only accurate at low temperature and solute concentration levels. Some solutions used in medicine may need their osmotic potentials calculated more accurately to take into account solute concentrations and temperatures. Methods: The authors experimented with their new equation for calculating the osmotic potentials of inorganic and organic aqueous solutions up to and beyond body temperatures by adjusting three of its factors; (a) the volume property of pure water, (b) the number of “free” water molecules per unit volume of solution, “N f ,” and (c) the “t” factor expressing the cooperative structural relaxation time of pure water at given temperatures. Adequate information on the volume property of pure water at different temperatures is available in the literature. However, as little information on the relative densities of inorganic and organic solutions, respectively, at varying temperatures needed to calculate N f was available, provisional equations were formulated to approximate values. Those values together with tentative t values for different temperatures chosen from values calculated by different workers were substituted into the authors’ equation to demonstrate how osmotic potentials could be estimated over temperatures up to and beyond bodily temperatures. Results: The provisional equations formulated to calculate N f , the number of free water molecules per unit volume of inorganic and organic solute solutions, respectively, over wide concentration ranges compared well with the calculations of N f using recorded

Analytic solutions of hydrodynamics equations

International Nuclear Information System (INIS)

Coggeshall, S.V.

1991-01-01

Many similarity solutions have been found for the equations of one-dimensional (1-D) hydrodynamics. These special combinations of variables allow the partial differential equations to be reduced to ordinary differential equations, which must then be solved to determine the physical solutions. Usually, these reduced ordinary differential equations are solved numerically. In some cases it is possible to solve these reduced equations analytically to obtain explicit solutions. In this work a collection of analytic solutions of the 1-D hydrodynamics equations is presented. These can be used for a variety of purposes, including (i) numerical benchmark problems, (ii) as a basis for analytic models, and (iii) to provide insight into more complicated solutions

Solute diffusivity in undisturbed soil

DEFF Research Database (Denmark)

Lægdsmand, Mette; Møldrup, Per; Schjønning, Per

2012-01-01

Solute diffusivity in soil plays a major role in many important processes with relation to plant growth and environmental issues. Soil solute diffusivity is affected by the volumetric water content as well as the morphological characteristics of water-filled pores. The solute diffusivity in intact...

f(R) global monopole revisited

Energy Technology Data Exchange (ETDEWEB)

Carames, Thiago R.P.; Fabris, Julio C.; Belich, H. [Universidade Federal do Espirito Santo (UFES), Vitoria, ES (Brazil); Bezerra de Mello, E.R. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil)

2017-07-15

In this paper the f(R) global monopole is reexamined. We provide an exact solution for the modified field equations in the presence of a global monopole for regions outside its core, generalizing previous results. Additionally, we discuss some particular cases obtained from this solution. We consider a setup consisting of a possible Schwarzschild black hole that absorbs the topological defect, giving rise to a static black hole endowed with a monopole's charge. Besides, we demonstrate how the asymptotic behavior of the Higgs field far from the monopole's core is shaped by a class of spacetime metrics which includes the ones analyzed here. In order to assess the gravitational properties of this system, we analyze the geodesic motion of both massive and massless test particles moving in the vicinity of such configuration. For the material particles we set the requirements they have to obey in order to experience stable orbits. On the other hand, for the photons we investigate how their trajectories are affected by the gravitational field of this black hole. (orig.)

The Solar System According to General Relativity: The Sun's Space Breaking Meets the Asteroid Strip

Directory of Open Access Journals (Sweden)

Borissova L.

2010-04-01

Full Text Available This study deals with the exact solution of Einstein’s field equations for a sphere of incompressible liquid without the additional limitation initially introduced in 1916 by Schwarzschild, by which the space-time metric must have no singularities. The ob- tained exact solution is then applied to the Universe, the Sun, and the planets, by the assumption that these objects can be approximated as spheres of incompressible liq- uid. It is shown that gravitational collapse of such a sphere is permitted for an object whose characteristics (mass, density, and size are close to the Universe. Meanwhile, there is a spatial break associated with any of the mentioned stellar objects: the break is determined as the approaching to infinity of one of the spatial components of the metric tensor. In particular, the break of the Sun’s space meets the Asteroid strip, while Jupiter’s space break meets the Asteroid strip from the outer side. Also, the space breaks of Mercury, Venus, Earth, and Mars are located inside the Asteroid strip (inside the Sun’s space break.

Advection-dominated Inflow/Outflows from Evaporating Accretion Disks.

