Schwarzschild, Martin (1912-97)

Science.gov (United States)

Murdin, P.

2000-11-01

Astrophysicist, born in Potsdam, Germany, the son of KARL SCHWARZSCHILD, left Germany, became professor at Princeton University. Working with John von Neumann, Schwarzschild used the powers of the newly developed electronic digital computers to work on the theory of stellar structure and evolution. He uncovered phenomena in red giant stars, including how they evolve off the main sequence in the H...

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 ...

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...

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.

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.

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.

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.

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.

The scalar wave equation in a Schwarzschild spacetime

International Nuclear Information System (INIS)

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

1978-09-01

This paper studies the asymptotic behaviour of solutions of the zero rest mass scalar wave equation in the Schwarzschild spacetime in a neighbourhood of spatial infinity, which includes parts of future and past null infinity. The behaviour of such fields is essentially different from that which accurs in a flat spacetime. (orig.) [de

Aplanatic telescopes based on Schwarzschild optical configuration: from grazing incidence Wolter-like x-ray optics to Cherenkov two-mirror normal incidence telescopes

Science.gov (United States)

Sironi, Giorgia

2017-09-01

At the beginning of XX century Karl Schwarzschild defined a method to design large-field aplanatic telescopes based on the use of two aspheric mirrors. The approach was then refined by Couder (1926) who, in order to correct for the astigmatic aberration, introduced a curvature of the focal plane. By the way, the realization of normal-incidence telescopes implementing the Schwarzschild aplanatic configuration has been historically limited by the lack of technological solutions to manufacture and test aspheric mirrors. On the other hand, the Schwarzschild solution was recovered for the realization of coma-free X-ray grazing incidence optics. Wolter-like grazing incidence systems are indeed free of spherical aberration, but still suffer from coma and higher order aberrations degrading the imaging capability for off-axis sources. The application of the Schwarzschild's solution to X-ray optics allowed Wolter to define an optical system that exactly obeys the Abbe sine condition, eliminating coma completely. Therefore these systems are named Wolter-Schwarzschild telescopes and have been used to implement wide-field X-ray telescopes like the ROSAT WFC and the SOHO X-ray telescope. Starting from this approach, a new class of X-ray optical system was proposed by Burrows, Burg and Giacconi assuming polynomials numerically optimized to get a flat field of view response and applied by Conconi to the wide field x-ray telescope (WFXT) design. The Schwarzschild-Couder solution has been recently re-discovered for the application to normal-incidence Cherenkov telescopes, thanks to the suggestion by Vassiliev and collaborators. The Italian Institute for Astrophysics (INAF) realized the first Cherenkov telescope based on the polynomial variation of the Schwarzschild configuration (the so-called ASTRI telescope). Its optical qualification was successfully completed in 2016, demonstrating the suitability of the Schwarzschild-like configuration for the Cherenkov astronomy requirements

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...

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

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.

Schwarzschild Solution: A Historical Perspective

Science.gov (United States)

Bartusiak, Marcia

2016-03-01

While eighteenth-century Newtonians had imagined a precursor to the black hole, the modern version has its roots in the first full solution to Einstein's equations of general relativity, derived by the German astronomer Karl Schwarzschild on a World War I battlefront just weeks after Einstein introduced his completed theory in November 1915. This talk will demonstrate how Schwarzschild's solution is linked to the black hole and how it took more than half a century for the physics community to accept that such a bizarre celestial object could exist in the universe.

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.

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.

Uniqueness of the electrostatic solution in Schwarzschild space

International Nuclear Information System (INIS)

Molnar, Pal G.; Elsaesser, Klaus

2003-01-01

In this Brief Report we give the proof that the solution of any static test charge distribution in Schwarzschild space is unique. In order to give the proof we derive the first Green's identity written with p-forms on (pseudo) Riemannian manifolds. Moreover, the proof of uniqueness can be shown for either any purely electric or purely magnetic field configuration. The spacetime geometry is not crucial for the proof

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.)

Analytic extension of the Schwarzschild-de Sitter metric

International Nuclear Information System (INIS)

Bazanski, S.L.; Ferrari, V.

1986-01-01

In this paper, co-ordinates are derived that are regular, respectively, in the neighbourhood of the two horizons which exist in the so-called Schwarzschild-de Sitter solution known in general relativity, and it is constructed a manifold that is the analytic extension of the manifold being the domain of classical Schwarzschild-de Sitter co-ordinates

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 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.

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.

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)

Heuristic extension of the Schwarzschild metric

International Nuclear Information System (INIS)

Espinosa, J.M.

1982-01-01

The Schwarzschild solution of Einstein's equations of gravitation has several singularities. It is known that the singularity at r = 2Gm/c 2 is only apparent, a result of the coordinates in which the solution was found. Paradoxical results occuring near the singularity show the system of coordinates is incomplete. We introduce a simple, two-dimensional metric with an apparent singularity that makes it incomplete. By a straightforward, heuristic procedure we extend and complete this simple metric. We then use the same procedure to give a heuristic derivation of the Kruskal system of coordinates, which is known to extend the Schwarzschild manifold past its apparent singularity and produce a complete manifold

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)

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.

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.

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)

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...

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 effect of spherical shells of matter on the Schwarzschild black hole

International Nuclear Information System (INIS)

Dray, T.; Rijksuniversiteit Utrecht; Hooft, G. 't

1985-01-01

Based on previous work we show how to join two Schwarzschild solutions, possibly with different masses along null cylinders each representing a spherical shell of infalling or outgoing massless matter. One of the Schwarzschild masses can be zero, i.e. one region can be flat. The above procedure can be repeated to produce spacetimes with a C 0 metric describing several different (possibly flat) Schwarzschild regions separated by shells of matter. An exhaustive treatment of the ways of combining four such regions is given; the extension to many regions is then straightforward. Cases of special interest are: (1) the scattering of two spherical gravitational ''shock waves'' at the horizon of a Schwarzschild black hole, and (2) a configuration involving only one external universe, which may be relevant to quantization problems in general relativity. In the latter example, only an infinitesimal amount of matter is sufficient to remove the ''Wheeler wormhole'' to another universe. (orig.)

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.)

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.)

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

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.

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.)

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 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

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.

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

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.

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.

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

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

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

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.

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.

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

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.

The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge

OpenAIRE

Johnson, Thomas

2018-01-01

In a recent seminal paper \\cite{D--H--R} of Dafermos, Holzegel and Rodnianski the linear stability of the Schwarzschild family of black hole solutions to the Einstein vacuum equations was established by imposing a double null gauge. In this paper we shall prove that the Schwarzschild family is linearly stable as solutions to the Einstein vacuum equations by imposing instead a generalised wave gauge: all sufficiently regular solutions to the system of equations that result from linearising the...

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.

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

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.

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

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...

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

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.)

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.)

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

Hawking radiation inside a Schwarzschild black hole

Science.gov (United States)

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...

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.

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.

Canonical quantization of the Proca field in the Rindler wedge

International Nuclear Information System (INIS)

Castineiras, Jorge; Correa, Emerson Benedito Sousa; Crispino, Luis Carlos Bassalo; Matsas, George Emanuel Avraam

2009-01-01

Full text. We perform the canonical quantization of a massive vector field in Rindler spacetime. We pay special attention to the zero frequency modes of the Proca field because these are the modes that interact with structureless sources which are static in the Rindler spacetime. Our motivation is the computation of the total response of a static source with some fixed proper acceleration a 0 in Rindler spacetime interacting with the zero energy massive vector particle of the Fulling-Davies-Unruh (FDU) thermal bath and compare it with the response of a static source with the same proper acceleration a 0 outside a Schwarzschild black hole interacting with the massive vector particles of the Hawking thermal radiation. Surprisingly, as it was already shown in a resent article, these responses would be identical if a massless scalar field is consider instead of the massive vector field, the field outside the Schwarzschild black hole is supposed to be in the Unruh vacuum and the source proper acceleration is the same in both cases. This came as a surprise because structureless static sources can only interact with zero-frequency field modes. Such modes can probe the global geometry of spacetime and are accordingly quite different in Schwarzschild spacetime and in the Rindler wedge. (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

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

Unified field theory

International Nuclear Information System (INIS)

Vollendorf, F.

1976-01-01

A theory is developed in which the gravitational as well as the electromagnetic field is described in a purely geometrical manner. In the case of a static central symmetric field Newton's law of gravitation and Schwarzschild's line element are derived by means of an action principle. The same principle leads to Fermat's law which defines the world lines of photons. (orig.) [de

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.)

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.

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)

Science.gov (United States)

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 ...

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

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

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

Science.gov (United States)

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

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 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.)

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.

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.

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.

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.

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.

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)

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.

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)

Cancellation of the central singularity of the Schwarzschild solution with natural mass inversion process

Science.gov (United States)

Petit, Jean-Pierre; D'Agostini, G.

2015-03-01

We reconsider the classical Schwarzschild solution in the context of a Janus cosmological model. We show that the central singularity can be eliminated through a simple coordinate change and that the subsequent transit from one fold to the other is accompanied by mass inversion. In such scenario matter swallowed by black holes could be ejected as invisible negative mass and dispersed in space.

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.

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

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.

Null Geodesics and Strong Field Gravitational Lensing of Black Hole with Global Monopole

International Nuclear Information System (INIS)

Iftikhar, Sehrish; Sharif, M.

2015-01-01

We study two interesting features of a black hole with an ordinary as well as phantom global monopole. Firstly, we investigate null geodesics which imply unstable orbital motion of particles for both cases. Secondly, we evaluate deflection angle in strong field regime. We then find Einstein rings, magnifications, and observables of the relativistic images for supermassive black hole at the center of galaxy NGC4486B. We also examine time delays for different galaxies and present our results numerically. It is found that the deflection angle for ordinary/phantom global monopole is greater/smaller than that of Schwarzschild black hole. In strong field limit, the remaining properties of these black holes are quite different from the Schwarzschild black hole

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.

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

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.

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.)

Gravitation and bilocal field theory

International Nuclear Information System (INIS)

Vollendorf, F.

1975-01-01

The starting point is the conjecture that a field theory of elementary particles can be constructed only in a bilocal version. Thus the 4-dimensional space time has to be replaced by the 8-dimensional manifold R 8 of all ordered pairs of space time events. With special reference to the Schwarzschild metric it is shown that the embedding of the time space into the manifold R 8 yields a description of the gravitational field. (orig.) [de

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…

Theory of gravitational-inertial field of universe. 2

International Nuclear Information System (INIS)

Davtyan, O.K.

1978-01-01

Application of the equations of the gravitational-inertial field to the problem of free motion in the inertial field (to the cosmologic problem) leads to results according to which (1) all Galaxies in the Universe 'disperse' from each other according to Hubble's law, (2) the 'dispersion' of bodies represents a free motion in the inertial field and Hubble's law represents a law of motion of free body in the inertial field, (3) for arbitrary mean distribution densities of space masses different from zero the space is Lobachevskian. All critical systems (with Schwarzschild radius) are specific because they exist in maximal-inertial and gravitational potentials. The Universe represents a critical system, it exists under the Schwarzschild radius. In high-potential inertial and gravitational fields the material mass in a static state or in motion with deceleration is subject to an inertial and gravitational 'annihilation'. At the maximal value of inertial and gravitational potentials (= c 2 ) the material mass is being completely 'evaporated' transforming into radiation mass. The latter is being concentrated in the 'horizon' of the critical system. All critical systems-black holes-represent geon systems, i.e. local formations of gravitational-electromagnetic radiations, held together by their own gravitational and inertial fields. The Universe, being a critical system, is 'wrapped' in a geon crown. (author)

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.

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)

Algebraically special perturbations of the Schwarzschild solution in higher dimensions

International Nuclear Information System (INIS)

Dias, Óscar J C; Reall, Harvey S

2013-01-01

We study algebraically special perturbations of a generalized Schwarzschild solution in any number of dimensions. There are two motivations. First, to learn whether there exist interesting higher-dimensional algebraically special solutions beyond the known ones. Second, algebraically special perturbations present an obstruction to the unique reconstruction of general metric perturbations from gauge-invariant variables analogous to the Teukolsky scalars and it is desirable to know the extent of this non-uniqueness. In four dimensions, our results generalize those of Couch and Newman, who found infinite families of time-dependent algebraically special perturbations. In higher dimensions, we find that the only regular algebraically special perturbations are those corresponding to deformations within the Myers–Perry family. Our results are relevant for several inequivalent definitions of ‘algebraically special’. (paper)

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

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

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.

Absorption of massive scalar field by a charged black hole

Energy Technology Data Exchange (ETDEWEB)

Nakamura, T [Kyoto Univ. (Japan). Dept. of Physics; Sato, H [Kyoto Univ. (Japan). Research Inst. for Fundamental Physics

1976-04-12

Absorption and reflection of charged, massive scalar field by the Reisner-Nordstrom black hole are investigated through a numerical computation. The absorption is suppressed when (Schwarzschild radius)<(Compton wave length) and the amplification of the wave occurs when the level crossing condition is satisfied.

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

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)

Gauge field back reaction on a black hole

International Nuclear Information System (INIS)

Hochberg, D.; Kephart, T.W.

1993-01-01

The order-ℎ fluctuations of gauge fields in the vicinity of a black hole can create a repulsive antigravity region extending out beyond the renormalized Schwarzschild horizon. If the strength of this repulsive force increases as higher orders in the back reaction are included, the formation of a wormholelike object could occur

Particle field in bimetric general relativity

International Nuclear Information System (INIS)

Falik, D.; Rosen, N.

1980-01-01

The field equations of the bimetric general relativity theory proposed recently by one of the authors (N. Rosen) are put into a static form. The equations are solved near the Schwarzschild sphere, and it is found that the field differs from that of the Einstein general relativity theory: instead of a black hole, one has an impenetrable sphere. For larger distances the field is found to agree with that of ordinary general relativity, so that solar system observations cannot distinguish between the two theories. For very large distances one gets a cosmic contribution to the field which may affect the dynamics of clusters of galaxies

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.

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

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

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.

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

Zero-point field in curved spaces

International Nuclear Information System (INIS)

Hacyan, S.; Sarmiento, A.; Cocho, G.; Soto, F.

1985-01-01

Boyer's conjecture that the thermal effects of acceleration are manifestations of the zero-point field is further investigated within the context of quantum field theory in curved spaces. The energy-momentum current for a spinless field is defined rigorously and used as the basis for investigating the energy density observed in a noninertial frame. The following examples are considered: (i) uniformly accelerated observers, (ii) two-dimensional Schwarzschild black holes, (iii) the Einstein universe. The energy spectra which have been previously calculated appear in the present formalism as an additional contribution to the energy of the zero-point field, but particle creation does not occur. It is suggested that the radiation produced by gravitational fields or by acceleration is a manifestation of the zero-point field and of the same nature (whether real or virtual)

Bound states of spin-half particles in a static gravitational field close to the black hole field

Science.gov (United States)

Spencer-Smith, A. F.; Gossel, G. H.; Berengut, J. C.; Flambaum, V. V.

2013-03-01

We consider the bound-state energy levels of a spin-1/2 fermion in the gravitational field of a near-black hole object. In the limit that the metric of the body becomes singular, all binding energies tend to the rest-mass energy (i.e. total energy approaches zero). We present calculations of the ground state energy for three specific interior metrics (Florides, Soffel and Schwarzschild) for which the spectrum collapses and becomes quasi-continuous in the singular metric limit. The lack of zero or negative energy states prior to this limit being reached prevents particle pair production occurring. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides and Soffel metrics the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the centre. The behaviour of the energy level spectrum is discussed in the context of the semi-classical approximation and using general properties of the metric.

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)

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

Solar system tests of scalar field models with an exponential potential

International Nuclear Information System (INIS)

Paramos, J.; Bertolami, O.

2008-01-01

We consider a scenario where the dynamics of a scalar field is ruled by an exponential potential, such as those arising from some quintessence-type models, and aim at obtaining phenomenological manifestations of this entity within our Solar System. To do so, we assume a perturbative regime, derive the perturbed Schwarzschild metric, and extract the relevant post-Newtonian parameters.

Membrane viewpoint on black holes: Dynamical electromagnetic fields near the horizon

International Nuclear Information System (INIS)

Macdonald, D.A.; Suen, W.

1985-01-01

This paper is part of a series of papers with the aim of developing a complete self-consistent formalism for the treatment of electromagnetic and gravitational fields in the neighborhood of a black-hole horizon. In this membrane formalism, the horizon is treated as a closed two-dimensional membrane lying in a curved three-dimensional space, and endowed with familiar physical properties such as entropy and temperature, surface pressure and viscosity, and electrical conductivity, charge, and current. This paper develops the concept of the ''stretched horizon,'' which will be vital for both the electromagnetic and gravitational aspects of the formalism, and it presents several model problems illustrating the interaction of dynamical electromagnetic fields with stationary black-hole horizons: The field of a test charge in various states of motion outside the Schwarzschild horizon is analyzed in the near-horizon limit, where the spatial curvature may be ignored and the metric may be approximated by that of Rindler. This analysis elucidates the influence of the horizon on the shapes and motions of electric and magnetic field lines when external agents move the field lines in arbitrary manners. It also illustrates how the field lines interact with the horizon's charge and current to produce an exchange of energy and momentum between the external agent and the horizon. A numerical calculation of the dynamical relaxation of a magnetic field threading a Schwarzschild black hole is also presented, illustrating the ''cleaning'' of a complicated field structure by a black-hole horizon, and elucidating the constraints on the location of the stretched horizon

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.

The deflection angle of a gravitational source with a global monopole in the strong field limit

International Nuclear Information System (INIS)

Cheng Hongbo; Man Jingyun

2011-01-01

We investigate the gravitational lensing effect in the strong field background around the Schwarzschild black hole with extremely small mass and solid deficit angle subject to the global monopole by means of the strong field limit issue. We obtain the angular position and magnification of the relativistic images and show that they relate to the global monopole parameter η. We discuss that with the increase of the parameter η, the minimum impact parameter u m and angular separation s increase and the relative magnification r decreases. We also find that s grows extremely as the increasing parameter η becomes large enough. The deflection angle will become larger when the parameter η grows. The effect from the solid deficit angle is the dependence of angular position, angular separation, relative magnification and deflection angle on the parameter η, which may offer a way to characterize some possible distinct signatures of the Schwarzschild black hole with a solid deficit angle associated with the global monopole.

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.

Scalar fields in black hole spacetimes

Science.gov (United States)

Thuestad, Izak; Khanna, Gaurav; Price, Richard H.

2017-07-01

The time evolution of matter fields in black hole exterior spacetimes is a well-studied subject, spanning several decades of research. However, the behavior of fields in the black hole interior spacetime has only relatively recently begun receiving some attention from the research community. In this paper, we numerically study the late-time evolution of scalar fields in both Schwarzschild and Kerr spacetimes, including the black hole interior. We recover the expected late-time power-law "tails" on the exterior (null infinity, timelike infinity, and the horizon). In the interior region, we find an interesting oscillatory behavior that is characterized by the multipole index ℓ of the scalar field. In addition, we also study the extremal Kerr case and find strong indications of an instability developing at the horizon.

Electromagnetic radiation damping of charges in external gravitational fields (weak field, slow motion approximation). [Harmonic coordinates, weak field slow-motion approximation, Green function

Energy Technology Data Exchange (ETDEWEB)

Rudolph, E [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (F.R. Germany)

1975-01-01

As a model for gravitational radiation damping of a planet the electromagnetic radiation damping of an extended charged body moving in an external gravitational field is calculated in harmonic coordinates using a weak field, slowing-motion approximation. Special attention is paid to the case where this gravitational field is a weak Schwarzschild field. Using Green's function methods for this purpose it is shown that in a slow-motion approximation there is a strange connection between the tail part and the sharp part: radiation reaction terms of the tail part can cancel corresponding terms of the sharp part. Due to this cancelling mechanism the lowest order electromagnetic radiation damping force in an external gravitational field in harmonic coordinates remains the flat space Abraham Lorentz force. It is demonstrated in this simplified model that a naive slow-motion approximation may easily lead to divergent higher order terms. It is shown that this difficulty does not arise up to the considered order.