Science.gov (United States)

Turolla; Dullemond

2000-03-01

In this Letter we investigate the properties of advection-dominated accretion flows (ADAFs) fed by the evaporation of a Shakura-Sunyaev accretion disk (SSD). In our picture, the ADAF fills the central cavity evacuated by the SSD and extends beyond the transition radius into a coronal region. We find that, because of global angular momentum conservation, a significant fraction of the hot gas flows away from the black hole, forming a transsonic wind, unless the injection rate depends only weakly on radius (if r2sigma&d2;~r-xi, xiBernoulli number of the inflowing gas is negative if the transition radius is less, similar100 Schwarzschild radii, so matter falling into the hole is gravitationally bound. The ratio of inflowing to outflowing mass is approximately 1/2, so in these solutions the accretion rate is of the same order as in standard ADAFs and much larger than in advection-dominated inflow/outflow models. The possible relevance of evaporation-fed solutions to accretion flows in black hole X-ray binaries is briefly discussed.

Exact Solutions for Two Equation Hierarchies

International Nuclear Information System (INIS)

Song-Lin, Zhao; Da-Jun, Zhang; Jie, Ji

2010-01-01

Bilinear forms and double-Wronskian solutions are given for two hierarchies, the (2+1)-dimensional breaking Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy and the negative order AKNS hierarchy. According to some choices of the coefficient matrix in the Wronskian condition equation set, we obtain some kinds of solutions for these two hierarchies, such as solitons, Jordan block solutions, rational solutions, complexitons and mixed solutions. (general)

Thermodynamic stability of radioactivity standard solutions

International Nuclear Information System (INIS)

Iroulard, M.G.

2007-04-01

The basic requirement when preparing radioactivity standard solutions is to guarantee the concentration of a radionuclide or a radioelement, expressed in the form of activity concentration (Ac = A/m (Bq/g), with A: activity and m: mass of solution). Knowledge of the law of radioactive decay and the half-life of a radionuclide or radioelement makes it possible to determine the activity concentration at any time, and this must be confirmed subsequently by measurement. Furthermore, when radioactivity standard solutions are prepared, it is necessary to establish optimal conditions of thermodynamic stability of the standard solutions. Radioactivity standard solutions are prepared by metrology laboratories from original solutions obtained from a range of suppliers. These radioactivity standard solutions must enable preparation of liquid and/or solid radioactivity standard sources of which measurement by different methods can determine, at a given instant, the activity concentration of the radionuclide or radioelement present in the solution. There are a number of constraints associated with the preparation of such sources. Here only those that relate to the physical and chemical properties of the standard solution are considered, and therefore need to be taken into account when preparing a radioactivity standard solution. These issues are considered in this document in accordance with the following plan: - A first part devoted to the chemical properties of the solutions: - the solubilization media: ultra-pure water and acid media, - the carriers: concentration, oxidation state of the radioactive element and the carrier element. - A second part describing the methodology of the preparation, packaging and storage of standard solutions: - glass ampoules: the structure of glasses, the mechanisms of their dissolution, the sorption phenomenon at the solid-solution interface, - quartz ampoules, - cleaning and packaging: cleaning solutions, internal surface coatings and

Thermodynamic stability of radioactivity standard solutions

Energy Technology Data Exchange (ETDEWEB)

Iroulard, M.G

2007-04-15

The basic requirement when preparing radioactivity standard solutions is to guarantee the concentration of a radionuclide or a radioelement, expressed in the form of activity concentration (Ac = A/m (Bq/g), with A: activity and m: mass of solution). Knowledge of the law of radioactive decay and the half-life of a radionuclide or radioelement makes it possible to determine the activity concentration at any time, and this must be confirmed subsequently by measurement. Furthermore, when radioactivity standard solutions are prepared, it is necessary to establish optimal conditions of thermodynamic stability of the standard solutions. Radioactivity standard solutions are prepared by metrology laboratories from original solutions obtained from a range of suppliers. These radioactivity standard solutions must enable preparation of liquid and/or solid radioactivity standard sources of which measurement by different methods can determine, at a given instant, the activity concentration of the radionuclide or radioelement present in the solution. There are a number of constraints associated with the preparation of such sources. Here only those that relate to the physical and chemical properties of the standard solution are considered, and therefore need to be taken into account when preparing a radioactivity standard solution. These issues are considered in this document in accordance with the following plan: - A first part devoted to the chemical properties of the solutions: - the solubilization media: ultra-pure water and acid media, - the carriers: concentration, oxidation state of the radioactive element and the carrier element. - A second part describing the methodology of the preparation, packaging and storage of standard solutions: - glass ampoules: the structure of glasses, the mechanisms of their dissolution, the sorption phenomenon at the solid-solution interface, - quartz ampoules, - cleaning and packaging: cleaning solutions, internal surface coatings and