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.

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

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.

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.

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.

Gravitational waves from scalar field accretion

International Nuclear Information System (INIS)

Nunez, Dario; Degollado, Juan Carlos; Moreno, Claudia

2011-01-01

Our aim in this work is to outline some physical consequences of the interaction between black holes and scalar field halos in terms of gravitational waves. In doing so, the black hole is taken as a static and spherically symmetric gravitational source, i.e. the Schwarzschild black hole, and we work within the test field approximation, considering that the scalar field lives in the curved space-time outside the black hole. We focused on the emission of gravitational waves when the black hole is perturbed by the surrounding scalar field matter. The symmetries of the space-time and the simplicity of the matter source allow, by means of a spherical harmonic decomposition, to study the problem by means of a one-dimensional description. Some properties of such gravitational waves are discussed as a function of the parameters of the infalling scalar field, and allow us to make the conjecture that the gravitational waves carry information on the type of matter that generated them.

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.

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

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

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.

Mean-field dynamos: The old concept and some recent developments. Karl Schwarzschild Award Lecture 2013

Science.gov (United States)

Rädler, K.-H.

This article elucidates the basic ideas of electrodynamics and magnetohydrodynamics of mean fields in turbulently moving conducting fluids. It is stressed that the connection of the mean electromotive force with the mean magnetic field and its first spatial derivatives is in general neither local nor instantaneous and that quite a few claims concerning pretended failures of the mean-field concept result from ignoring this aspect. In addition to the mean-field dynamo mechanisms of α2 and α Ω type several others are considered. Much progress in mean-field electrodynamics and magnetohydrodynamics results from the test-field method for calculating the coefficients that determine the connection of the mean electromotive force with the mean magnetic field. As an important example the memory effect in homogeneous isotropic turbulence is explained. In magnetohydrodynamic turbulence there is the possibility of a mean electromotive force that is primarily independent of the mean magnetic field and labeled as Yoshizawa effect. Despite of many efforts there is so far no convincing comprehensive theory of α quenching, that is, the reduction of the α effect with growing mean magnetic field, and of the saturation of mean-field dynamos. Steps toward such a theory are explained. Finally, some remarks on laboratory experiments with dynamos are made.

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

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

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.

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.

Quantum vacuum energy near a black hole: the Maxwell field

International Nuclear Information System (INIS)

Elster, T.

1984-01-01

A quantised Maxwell field is considered propagating in the gravitational field of a Schwarzschild black hole. The vector Hartle-Hawking propagator is defined on the Riemannian section of the analytically continued space-time and expanded in terms of four-dimensional vector spherical harmonics. The equations for the radial functions appearing in the expansion are derived for both odd and even parity. Using the expansion of the vector Hartle-Hawking propagator, the point-separated expectation value of the Maxwellian energy-momentum tensor in the Hartle-Hawking vacuum is derived. The renormalised values of radial pressure, tangential pressure and energy density are obtained near the horizon of the black hole. In contrast to the scalar field, the Maxwell field exhibits a positive energy density near the horizon in the Hartle-Hawking vacuum state. (author)

'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

Null Geodesics and Strong Field Gravitational Lensing in a String Cloud Background

International Nuclear Information System (INIS)

Iftikhar, Sehrish; Sharif, M.

2015-01-01

This paper is devoted to studying two interesting issues of a black hole with string cloud background. Firstly, we investigate null geodesics and find unstable orbital motion of particles. Secondly, we calculate deflection angle in strong field limit. We then find positions, magnifications, and observables of relativistic images for supermassive black hole at the galactic center. We conclude that string parameter highly affects the lensing process and results turn out to be quite different from the Schwarzschild black hole

A Field Theory with Curvature and Anticurvature

Directory of Open Access Journals (Sweden)

M. I. Wanas

2014-01-01

Full Text Available The present work is an attempt to construct a unified field theory in a space with curvature and anticurvature, the PAP-space. The theory is derived from an action principle and a Lagrangian density using a symmetric linear parameterized connection. Three different methods are used to explore physical contents of the theory obtained. Poisson’s equations for both material and charge distributions are obtained, as special cases, from the field equations of the theory. The theory is a pure geometric one in the sense that material distribution, charge distribution, gravitational and electromagnetic potentials, and other physical quantities are defined in terms of pure geometric objects of the structure used. In the case of pure gravity in free space, the spherical symmetric solution of the field equations gives the Schwarzschild exterior field. The weak equivalence principle is respected only in the case of pure gravity in free space; otherwise it is violated.

Field-reversed configuration produced by a linear theta-pinch, Tupa-1

International Nuclear Information System (INIS)

Kayama, M.E.; Boeckelmann, H.K.; Sakanaka, P.H.; Machida, M.

1987-01-01

The formation of field reversed configuration, FRC, in one meter mirrorless linear theta-pinch device Tupa-I was observed. This configuration was studied during the first half magnetic cycle of ringing main bank discharge using magnetic probes. The separatrix radius by the exclude flux probe and the ion temperature by visible spectroscopy were measured. The plasma dynamics was observed by the image converter camera. A clear indication of the formation of FRC due to reconnection of the antiparallel bias to the main field and a fast reconnection, less than 0.2 microsec, that is explained in terms of forced reconnection driven by the Kruskal-Schwarzschild instability, are also observed. (author) [pt

On tidal phenomena in a strong gravitational field

International Nuclear Information System (INIS)

Mashoon, B.

1975-01-01

A simple framework based on the concept of quadrupole tidal potential is presented for the calculation of tidal deformation of an extended test body in a gravitational field. This method is used to study the behavior of an initially faraway nonrotating spherical body that moves close to a Schwarzschild or an extreme Kerr black hole. In general, an extended body moving in an external gravitational field emits gravitational radiation due to its center of mass motion, internal tidal deformation, and the coupling between the internal and center of mass motions. Estimates are given of the amount of tidal radiation emitted by the body in the gravitational fields considered. The results reported in this paper are expected to be of importance in the dynamical evolution of a dense stellar system with a massive black hole in its center

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

Resolved magnetic-field structure and variability near the event horizon of Sagittarius A.

Science.gov (United States)

Johnson, Michael D; Fish, Vincent L; Doeleman, Sheperd S; Marrone, Daniel P; Plambeck, Richard L; Wardle, John F C; Akiyama, Kazunori; Asada, Keiichi; Beaudoin, Christopher; Blackburn, Lindy; Blundell, Ray; Bower, Geoffrey C; Brinkerink, Christiaan; Broderick, Avery E; Cappallo, Roger; Chael, Andrew A; Crew, Geoffrey B; Dexter, Jason; Dexter, Matt; Freund, Robert; Friberg, Per; Gold, Roman; Gurwell, Mark A; Ho, Paul T P; Honma, Mareki; Inoue, Makoto; Kosowsky, Michael; Krichbaum, Thomas P; Lamb, James; Loeb, Abraham; Lu, Ru-Sen; MacMahon, David; McKinney, Jonathan C; Moran, James M; Narayan, Ramesh; Primiani, Rurik A; Psaltis, Dimitrios; Rogers, Alan E E; Rosenfeld, Katherine; SooHoo, Jason; Tilanus, Remo P J; Titus, Michael; Vertatschitsch, Laura; Weintroub, Jonathan; Wright, Melvyn; Young, Ken H; Zensus, J Anton; Ziurys, Lucy M

2015-12-04

Near a black hole, differential rotation of a magnetized accretion disk is thought to produce an instability that amplifies weak magnetic fields, driving accretion and outflow. These magnetic fields would naturally give rise to the observed synchrotron emission in galaxy cores and to the formation of relativistic jets, but no observations to date have been able to resolve the expected horizon-scale magnetic-field structure. We report interferometric observations at 1.3-millimeter wavelength that spatially resolve the linearly polarized emission from the Galactic Center supermassive black hole, Sagittarius A*. We have found evidence for partially ordered magnetic fields near the event horizon, on scales of ~6 Schwarzschild radii, and we have detected and localized the intrahour variability associated with these fields. Copyright © 2015, American Association for the Advancement of Science.

Gravitational Field effects on the Decoherence Process and the Quantum Speed Limit.

Science.gov (United States)

Dehdashti, Sh; Avazzadeh, Z; Xu, Z; Shen, J Q; Mirza, B; Wang, H

2017-11-08

In this paper we use spinor transformations under local Lorentz transformations to investigate the curvature effect on the quantum-to-classical transition, described in terms of the decoherence process and of the quantum speed limit. We find that gravitational fields (introduced adopting the Schwarzschild and anti-de Sitter geometries) affect both the decoherence process and the quantum speed limit of a quantum particle with spin-1/2. In addition, as a tangible example, we study the effect of the Earth's gravitational field, characterized by the Rindler space-time, on the same particle. We find that the effect of the Earth's gravitational field on the decoherence process and quantum speed limit is very small, except when the mean speed of the quantum particle is comparable to the speed of light.

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.

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.

Heavy fields and gravity

Energy Technology Data Exchange (ETDEWEB)

Goon, Garrett [Institute of Physics, Universiteit van Amsterdam,Science Park 904, Amsterdam, 1090 GL (Netherlands)

2017-01-11

We study the effects of heavy fields on 4D spacetimes with flat, de Sitter and anti-de Sitter asymptotics. At low energies, matter generates specific, calculable higher derivative corrections to the GR action which perturbatively alter the Schwarzschild-(A)dS family of solutions. The effects of massive scalars, Dirac spinors and gauge fields are each considered. The six-derivative operators they produce, such as ∼R{sup 3} terms, generate the leading corrections. The induced changes to horizon radii, Hawking temperatures and entropies are found. Modifications to the energy of large AdS black holes are derived by imposing the first law. An explicit demonstration of the replica trick is provided, as it is used to derive black hole and cosmological horizon entropies. Considering entropy bounds, it’s found that scalars and fermions increase the entropy one can store inside a region bounded by a sphere of fixed size, but vectors lead to a decrease, oddly. We also demonstrate, however, that many of the corrections fall below the resolving power of the effective field theory and are therefore untrustworthy. Defining properties of black holes, such as the horizon area and Hawking temperature, prove to be remarkably robust against higher derivative gravitational corrections.

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.