Influence of thermal treatment on bentonite used as adsorbent for Cd, Pb, Zn retention from mono-solute and poly-solute aqueous solutions

Directory of Open Access Journals (Sweden)

Susana Yamila Martinez Stagnaro

2012-08-01

Full Text Available The retentions of Zn, Cd and Pb cations by one treated bentonite up to 750 °C were analyzed. The retentions were evaluated by using mono-and poly-solute aqueous solutions of such cations. The adsorptions were carried out in batch system at room temperature. The solid/liquid ratio was 2% wt.v-1. The solids were characterized by X-ray diffraction, thermal and chemical analyses. The Zn cation from mono- or polysolute-solutions was retained in higher amount than Cd and Pb cations in similar solution types by bentonite. The retentions were effective up to 450 °C calcined bentonite, after that, the retention capacity decreased in concordance with dehydroxylation of the structure of clay minerals.

Colliding black hole solution

International Nuclear Information System (INIS)

Ahmed, Mainuddin

2005-01-01

A new solution of Einstein equation in general relativity is found. This solution solves an outstanding problem of thermodynamics and black hole physics. Also this work appears to conclude the interpretation of NUT spacetime. (author)

Superstrings fermionic solutions

International Nuclear Information System (INIS)

Rausch de Traubenberg, M.

1990-06-01

The solutions proposed by the superstring theory are classified and compared. In order to obtain some of the equivalences, the demonstration is based on the coincidence of the excitation spectrum and the quantum numbers from different states. The fermionic representation of the heterotical strings is discussed. The conformal invariance and the supersymmetric results extended to two dimensions are investigated. Concerning the fermionic strings, the formalism and a phenomenological solution involving three families of quarks, chiral leptons and leptons from the E 6 gauge group are presented. The equivalence between real and complex fermions is discussed. The similarity between some of the solutions of the Wess-Zumino-Witten model and the orbifolds is considered. The formal calculation program developed for reproducing the theory's low energy spectra, in the fermionic string formalism is given [fr

Quasi-exact solutions of nonlinear differential equations

OpenAIRE

Kudryashov, Nikolay A.; Kochanov, Mark B.

2014-01-01

The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters of differential equation. These solutions are approximate solutions of nonlinear differential equations but they are close to exact solutions. Quasi-exact solutions of the the Kuramoto--Sivashinsky, the Korteweg--de Vries--Burgers and the Kawahara equations are founded.

ERP SOLUTIONS FOR SMEs

Directory of Open Access Journals (Sweden)

TUTUNEA MIHAELA FILOFTEIA

2012-09-01

Full Text Available The integration of activities, the business processes as well as their optimization, bring the perspective of profitable growth and create significant and competitive advantages in any company. The adoption of some ERP integrated software solutions, from SMEs’ perspective, must be considered as a very important management decision in medium and long term. ERP solutions, along with the transparent and optimized management of all internal processes, also offer an intra and inter companies collaborative platform, which allows a rapid expansion of activities towards e- business and mobile-business environments. This material introduces ERP solutions for SMEs from commercial offer and open source perspective; the results of comparative analysis of the solutions on the specific market, can be an useful aid to the management of the companies, in making the decision to integrate business processes, using ERP as a support.

Structure and dynamics of solutions

CERN Document Server

Ohtaki, H

2013-01-01

Recent advances in the study of structural and dynamic properties of solutions have provided a molecular picture of solute-solvent interactions. Although the study of thermodynamic as well as electronic properties of solutions have played a role in the development of research on the rate and mechanism of chemical reactions, such macroscopic and microscopic properties are insufficient for a deeper understanding of fast chemical and biological reactions. In order to fill the gap between the two extremes, it is necessary to know how molecules are arranged in solution and how they change their pos

The Black Hole in the Most Massive Ultracompact Dwarf Galaxy M59-UCD3

Science.gov (United States)

Ahn, Christopher P.; Seth, Anil C.; Cappellari, Michele; Krajnović, Davor; Strader, Jay; Voggel, Karina T.; Walsh, Jonelle L.; Bahramian, Arash; Baumgardt, Holger; Brodie, Jean; Chilingarian, Igor; Chomiuk, Laura; den Brok, Mark; Frank, Matthias; Hilker, Michael; McDermid, Richard M.; Mieske, Steffen; Neumayer, Nadine; Nguyen, Dieu D.; Pechetti, Renuka; Romanowsky, Aaron J.; Spitler, Lee