Analysis of interacting quantum field theory in curved spacetime

International Nuclear Information System (INIS)

Birrell, N.D.; Taylor, J.G.

1980-01-01

A detailed analysis of interacting quantized fields propagating in a curved background spacetime is given. Reduction formulas for S-matrix elements in terms of vacuum Green's functions are derived, special attention being paid to the possibility that the ''in'' and ''out'' vacuum states may not be equivalent. Green's functions equations are obtained and a diagrammatic representation for them given, allowing a formal, diagrammatic renormalization to be effected. Coordinate space techniques for showing renormalizability are developed in Minkowski space, for lambdaphi 3 /sub() 4,6/ field theories. The extension of these techniques to curved spacetimes is considered. It is shown that the possibility of field theories becoming nonrenormalizable there cannot be ruled out, although, allowing certain modifications to the theory, phi 3 /sub( 4 ) is proven renormalizable in a large class of spacetimes. Finally particle production from the vacuum by the gravitational field is discussed with particular reference to Schwarzschild spacetime. We shed some light on the nonlocalizability of the production process and on the definition of the S matrix for such processes

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 ...

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.

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)

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.)

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.

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

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.

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.

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

Science.gov (United States)

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.

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.

Thermodynamic Analysis of the Static Spherically Symmetric Field Equations in Rastall Theory

International Nuclear Information System (INIS)

Moradpour, Hooman; Salako, Ines G.

2016-01-01

The restrictions on the Rastall theory due to application of the Newtonian limit to the theory are derived. In addition, we use the zero-zero component of the Rastall field equations as well as the unified first law of thermodynamics to find the Misner-Sharp mass content confined to the event horizon of the spherically symmetric static spacetimes in the Rastall framework. The obtained relation is calculated for the Schwarzschild and de-Sitter back holes as two examples. Bearing the obtained relation for the Misner-Sharp mass in mind together with recasting the one-one component of the Rastall field equations into the form of the first law of thermodynamics, we obtain expressions for the horizon entropy and the work term. Finally, we also compare the thermodynamic quantities of system, including energy, entropy, and work, with their counterparts in the Einstein framework to have a better view about the role of the Rastall hypothesis on the thermodynamics of system.

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.

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)\

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.

The magnetic field and the evolution of element spots on the surface of the HgMn eclipsing binary ARAur

Science.gov (United States)

Hubrig, S.; Savanov, I.; Ilyin, I.; González, J. F.; Korhonen, H.; Lehmann, H.; Schöller, M.; Granzer, T.; Weber, M.; Strassmeier, K. G.; Hartmann, M.; Tkachenko, A.

2010-10-01

The system ARAur is a young late B-type double-lined eclipsing binary with a primary star of HgMn peculiarity. We applied the Doppler imaging method to reconstruct the distribution of Fe and Y over the surface of the primary using spectroscopic time series obtained in 2005 and from 2008 October to 2009 February. The results show a remarkable evolution of the element distribution and overabundances. Measurements of the magnetic field with the moment technique using several elements reveal the presence of a longitudinal magnetic field of the order of a few hundred gauss in both stellar components and a quadratic field of the order of 8kG on the surface of the primary star. Based on observations obtained at the 2.56-m Nordic Optical Telescope on La Palma, the Karl-Schwarzschild-Observatorium in Tautenburg and the STELLA robotic telescope on Tenerife. E-mail: shubrig@aip.de

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.

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

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...

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

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.

Radiation drag in the field of a non-spherical source

Science.gov (United States)

Bini, D.; Geralico, A.; Passamonti, A.

2015-01-01

The motion of a test particle in the gravitational field of a non-spherical source endowed with both mass and mass quadrupole moment is investigated when a test radiation field is also present. The background is described by the Erez-Rosen solution, which is a static space-time belonging to the Weyl class of solutions to the vacuum Einstein's field equations, and reduces to the familiar Schwarzschild solution when the quadrupole parameter vanishes. The radiation flux has a fixed but arbitrary (non-zero) angular momentum. The interaction with the radiation field is assumed to be Thomson-like, i.e. the particles absorb and re-emit radiation, thus suffering for a friction-like drag force. Such an additional force is responsible for the Poynting-Robertson effect, which is well established in the framework of Newtonian gravity and has been recently extended to the general theory of relativity. The balance between gravitational attraction, centrifugal force and radiation drag leads to the occurrence of equilibrium circular orbits which are attractors for the surrounding matter for every fixed value of the interaction strength. The presence of the quadrupolar structure of the source introduces a further degree of freedom: there exists a whole family of equilibrium orbits parametrized by the quadrupole parameter, generalizing previous works. This scenario is expected to play a role in the context of accretion matter around compact objects.

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

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

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

Regularization of fields for self-force problems in curved spacetime: Foundations and a time-domain application

International Nuclear Information System (INIS)

Vega, Ian; Detweiler, Steven

2008-01-01

We propose an approach for the calculation of self-forces, energy fluxes and waveforms arising from moving point charges in curved spacetimes. As opposed to mode-sum schemes that regularize the self-force derived from the singular retarded field, this approach regularizes the retarded field itself. The singular part of the retarded field is first analytically identified and removed, yielding a finite, differentiable remainder from which the self-force is easily calculated. This regular remainder solves a wave equation which enjoys the benefit of having a nonsingular source. Solving this wave equation for the remainder completely avoids the calculation of the singular retarded field along with the attendant difficulties associated with numerically modeling a delta-function source. From this differentiable remainder one may compute the self-force, the energy flux, and also a waveform which reflects the effects of the self-force. As a test of principle, we implement this method using a 4th-order (1+1) code, and calculate the self-force for the simple case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. We achieve agreement with frequency-domain results to ∼0.1% or better.

Stress-energy tensors for vector fields outside a static black hole

International Nuclear Information System (INIS)

Barrios, F.A.; Vaz, C.

1989-01-01

We obtain new, approximate stress-energy tensors to describe gauge fields in the neighborhood of a Schwarzschild black hole. We assume that the coefficient of ∇ 2 R in the trace anomaly is correctly given by ζ-function regularization. Our approximation differs from that of Page and of Brown and Ottewill and relies upon a new, improved ansatz for the form of the stress-energy tensor in the ultrastatic optical metric of the black hole. The Israel-Hartle-Hawking thermal tensor is constructed to be regular on the horizon and possess the correct asymptotic behavior. Our approximation of Unruh's tensor is likewise constructed to be regular on the future horizon and exhibit a luminosity which agrees with Page's numerically obtained value. Geometric expressions for the approximate tensors are given, and the approximate energy density of the thermal tensor on the horizon is compared with recent numerical estimates

On particle creation by black holes. [Quantum mechanical state vector, gravitational collapse, Hermition scalar field, density matrix

Energy Technology Data Exchange (ETDEWEB)

Wald, R M [Chicago Univ., Ill. (USA). Lab. for Astrophysics and Space Research

1975-11-01

Hawking's analysis of particle creation by black holes is extended by explicity obtaining the expression for the quantum mechanical state vector PSI which results from particle creation starting from the vacuum during gravitational collapse. We first discuss the quantum field theory of a Hermitian scalar field in an external potential or in a curved but asymptotically flat spacetime with no horizon present. Making the necessary modification for the case when a horizon is present, we apply this theory for a massless Hermitian scalar field to get the state vector describing the steady state emission at late times for particle creation during gravitational collapse to a Schwarzschild black hole. We find that the state vector describing particle creation from the vacuum decomposes into a simple product of state vectors for each individual mode. The density matrix describing emission of particles to infinity by this particle creation process is found to be identical to that of black body emission. Thus, black hole emission agrees in complete detail with black body emission (orig./BJ).

''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)

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.

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.

Optical Design for a Survey X-Ray Telescope

Science.gov (United States)

Saha, Timo T.; Zhang, William W.; McClelland, Ryan S.

2014-01-01

Optical design trades are underway at the Goddard Space Flight Center to define a telescope for an x-ray survey mission. Top-level science objectives of the mission include the study of x-ray transients, surveying and long-term monitoring of compact objects in nearby galaxies, as well as both deep and wide-field x-ray surveys. In this paper we consider Wolter, Wolter-Schwarzschild, and modified Wolter-Schwarzschild telescope designs as basic building blocks for the tightly nested survey telescope. Design principles and dominating aberrations of individual telescopes and nested telescopes are discussed and we compare the off-axis optical performance at 1.0 KeV and 4.0 KeV across a 1.0-degree full field-of-view.

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.

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.

Nonrotating and slowly rotating holes

International Nuclear Information System (INIS)

Macdonald, D.A.; Price, R.H.; Thorne, K.S.; Suen, W.M.

1986-01-01

The 3+1 formalism is applied to model Schwarzschild spacetime around a black hole. Particular note is taken of the 3+1 split of the laws of electrodynamics, and of the tendency of the approach to freeze motion at the event horizon. The null horizon is replaced with a timelike physical membrane which exhibits mechanical, thermodynamic and electrical properties, and which stretches the horizon. The usefulness of the stretching approach is illustrated by considering a black hole penetrated by vibrating magnetic field lines anchored in a perfectly conducting surrounding sphere. The necessity of modeling the field structure near the actual horizon is avoided by having the field end at the membrane. The surface charge, current, resistivity and ohmic heating of the stretched horizon are also considered, and the Lorentz force imparted to the stretched horizon surface by the field lines is investigated by examining a nearly Schwarzschild hole behaving as the rotor of an electric motor

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.

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.

Motion of a spinning test particle in Vaidya's radiating metric

International Nuclear Information System (INIS)

Carmeli, M.; Charach, C.; Kaye, M.

1977-01-01

The motion of a spinning test particle in Vaidya's gravitational field is considered in the framework of Papapetrou's equations of motion. Use is made of the supplementary condition S/sup μ//sup u/ = 0, where u is the retarded Schwarzschild time coordinate. We derive the equations for the dynamical variables, and consider the conservation laws, that follow from the equations of motion. Particular cases of motion are also discussed and additional first integrals corresponding to these cases are found. Some of the new extra integrals are related to the Casimir operators of the Poincare group. It is found that under special conditions on the spin tensor components the particle follows a geodesic. Motion of the spinning test particle in the Schwarzschild field is considered as one of the particular cases

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.

Scalar-field amplitudes in black-hole evaporation

International Nuclear Information System (INIS)

Farley, A.N.St.J.; D'Eath, P.D.

2004-01-01

We consider the quantum-mechanical decay of a Schwarzschild-like black hole into almost-flat space and weak radiation at a very late time. That is, we are concerned with evaluating quantum amplitudes (not just probabilities) for transitions from initial to final states. In this quantum description, no information is lost because of the black hole. The Lagrangian is taken, in the first instance, to consist of the simplest locally supersymmetric generalization of Einstein gravity and a massless scalar field. The quantum amplitude to go from given initial to final bosonic data in a slightly complexified time-interval T=τexp(-iθ) at infinity may be approximated by the form constxexp(-I), where I is the (complex) Euclidean action of the classical solution filling in between the boundary data. Additionally, in a pure supergravity theory, the amplitude constxexp(-I) is exact. Suppose that Dirichlet boundary data for gravity and the scalar field are posed on an initial spacelike hypersurface extending to spatial infinity, just prior to collapse, and on a corresponding final spacelike surface, sufficiently far to the future of the initial surface to catch all the Hawking radiation. Only in an averaged sense will this radiation have an approximately spherically-symmetric distribution. If the time-interval T had been taken to be exactly real, then the resulting 'hyperbolic Dirichlet boundary-value problem' would, as is well known, not be well posed. Provided instead ('Euclidean strategy') that one takes T complex, as above (0<θ=<π/2), one expects that the field equations become strongly elliptic, and that there exists a unique solution to the classical boundary-value problem. Within this context, by expanding the bosonic part of the action to quadratic order in perturbations about the classical solution, one obtains the quantum amplitude for weak-field final configurations, up to normalization. Such amplitudes are here calculated for weak final scalar fields

Non-Gaussian ground-state deformations near a black-hole singularity

Science.gov (United States)

Hofmann, Stefan; Schneider, Marc

2017-03-01

The singularity theorem by Hawking and Penrose qualifies Schwarzschild black holes as geodesic incomplete space-times. Albeit this is a mathematically rigorous statement, it requires an operational framework that allows us to probe the spacelike singularity via a measurement process. Any such framework necessarily has to be based on quantum theory. As a consequence, the notion of classical completeness needs to be adapted to situations where the only adequate description is in terms of quantum fields in dynamical space-times. It is shown that Schwarzschild black holes turn out to be complete when probed by self-interacting quantum fields in the ground state and in excited states. The measure for populating quantum fields on hypersurfaces in the vicinity of the black-hole singularity goes to zero towards the singularity. This statement is robust under non-Gaussian deformations of and excitations relative to the ground state. The physical relevance of different completeness concepts for black holes is discussed.

THE EFFECT OF GRAVITATION ON THE POLARIZATION STATE OF A LIGHT RAY

Energy Technology Data Exchange (ETDEWEB)

Ghosh, Tanay; Sen, A. K. [Department of Physics Assam University, Silchar-788011, Assam (India)

2016-12-10

In the present work, detailed calculations have been carried out on the rotation of the polarization vector of an electromagnetic wave due to the presence of a gravitational field of a rotating body. This has been done using the general expression of Maxwell’s equation in curved spacetime. Considering the far-field approximation (i.e., the impact parameter is greater than the Schwarzschild radius and rotation parameter), the amount of rotation of the polarization vector as a function of impact parameter has been obtained for a rotating body (considering Kerr geometry). The present work shows that the rotation of the polarization vector cannot be observed in the case of Schwarzschild geometry. This work also calculates the rotational effect when considering prograde and retrograde orbits for the light ray. Although the present work demonstrates the effect of rotation of the polarization vector, it confirms that there would be no net polarization of an electromagnetic wave due to the curved spacetime geometry in a Kerr field.

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.

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.

A Useful Expression for Relativistic Energy Conservation of a Point Mass in an Isotropic Static Gravitational Field

Science.gov (United States)

Augousti, A. T.; Radosz, A.; Ostasiewicz, K.

2011-01-01

By using the symmetry and time-independence properties of Schwarzschild spacetime it is demonstrated that an energy conservation law may be expressed in terms of local velocity. From this form three important results may be derived very concisely. This highlights analogies and differences between relativistic and classical approaches to mechanics…

Quantum stress tensor in Schwarzschild space-time

International Nuclear Information System (INIS)

Howard, K.W.; Candelas, P.

1984-01-01

The vacuum expectation value of the stress-energy tensor for the Hartle-Hawking state in Schwartzschild space-time has been calculated for the conformal scalar field. separates naturally into the sum of two terms. The first coincides with an approximate expression suggested by Page. The second term is a ''remainder'' that may be evaluated numerically. The total expression is in good qualitative agreement with Page's approximation. These results are at variance with earlier results given by Fawcett whose error is explained

A superfield generalization of the classical action-at-a-distance theory

International Nuclear Information System (INIS)

Tugai, V.V.; Zheltukhin, A.A.

1994-07-01

A generalization of the Fokker-Schwarzschild-Tetrode-Wheeler-Feynman electromagnetic theory onto the superspace is considered. The classical vector and spinor fields belonging to the Maxwell supermultiplet are built of the world-line coordinates of the charged particles in superspace. (author). 9 refs

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.)

Morpho-kinematic properties of field S0 bulges in the CALIFA survey

Science.gov (United States)

Méndez-Abreu, J.; Aguerri, J. A. L.; Falcón-Barroso, J.; Ruiz-Lara, T.; Sánchez-Menguiano, L.; de Lorenzo-Cáceres, A.; Costantin, L.; Catalán-Torrecilla, C.; Zhu, L.; Sánchez-Blazquez, P.; Florido, E.; Corsini, E. M.; Wild, V.; Lyubenova, M.; van de Ven, G.; Sánchez, S. F.; Bland-Hawthorn, J.; Galbany, L.; García-Benito, R.; García-Lorenzo, B.; González Delgado, R. M.; López-Sánchez, A. R.; Marino, R. A.; Márquez, I.; Ziegler, B.; Califa Collaboration

2018-02-01

We study a sample of 28 S0 galaxies extracted from the integral field spectroscopic (IFS) survey Calar Alto Legacy Integral Field Area. We combine an accurate two-dimensional (2D) multicomponent photometric decomposition with the IFS kinematic properties of their bulges to understand their formation scenario. Our final sample is representative of S0s with high stellar masses (M⋆/M⊙ > 1010). They lay mainly on the red sequence and live in relatively isolated environments similar to that of the field and loose groups. We use our 2D photometric decomposition to define the size and photometric properties of the bulges, as well as their location within the galaxies. We perform mock spectroscopic simulations mimicking our observed galaxies to quantify the impact of the underlying disc on our bulge kinematic measurements (λ and v/σ). We compare our bulge corrected kinematic measurements with the results from Schwarzschild dynamical modelling. The good agreement confirms the robustness of our results and allows us to use bulge deprojected values of λ and v/σ. We find that the photometric (n and B/T) and kinematic (v/σ and λ) properties of our field S0 bulges are not correlated. We demonstrate that this morpho-kinematic decoupling is intrinsic to the bulges and it is not due to projection effects. We conclude that photometric diagnostics to separate different types of bulges (disc-like versus classical) might not be useful for S0 galaxies. The morpho-kinematics properties of S0 bulges derived in this paper suggest that they are mainly formed by dissipational processes happening at high redshift, but dedicated high-resolution simulations are necessary to better identify their origin.

Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field

Science.gov (United States)

Karagiorgos, A.; Pailas, T.; Dimakis, N.; Terzis, Petros A.; Christodoulakis, T.

2018-03-01

We consider a Bianchi type III axisymmetric geometry in the presence of an electromagnetic field. A first result at the classical level is that the symmetry of the geometry need not be applied on the electromagnetic tensor Fμν the algebraic restrictions, implied by the Einstein field equations to the stress energy tensor Tμν, suffice to reduce the general Fμν to the appropriate form. The classical solution thus found contains a time dependent electric and a constant magnetic charge. The solution is also reachable from the corresponding mini-superspace action, which is strikingly similar to the Reissner-Nordstr{öm one. This points to a connection between the black hole geometry and the cosmological solution here found, which is the analog of the known correlation between the Schwarzschild and the Kantowski-Sachs metrics. The configuration space is drastically modified by the presence of the magnetic charge from a 3D flat to a 3D pp wave geometry. We map the emerging linear and quadratic classical integrals of motion, to quantum observables. Along with the Wheeler-DeWitt equation these observables provide unique, up to constants, wave functions. The employment of a Bohmian interpretation of these quantum states results in deterministic (semi-classical) geometries most of which are singularity free.

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.)

Classical field theory. On electrodynamics, non-Abelian gauge theories and gravitation. 2. ed.

Energy Technology Data Exchange (ETDEWEB)

Scheck, Florian

2018-04-01

Scheck's successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes with a discussion of the Schwarzschild solution of Einstein's equations and the classical tests of general relativity. The new concept of this edition presents the content divided into two tracks: the fast track for master's students, providing the essentials, and the intensive track for all wanting to get in depth knowledge of the field. Cleary labeled material and sections guide students through the preferred level of treatment. Numerous problems and worked examples will provide successful access to Classical Field Theory.

No-Hair Theorem for Black Holes in Astrophysical Environments

Science.gov (United States)

Gürlebeck, Norman

2015-04-01

According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.

No-hair theorem for black holes in astrophysical environments.

Science.gov (United States)

Gürlebeck, Norman

2015-04-17

According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.

Correction of Cardy–Verlinde formula for Fermions and Bosons with modified dispersion relation

Energy Technology Data Exchange (ETDEWEB)

Sadatian, S. Davood, E-mail: sd-sadatian@um.ac.ir; Dareyni, H.

2017-05-15

Cardy–Verlinde formula links the entropy of conformal symmetry field to the total energy and its Casimir energy in a D-dimensional space. To correct black hole thermodynamics, modified dispersion relation can be used which is proposed as a general feature of quantum gravity approaches. In this paper, the thermodynamics of Schwarzschild four-dimensional black hole is corrected using the modified dispersion relation for Fermions and Bosons. Finally, using modified thermodynamics of Schwarzschild four-dimensional black hole, generalization for Cardy–Verlinde formula is obtained. - Highlights: • The modified Cardy–Verlinde formula obtained using MDR for Fermions and Bosons. • The modified entropy of the black hole used to correct the Cardy–Verlinde formula. • The modified entropy of the CFT has been obtained.