2018-05-01

We examine the internal properties of the most massive ultracompact dwarf galaxy (UCD), M59-UCD3, by combining adaptive-optics-assisted near-IR integral field spectroscopy from Gemini/NIFS and Hubble Space Telescope (HST) imaging. We use the multiband HST imaging to create a mass model that suggests and accounts for the presence of multiple stellar populations and structural components. We combine these mass models with kinematics measurements from Gemini/NIFS to find a best-fit stellar mass-to-light ratio (M/L) and black hole (BH) mass using Jeans anisotropic models (JAMs), axisymmetric Schwarzschild models, and triaxial Schwarzschild models. The best-fit parameters in the JAM and axisymmetric Schwarzschild models have BHs between 2.5 and 5.9 million solar masses. The triaxial Schwarzschild models point toward a similar BH mass but show a minimum χ 2 at a BH mass of ∼0. Models with a BH in all three techniques provide better fits to the central V rms profiles, and thus we estimate the BH mass to be {4.2}-1.7+2.1× {10}6 M ⊙ (estimated 1σ uncertainties). We also present deep radio imaging of M59-UCD3 and two other UCDs in Virgo with dynamical BH mass measurements, and we compare these to X-ray measurements to check for consistency with the fundamental plane of BH accretion. We detect faint radio emission in M59cO but find only upper limits for M60-UCD1 and M59-UCD3 despite X-ray detections in both these sources. The BH mass and nuclear light profile of M59-UCD3 suggest that it is the tidally stripped remnant of a ∼109–1010 M ⊙ galaxy.

Modified Bateman solution for identical eigenvalues

International Nuclear Information System (INIS)

Dreher, Raymond

2013-01-01

Highlights: ► Solving indeterminacies due to identical eigenvalues in Bateman’s solution. ► Exact analytical solution of Bateman’s equations for identical eigenvalues. ► Algorithm calculating higher order derivatives appearing in this solution. ► Alternative evaluation of the derivatives through the Taylor polynomial. ► Implementation of an example program demonstrating the developed solution. - Abstract: In this paper we develop a general solution to the Bateman equations taking into account the special case of identical eigenvalues. A characteristic of this new solution is the presence of higher order derivatives. It is shown that the derivatives can be obtained analytically and also computed in an efficient manner

Solution microcalorimeter for measuring heats of solution of radioactive elements and compounds

International Nuclear Information System (INIS)

Raschella, D.L.

1978-12-01

The microcalorimeter vessel is constructed of tantalum metal, with a nominal volume of 5 cm 3 . Its energy equivalent is 24 J K -1 when containing 5 cm 3 H 2 O. The thermal leakage modulus is 0.010 min -1 . A thermistor is employed as the temperature sensor. The operating sensitivity is about 1 x 10 -5 K (300 μJ). The performance of the calorimetry system was tested using tris(hydroxymethyl)aminomethane (TRIS) and magnesium metal. The results of the TRIS experiments, at a concentration of 1 g dm -3 in 0.1 N HCl at 298 K, yielded a heat of solution of -29.606 +- 0.063 kJ mol -1 . The magnesium experiments, in 1 N HCl at 298 K, gave a heat of solution of -465.965 +- 1.136 kJ mol -1 . The heat of solution of curium-248 metal in 1 N HCl at 298 K was measured. The experiments, which should not be considered definitive, yielded a heat of solution of -606.4 +- 1.8 kJ mol -1 . A single measurement in 6 N HCl gave a heat of solution of -602.3 kJ mol -1 . From these results the heat of formation of Cm 3+ /sub (aq)/ is calculated to be -607.2 +- 2.5 kJ mol -1

Radiolysis of Aqueous Toluene Solutions

International Nuclear Information System (INIS)

Christensen, H.C.; Gustafson, R.

1971-04-01

Aqueous toluene solutions have been irradiated with Co γ-rays. In unbuffered solutions the various cresol isomers are formed in a total yield of 0.45, 0.87 and 0.94 molecules/100 eV absorbed energy in argon-, N 2 O- and air - saturated solutions, respectively. The yields are reduced in acid (pH 3) solutions (G 0.14, 0.14 and 0.52, respectively) but the reduction is compensated by the formation of 1,2-di-phenylethane in yields of 0.49 and 1.60 in argon- and N 2 O-saturated solutions, respectively. Benzyl radicals are formed through an acid catalysed water elimination reaction from the initially formed hydroxymethylcyclohexadienyl radical. Phenyltolylmethanes, dimethylbiphenyls and partly reduced dimers are also formed during the radiolysis. Hydrogen is formed in the same yield as the molecular yield, g(H 2 ). Xylene isomers and benzene are formed in trace quantities. The most remarkable effects of the addition of Fe(III) ions to deaerated acid toluene solutions are the formation of benzyl alcohol and benzaldehyde and an increase in the yield of 1,2-diphenylethane

The world solution for world problems : the problem, its cause, its solution

NARCIS (Netherlands)

León, L.