Newton's second law, radiation reaction and type II Einstein-Maxwell fields

International Nuclear Information System (INIS)

Newman, Ezra T

2011-01-01

Considering perturbations of the Reissner-Nordstroem metric while keeping the perturbations in the class of type II Einstein-Maxwell metrics, we perform a spherical harmonic expansion of all the variables up to the quadrupole term. This leads to rather surprising results. Referring to the source of the metric as a type II particle (analogous to referring to a Schwarzschild-Reissner-Nordstroem or Kerr-Newman particle), we see immediately that the Bondi momentum of the particle takes the classical form of mass times velocity plus an electromagnetic radiation reaction term, while the Bondi mass loss equation becomes the classical gravitational and electromagnetic (electric and magnetic) dipole and quadrupole radiation. The Bondi momentum loss equation turns into Newton's second law of motion containing the Abraham-Lorentz-Dirac radiation reaction force plus a momentum recoil (rocket) force, while the reality condition on the Bondi mass aspect yields the conservation of angular momentum. Two things must be pointed out: (1) these results, (equations of motion, etc) take place, not in the spacetime of the type II metric but in an auxiliary space referred to as H-space, whose physical meaning is rather obscure and (2) this analysis of the type II field equations is a very special case of a similar analysis of the general asymptotically flat Einstein-Maxwell equations. Although the final results are similar (though not the same), the analysis uses different equations (specifically, the type II field equations) and is vastly simpler than the general case. Without a great deal of the technical structures needed in the general case, one can see rather easily where the basic results reside in the type II field equations. (paper)

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.

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

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

Journal of Astrophysics and Astronomy | Indian Academy of Sciences

Indian Academy of Sciences (India)

We explore the global structure of the accretion flow around a Schwarzschild black hole where the accretion disc is threaded by toroidal magnetic fields. The accretion flow is optically thin and advection dominated. The synchrotron radiation is considered to be the active cooling mechanism in the flow. With this, we obtain ...

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

STRONG FIELD EFFECTS ON EMISSION LINE PROFILES: KERR BLACK HOLES AND WARPED ACCRETION DISKS

International Nuclear Information System (INIS)

Wang Yan; Li Xiangdong

2012-01-01

If an accretion disk around a black hole is illuminated by hard X-rays from non-thermal coronae, fluorescent iron lines will be emitted from the inner region of the accretion disk. The emission line profiles will show a variety of strong field effects, which may be used as a probe of the spin parameter of the black hole and the structure of the accretion disk. In this paper, we generalize the previous relativistic line profile models by including both the black hole spinning effects and the non-axisymmetries of warped accretion disks. Our results show different features from the conventional calculations for either a flat disk around a Kerr black hole or a warped disk around a Schwarzschild black hole by presenting, at the same time, multiple peaks, rather long red tails, and time variations of line profiles with the precession of the disk. We show disk images as seen by a distant observer, which are distorted by the strong gravity. Although we are primarily concerned with the iron K-shell lines in this paper, the calculation is general and is valid for any emission lines produced from a warped accretion disk around a black hole.

The Hawking effect

International Nuclear Information System (INIS)

Saffary, T.

2001-02-01

The subject of this diploma thesis is the Hawking effect. We study Fredenhagen and Haag's proof of the Hawking radiation in the framework of a semiclassical theory, the quantum field theory in curved spacetime. In particular we give an exact derivation for the short distance behaviour of the two-point function on the Schwarzschild radius

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…

The theory of everything quantum and relativity is everywhere : a Fermat Universe

CERN Document Server

Schwarzer, Norbert

2018-01-01

The book unifies quantum theory and the general theory of relativity. As an unsolved problem for about 100 years and influencing so many fields, this is probably of some importance to the scientific community. Examples like Higgs field, limit to classical Dirac and Klein–Gordon or Schrödinger cases, quantized Schwarzschild, Kerr, Kerr–Newman objects, and the photon are considered for illustration. An interesting explanation for the asymmetry of matter and antimatter in the early universe was found while quantizing the Schwarzschild metric. Along the way, the methods outlined in the book are also used to tackle the problem of the proof of Fermat’s last theorem, as there is a connection between quantum theory and basic mathematical laws of integers. The book shows that the proof of Fermat’s last theorem can be brought down to a few lines by applying new quantum theoretical methods. Because such proof was sought for over 370 years, this book is of definite interest to mathematicians.

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.

Atomic structure in black hole

International Nuclear Information System (INIS)

Nagatani, Yukinori

2006-01-01

We propose that any black hole has atomic structure in its inside and has no horizon as a model of black holes. Our proposal is founded on a mean field approximation of gravity. The structure of our model consists of a (charged) singularity at the center and quantum fluctuations of fields around the singularity, namely, it is quite similar to that of atoms. Any properties of black holes, e.g. entropy, can be explained by the model. The model naturally quantizes black holes. In particular, we find the minimum black hole, whose structure is similar to that of the hydrogen atom and whose Schwarzschild radius is approximately 1.1287 times the Planck length. Our approach is conceptually similar to Bohr's model of the atomic structure, and the concept of the minimum Schwarzschild radius is similar to that of the Bohr radius. The model predicts that black holes carry baryon number, and the baryon number is rapidly violated. This baryon number violation can be used as verification of the model. (author)

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

Quantum energy-momentum tensor in space-time with time-like killing vector

International Nuclear Information System (INIS)

Frolov, V.P.; Zel'nikov, A.I.

1987-01-01

An approximate expression for the vacuum and thermal average μν > ren of the stress-energy tensor of conformal massless fields in static Ricci-flat space-times is constructed. The application of this approximation to the space-time of a Schwarzschild black hole and its relation to the Page-Brown-Ottewill approximation are briefly discussed. (orig.)

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.

Spin One Hawking Radiation from Dirty Black Holes

OpenAIRE

Petarpa Boonserm; Tritos Ngampitipan; Matt Visser

2013-01-01

A “clean” black hole is a black hole in vacuum such as the Schwarzschild black hole. However in real physical systems, there are matter fields around a black hole. Such a black hole is called a “dirty black hole”. In this paper, the effect of matter fields on the black hole and the greybody factor is investigated. The results show that matter fields make a black hole smaller. They can increase the potential energy to a black hole to obstruct Hawking radiation to propagate. This causes the gre...

Noncommutative gravity and quantum field theory on noncummutative curved spacetimes

International Nuclear Information System (INIS)

Schenkel, Alexander

2011-01-01

The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the noncommutative

Noncommutative gravity and quantum field theory on noncummutative curved spacetimes

Energy Technology Data Exchange (ETDEWEB)

Schenkel, Alexander

2011-10-24

The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the

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.

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.

Ricci cubic gravity in d dimensions, gravitons and SAdS/Lifshitz black holes

Energy Technology Data Exchange (ETDEWEB)

Ghodsi, Ahmad; Najafi, Farzaneh [Ferdowsi University of Mashhad, Department of Physics, Mashhad (Iran, Islamic Republic of)

2017-08-15

A special class of higher curvature theories of gravity, Ricci cubic gravity (RCG), in general d dimensional space-time has been investigated in this paper. We have used two different approaches, the linearized equations of motion and the auxiliary field formalism to study the massive and massless graviton propagating modes of the AdS background. Using the auxiliary field formalism, we have found the renormalized boundary stress tensor to compute the mass of the Schwarzschild-AdS and Lifshitz black holes in RCG theory. (orig.)

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.

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

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.

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.

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.

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

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.

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)

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

Dilaton field released under collision of dilatonic black holes with Gauss-Bonnet term

Energy Technology Data Exchange (ETDEWEB)

Gwak, Bogeun [Sejong University, Department of Physics and Astronomy, Seoul (Korea, Republic of); Ro, Daeho [POSTECH, Asia Pacific Center for Theoretical Physics, Pohang, Gyeongbuk (Korea, Republic of)

2017-08-15

We investigate the upper limit of the gravitational radiation released upon the collision of two dilatonic black holes by analyzing the Gauss-Bonnet term. Dilatonic black holes have a dilaton hair coupled with this term. Using the laws of thermodynamics, the upper limit of the radiation is obtained, which reflected the effects of the dilaton hair. The amount of radiation released is greater than that emitted by a Schwarzschild black hole due to the contribution from the dilaton hair. In the collision, most of the dilaton hair can be released through radiation, where the energy radiated by the dilaton hair is maximized when the horizon of one black hole is minimized for a fixed second black hole. (orig.)

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)

Solar physics in Potsdam. (German Title: Sonnenphysik in Potsdam)

Science.gov (United States)

Staude, Jürgen

Solar research initiated the establishment of the Astrophysical Observatory Potsdam (AOP) in 1874. The present contribution outlines the development of solar physics in Potsdam from the early history of the AOP to this day. The main topics are the work of Karl Schwarzschild, the investigations related to the general theory of relativity, the foundation of the Einstein tower, Walter Grotrian's founding of modern coronal physics, and the investigations of sunspot magnetic fields.

Black hole accretion discs and screened scalar hair

Energy Technology Data Exchange (ETDEWEB)

Davis, Anne-Christine; Jha, Rahul [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Gregory, Ruth, E-mail: acd@damtp.cam.ac.uk, E-mail: r.a.w.gregory@durham.ac.uk, E-mail: r.jha@damtp.cam.ac.uk [Centre for Particle Theory, Durham University, South Road, Durham, DH1 3LE (United Kingdom)

2016-10-01

We present a novel way to investigate scalar field profiles around black holes with an accretion disc for a range of models where the Compton wavelength of the scalar is large compared to other length scales. By analysing the problem in ''Weyl' coordinates, we are able to calculate the scalar profiles for accretion discs in the static Schwarzschild, as well as rotating Kerr, black holes. We comment on observational effects.

Numerical calculations near spatial infinity

International Nuclear Information System (INIS)

Zenginoglu, Anil

2007-01-01

After describing in short some problems and methods regarding the smoothness of null infinity for isolated systems, I present numerical calculations in which both spatial and null infinity can be studied. The reduced conformal field equations based on the conformal Gauss gauge allow us in spherical symmetry to calculate numerically the entire Schwarzschild-Kruskal spacetime in a smooth way including spacelike, null and timelike infinity and the domain close to the singularity

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.

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.

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

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.)

Bending of light in quantum gravity.

Science.gov (United States)

Bjerrum-Bohr, N E J; Donoghue, John F; Holstein, Barry R; Planté, Ludovic; Vanhove, Pierre

2015-02-13

We consider the scattering of lightlike matter in the presence of a heavy scalar object (such as the Sun or a Schwarzschild black hole). By treating general relativity as an effective field theory we directly compute the nonanalytic components of the one-loop gravitational amplitude for the scattering of massless scalars or photons from an external massive scalar field. These results allow a semiclassical computation of the bending angle for light rays grazing the Sun, including long-range ℏ contributions. We discuss implications of this computation, in particular, the violation of some classical formulations of the equivalence principle.

Black Holes with Anisotropic Fluid in Lyra Scalar-Tensor Theory

Directory of Open Access Journals (Sweden)

Melis ULU DOĞRU

2018-02-01

Full Text Available In this paper, we investigate distribution of anisotropic fluid which is a resource of black holes in regard to Lyra scalar-tensor theory. As part of the theory, we obtain field equations of spherically symmetric space-time with anisotropic fluid. By using field equations, we suggest distribution of anisotropic fluid, responsible for space-time geometries such as Schwarzschild, Reissner-Nordström, Minkowski type, de Sitter type, Anti-de Sitter type, BTZ and charged BTZ black holes. Finally, we discuss obtained pressures and density of the fluid for different values of arbitrary constants, geometrically and physically.

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

Coordinates system adapted to non-inertial frames in Minkowski spacetime

Energy Technology Data Exchange (ETDEWEB)

Felix, Patricio; Dahia, F. [Universidade Federal de Campo Grande (UFCG), PB (Brazil)

2011-07-01

Full text: Static observers in curved spacetimes may interpret their proper acceleration as the opposite of a local gravitation Field (in the Newtonian sense). Based on this interpretation and the equivalence principle, we are led to investigate congruences of timelike curves in Minkowski spacetime whose acceleration field coincides with the acceleration field of static observers of curved spaces. The congruences give rise to non-inertial frames that are examined. Specifically we find, based on the locality principle, the embedding of simultaneity hypersurfaces adapted to the non-inertial frame in an explicit form for arbitrary acceleration fields. This work has motivated the fact that according to the principle of equivalence, it is expected that some physical features of gravity cam be mimicked by accelerated frames in Minkowski spacetime. The Rindler frame, which is adapted to a family of uniformly accelerated observers, is a famous example of a non-inertial system that simulates some characteristics of a black hole's geometry. This frame has been widely investigated in the literature and here we are going to start our discussion pointing out a peculiar aspect of the Rindler frame. It is related to the remarkable characteristic that the proper acceleration 'a' of Rindler observers, which is constant along their world lines, varies according to the law a = 1/ρ in relation to the observers, where ρ corresponds to the initial distance of the observers with respect to the origin of an inertial frame. This particular dependence of a ρ is connected to the behavior of static observers in Schwarzschild geometry in the vicinity of the horizon. Indeed, if ρ denotes the radial distance of an observer to the horizon, then, the proper acceleration the observers need in order to stay at rest in their position close to the horizon is proportional to 1/ρ. Therefore the Rindler congruence and the static Schwarzschild observers have the same acceleration field

Coordinates system adapted to non-inertial frames in Minkowski spacetime

International Nuclear Information System (INIS)

Felix, Patricio; Dahia, F.

2011-01-01

Full text: Static observers in curved spacetimes may interpret their proper acceleration as the opposite of a local gravitation Field (in the Newtonian sense). Based on this interpretation and the equivalence principle, we are led to investigate congruences of timelike curves in Minkowski spacetime whose acceleration field coincides with the acceleration field of static observers of curved spaces. The congruences give rise to non-inertial frames that are examined. Specifically we find, based on the locality principle, the embedding of simultaneity hypersurfaces adapted to the non-inertial frame in an explicit form for arbitrary acceleration fields. This work has motivated the fact that according to the principle of equivalence, it is expected that some physical features of gravity cam be mimicked by accelerated frames in Minkowski spacetime. The Rindler frame, which is adapted to a family of uniformly accelerated observers, is a famous example of a non-inertial system that simulates some characteristics of a black hole's geometry. This frame has been widely investigated in the literature and here we are going to start our discussion pointing out a peculiar aspect of the Rindler frame. It is related to the remarkable characteristic that the proper acceleration 'a' of Rindler observers, which is constant along their world lines, varies according to the law a = 1/ρ in relation to the observers, where ρ corresponds to the initial distance of the observers with respect to the origin of an inertial frame. This particular dependence of a ρ is connected to the behavior of static observers in Schwarzschild geometry in the vicinity of the horizon. Indeed, if ρ denotes the radial distance of an observer to the horizon, then, the proper acceleration the observers need in order to stay at rest in their position close to the horizon is proportional to 1/ρ. Therefore the Rindler congruence and the static Schwarzschild observers have the same acceleration field a(ρ). However

MEASURING DARK MATTER PROFILES NON-PARAMETRICALLY IN DWARF SPHEROIDALS: AN APPLICATION TO DRACO

International Nuclear Information System (INIS)

Jardel, John R.; Gebhardt, Karl; Fabricius, Maximilian H.; Williams, Michael J.; Drory, Niv

2013-01-01

We introduce a novel implementation of orbit-based (or Schwarzschild) modeling that allows dark matter density profiles to be calculated non-parametrically in nearby galaxies. Our models require no assumptions to be made about velocity anisotropy or the dark matter profile. The technique can be applied to any dispersion-supported stellar system, and we demonstrate its use by studying the Local Group dwarf spheroidal galaxy (dSph) Draco. We use existing kinematic data at larger radii and also present 12 new radial velocities within the central 13 pc obtained with the VIRUS-W integral field spectrograph on the 2.7 m telescope at McDonald Observatory. Our non-parametric Schwarzschild models find strong evidence that the dark matter profile in Draco is cuspy for 20 ≤ r ≤ 700 pc. The profile for r ≥ 20 pc is well fit by a power law with slope α = –1.0 ± 0.2, consistent with predictions from cold dark matter simulations. Our models confirm that, despite its low baryon content relative to other dSphs, Draco lives in a massive halo.

Dirac Hamiltonian and Reissner-Nordström metric: Coulomb interaction in curved space-time

Science.gov (United States)

Noble, J. H.; Jentschura, U. D.

2016-03-01

We investigate the spin-1 /2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordström space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordström geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational and electrogravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electrogravitational correction terms to the potential proportional to αnG , where α is the fine-structure constant and G is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic coupling. The resulting spectrum of radially symmetric, electrostatically bound systems (with gravitational corrections) is evaluated for example cases.

Remarks on the motion of macroscopic and microscopic spinning particles in relativity; Remarques sur le mouvement des particules a spin macroscopiques et microscopiques en relativite

Energy Technology Data Exchange (ETDEWEB)

Micoulaut, R [Commissariat a l' Energie Atomique, Limeil-Brevannes (France). Centre d' Etudes

1968-07-01

The Papapetrou equations of motion of a spinning particle do not allow the unequivocal determination of the world-line described by the particle. The motion should be completely determined in adding a supplementary condition. For macroscopic particles, characterized by the conditions of Corinaldesi-Papapetrou and Tulczyjew, moving in a Schwarzschild field we obtain additional term in the expression for the advance of perihelion. For microscopic particles we summarize the results obtained using the conditions of Weyssenhoff, Nakano, Hoenl-Papapetrou and Wessel. (author) [French] Les equations de Papapetrou decrivant le mouvement d'une particule a spin ne permettent pas de fixer de maniere univoque la ligne d'univers que parcourt la particule. Le mouvement sera completement determine en imposant une condition supplementaire arbitraire. Pour des particules macroscopiques, caracterisees par les conditions de Corinaldesi-Papapetrou et Tulczyjew, se deplacant dans un champ de Schwarzschild on obtient un terme supplementaire dans l'expression de l'avance du perihelie. Pour les particules microscopiques on rappellera rapidement les resultats obtenus en utilisant les conditions simples de Weyssenhoff, Nakano, Hoenl-Papapetrou et Wessel. (auteur)

A New Model of Black Hole Formation

Directory of Open Access Journals (Sweden)

Thayer G. D.

2013-10-01

Full Text Available The formation of a black hole and its event horizon are described. Conclusions, which are the result of a thought experiment, show that Schwarzschild [1] was correct: A singularity develops at the event horizon of a newly-formed black hole. The intense gravitational field that forms near the event horizon results in the mass-energy of the black hole accumulating in a layer just inside the event horizon, rather than collapsing into a central singularity.

Black hole decay as geodesic motion

International Nuclear Information System (INIS)

Gupta, Kumar S.; Sen, Siddhartha

2003-01-01

We show that a formalism for analyzing the near-horizon conformal symmetry of Schwarzschild black holes using a scalar field probe is capable of describing black hole decay. The equation governing black hole decay can be identified as the geodesic equation in the space of black hole masses. This provides a novel geometric interpretation for the decay of black holes. Moreover, this approach predicts a precise correction term to the usual expression for the decay rate of black holes

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 ...

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...

Neutrino oscillations in curved spacetime: A heuristic treatment

International Nuclear Information System (INIS)

Cardall, C.Y.; Fuller, G.M.

1997-01-01

We discuss neutrino oscillations in curved spacetime. Our heuristic approach can accommodate matter effects and gravitational contributions to neutrino spin precession in the presence of a magnetic field. By way of illustration, we perform explicit calculations in the Schwarzschild geometry. In this case, gravitational effects on neutrino oscillations are intimately related to the redshift. We discuss how spacetime curvature could affect the resonance position and adiabaticity of matter-enhanced neutrino flavor conversion. copyright 1997 The American Physical Society

Distorted black holes in terms of multipole moments

International Nuclear Information System (INIS)

Suen, W.