2002-01-01

The book discusses the main world problem of today, which is the gradual, but lethal change of the soil and atmosphere, the main cause, which is the world-wide overpopulation, and the main solution, which is world government by lottocracy. It is a recipe for the solution of the one and only problem

Exact solutions in three-dimensional gravity

CERN Document Server

Garcia-Diaz, Alberto A

2017-01-01

A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...

Forced Spreading of Aqueous Solutions on Zwitterionic Sulfobetaine Surfaces for Rapid Evaporation and Solute Separation.

Science.gov (United States)

Wu, Cyuan-Jhang; Singh, Vickramjeet; Sheng, Yu-Jane; Tsao, Heng-Kwong

2017-08-01

Solute separation of aqueous mixtures is mainly dominated by water vaporization. The evaporation rate of an aqueous drop grows with increasing the liquid-gas interfacial area. The spontaneous spreading behavior of a water droplet on a total wetting surface provides huge liquid-gas interfacial area per unit volume; however, it is halted by the self-pinning phenomenon upon addition of nonvolatile solutes. In this work, it is shown that the solute-induced self-pinning can be overcome by gravity, leading to anisotropic spreading much faster than isotropic spreading. The evaporation rate of anisotropic spreading on a zwitterionic sulfobetaine surface is 25 times larger as that on a poly(methyl methacrylate) surface. Dramatic enhancement of evaporation is demonstrated by simultaneous formation of fog atop liquid film. During anisotropic spreading, the solutes are quickly precipitated out within 30 s, showing the rapid solute-water separation. After repeated spreading process for the dye-containing solution, the mean concentration of the collection is doubled, revealing the concentration efficiency as high as 100%. Gravity-enhanced spreading on total wetting surfaces at room temperature is easy to scale-up with less energy consumption, and thus it has great potentials for the applications of solute separation and concentration.

Linear superposition solutions to nonlinear wave equations

International Nuclear Information System (INIS)

Liu Yu

2012-01-01

The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed

An exploration of the black hole entropy via the Weyl tensor

Energy Technology Data Exchange (ETDEWEB)

Li, Nan [Northeastern University, Department of Physics, College of Sciences, Shenyang (China); Li, Xiao-Long [Beijing Normal University, Department of Astronomy, Beijing (China); Song, Shu-Peng [Beijing Normal University, Department of Physics, Beijing (China)

2016-03-15

The role of the Weyl tensor C{sub μνλρ} in black hole thermodynamics is explored by looking at the relation between the scalar invariant C{sub μνλρ}C{sup μνλρ} and the entropy of n-dimensional static black holes. It is found that this invariant can be identified as the entropy density of the gravitational fields for classical 5-dimensional black holes. We calculate the proper volume integrals of C{sub μνλρ}C{sup μνλρ} for the Schwarzschild and Schwarzschild-anti-de Sitter black holes and show that these integrals correctly lead to the Bekenstein-Hawking entropy formulas, only up to some coefficients. (orig.)

Energy levels of a scalar particle in a static gravitational field close to the black hole limit

Science.gov (United States)

Gossel, G. H.; Berengut, J. C.; Flambaum, V. V.

2011-10-01

The bound-state energy levels of a scalar particle in the gravitational field of finite-sized objects with interiors described by the Florides and Schwarzschild metrics are found. For these metrics, bound states with zero energy (where the binding energy is equal to the rest mass of the scalar particle) only exist when a singularity occurs in the metric. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides metric the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the center. Moreover, the energy spectrum is shown to become quasi-continuous as the metric becomes singular.

Topological properties and global structure of space-time

International Nuclear Information System (INIS)

Bergmann, P.G.; De Sabbata, V.

1986-01-01

This book presents information on the following topics: measurement of gravity and gauge fields using quantum mechanical probes; gravitation at spatial infinity; field theories on supermanifolds; supergravities and Kaluza-Klein theories; boundary conditions at spatial infinity; singularities - global and local aspects; matter at the horizon of the Schwarzschild black hole; introluction to string theories; cosmic censorship and the strengths of singularities; conformal quantisation in singular spacetimes; solar system tests in transition; integration and global aspects of supermanifolds; the space-time of the bimetric general relativity theory; gravitation without Lorentz invariance; a uniform static magnetic field in Kaluza-Klein theory; introduction to topological geons; and a simple model of a non-asymptotically flat Schwarzschild black hole