1986-01-01

In terms of a multipole-moment formalism previously developed for non-asymptotically-flat systems in general relativity, the metric of a Schwarzschild black hole in an external quadrupolar gravitational field is studied. Among other results, we find that the black hole develops an induced quadrupole moment, which in turn generates a tidal field opposing the applied field. This effect, plus the fact that the horizon cannot expand when a quasistatic tidal force is applied, can be described in terms of effective 2-dimensional elastic moduli for the black-hole horizon. The bulk modulus is kappa = ∞, and the shear modulus is mu = -63/(20πM), where M is the hole's mass

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...

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.

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

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

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.

ADM Mass for Asymptotically de Sitter Space-Time

International Nuclear Information System (INIS)

Huang Shiming; Yue Ruihong; Jia Dongyan

2010-01-01

In this paper, an ADM mass formula for asymptotically de Sitter(dS) space-time is derived from the energy-momentum tensor. We take the vacuum dS space as the background and investigate the ADM mass of the (d + 3)-dimensional sphere-symmetric space with a positive cosmological constant, and find that the ADM mass of asymptotically dS space is based on the ADM mass of Schwarzschild field and the cosmological background brings some small mass contribution as well. (general)

Probing the Higgs vacuum with general relativity

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Mannheim, Philip D.; Kazanas, Demosthenes

1991-01-01

It is shown that the structure of the Higgs vacuum can be revealed in gravitational experiments which probe the Schwarzschild geometry to only one order in MG/r beyond that needed for the classical tests of general relativity. The possibility that deviations from the conventional geometry are at least theoretically conceivable is explored. The deviations obtained provide a diagnostic test for searching for the existence of macroscopic scalar fields and open up the possiblity for further exploring the Higgs mechanism.

Punctuated eternal inflation via AdS/CFT duality

International Nuclear Information System (INIS)

Lowe, David A.; Roy, Shubho

2010-01-01

The work is an attempt to model a scenario of inflation in the framework of anti-de Sitter/conformal field theory duality, a potentially complete nonperturbative description of quantum gravity. We study bubble geometries with de Sitter interiors within an ambient Schwarzschild anti-de Sitter black hole spacetime and the properties of the corresponding states in the dual conformal field theory. It is argued the viable bubble states can be identified with a subset of the black hole microstates. Consistency checks are performed and a number of implications regarding cosmology are discussed including how the key problems or paradoxes of conventional eternal inflation are overcome in this scenario.

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

Enhanced quantum teleportation in the background of Schwarzschild spacetime by weak measurements

OpenAIRE

Xiao, Xing; Yao, Yao; Li, Yan-Ling; Xie, Ying-Mao

2017-01-01

It is commonly believed that the fidelity of quantum teleportation in the gravitational field would be degraded due to the heat up by the Hawking radiation. In this paper, we point out that the Hawking effect could be eliminated by the combined action of pre- and post-weak measurements, and thus the teleportation fidelity is almost completely protected. It is intriguing to notice that the enhancement of fidelity could not be attributed to the improvement of entanglement, but rather to the pro...

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.

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.

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.

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

New general relativity

International Nuclear Information System (INIS)

Hayashi, K.; Shirafuji, T.

1979-01-01

A gravitational theory is formulated on the Weitzenboeck space-time, characterized by the vanishing curvature tensor (absolute parallelism) and by the torsion tensor formed of four parallel vector fields. This theory is called new general relativity, since Einstein in 1928 first gave its original form. New general relativity has three parameters c 1 , c 2 , and lambda, besides the Einstein constant kappa. In this paper we choose c 1 = 0 = c 2 , leaving open lambda. We prove, among other things, that (i) a static, spherically symmetric gravitational field is given by the Schwarzschild metric, that (ii) in the weak-field approximation an antisymmetric field of zero mass and zero spin exists, besides gravitons, and that (iii) new general relativity agrees with all the experiments so far carried out

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

Accretion of a ghost condensate by black holes

International Nuclear Information System (INIS)

Frolov, Andrei V.

2004-01-01

The intent of this paper is to point out that the accretion of a ghost condensate by black holes could be extremely efficient. We analyze steady-state spherically symmetric flows of the ghost fluid in the gravitational field of a Schwarzschild black hole and calculate the accretion rate. Unlike minimally coupled scalar field or quintessence, the accretion rate is set not by the cosmological energy density of the field, but by the energy scale of the ghost condensate theory. If hydrodynamical flow is established, it could be as high as a tenth of a solar mass per second for 10 MeV scale ghost condensate accreting onto a stellar-sized black hole, which puts serious constraints on the parameters of the ghost condensate model

Accretion of Ghost Condensate by Black Holes

Energy Technology Data Exchange (ETDEWEB)

Frolov, A

2004-06-02

The intent of this letter is to point out that the accretion of a ghost condensate by black holes could be extremely efficient. We analyze steady-state spherically symmetric flows of the ghost fluid in the gravitational field of a Schwarzschild black hole and calculate the accretion rate. Unlike minimally coupled scalar field or quintessence, the accretion rate is set not by the cosmological energy density of the field, but by the energy scale of the ghost condensate theory. If hydrodynamical flow is established, it could be as high as tenth of a solar mass per second for 10MeV-scale ghost condensate accreting onto a stellar-sized black hole, which puts serious constraints on the parameters of the ghost condensate model.

Quantum and thermodynamical aspects of black holes

International Nuclear Information System (INIS)

Sande e Lemos, J.P. de.

1982-08-01

The collapse of a spherically symmetric matter distribution resulting in Schwarzschild's black holes (BH) is discussed. Using Kerr metric, some dynamical results envolving test particles orbiting around BH with rotation are obtained. Quantum field theory is used to discuss the results obtained by Hawking in which one BH can emit a stationary flux of particles working a BH in a given temperature. Then, thermodynamics is introduced, some properties are verified and some phenomena of BH-radiation and BH-BH interaction are studied. (L.C.) [pt

Strong lensing of a regular black hole with an electrodynamics source

Science.gov (United States)

Manna, Tuhina; Rahaman, Farook; Molla, Sabiruddin; Bhadra, Jhumpa; Shah, Hasrat Hussain

2018-05-01

In this paper we have investigated the gravitational lensing phenomenon in the strong field regime for a regular, charged, static black holes with non-linear electrodynamics source. We have obtained the angle of deflection and compared it to a Schwarzschild black hole and Reissner Nordström black hole with similar properties. We have also done a graphical study of the relativistic image positions and magnifications. We hope that this method may be useful in the detection of non-luminous bodies like this current black hole.

Hawking radiation from black holes in de Sitter spaces

International Nuclear Information System (INIS)

Jiang Qingquan

2007-01-01

Recently, Hawking radiation has been treated, by Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303), as a compensating flux of the energy-momentum tensor required to cancel a gravitational anomaly at the event horizon (EH) of a Schwarzschild-type black hole. In this paper, motivated by this work, Hawking radiation from the event horizon (EH) and the de Sitter cosmological horizon (CH) of black holes in de Sitter spaces, specifically including the purely de Sitter black hole and the static, spherically symmetric Schwarzschild-de Sitter black hole as well as the rotating Kerr-de Sitter black hole, have been studied by anomalies. The results show that the gauge-current and energy-momentum tensor fluxes, required to restore gauge invariance and general coordinate covariance at the EH and the CH, are precisely equal to those of Hawking radiation from the EH and the CH, respectively. It should be noted that gauge and gravitational anomalies taking place at the CH arise from the fact that the effective field theory is formulated inside the CH to integrate out the classically irrelevant outgoing modes at the CH, which are different from those at the black hole horizon

QED loop effects in the spacetime background of a Schwarzschild black hole

Science.gov (United States)

Emelyanov, Viacheslav A.

2017-12-01

The black-hole evaporation implies that the quantum-field propagators in a local Minkowski frame acquire a correction, which gives rise to this process. The modification of the propagators causes, in turn, non-trivial local effects due to the radiative/loop diagrams in non-linear QFTs. In particular, there should be imprints of the evaporation in QED, if one goes beyond the tree-level approximation. Of special interest in this respect is the region near the black-hole horizon, which, already at tree level, appears to show highly non-classical features, e.g., negative energy density and energy flux into the black hole.

Astronomical technology - the past and the future. Karl Schwarzschild Award Lecture 2015

Science.gov (United States)

Appenzeller, I.

2016-07-01

The past fifty years have been an epoch of impressive progress in the field of astronomical technology. Practically all the technical tools, which we use today, have been developed during that time span. While the first half of this period has been dominated by advances in the detector technologies, during the past two decades innovative telescope concepts have been developed for practically all wavelength ranges where astronomical observations are possible. Further important advances can be expected in the next few decades. Based on the experience of the past, some of the main sources of technological progress can be identified.

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

Vacuum polarization in curved spacetime

International Nuclear Information System (INIS)

Guy, R.W.

1979-01-01

A necessary step in the process of understanding the quantum theory of gravity is the calculation of the stress-energy tensor of quantized fields in curved space-times. The determination of the stress tensor, a formally divergent object, is made possible in this dissertation by utilizing the zeta-function method of regularization and renormalization. By employing this scheme's representation of the renormalized effective action functional, an expression of the stress tensor for a massless, conformally invariant scalar field, first given by DeWitt, is derived. The form of the renormalized stress tensor is first tested in various examples of flat space-times. It is shown to vanish in Minkowski space and to yield the accepted value of the energy density in the Casimir effect. Next, the stress tensor is calculated in two space-times of constant curvature, the Einstein universe and the deSitter universe, and the results are shown to agree with those given by an expression of the stress tensor that is valid in conformally flat space-times. This work culminates in the determination of the stress tensor on the horizon of a Schwarzschild black hole. This is accomplished by approximating the radial part of the eigen-functions and the metric in the vicinity of the horizon. The stress tensor at this level approximation is found to be pure trace. The approximated forms of the Schwarzschild metric describes a conformally flat space-time that possesses horizons

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

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.)

Ellipticity behaviour of relativistic Maclaurin spheroids

International Nuclear Information System (INIS)

Abramowicz, M.A.; Miller, J.C.; International School of Advanced Studies, Trieste; Oxford Univ.

1990-01-01

Chandrasekhar and Miller (1974 Mon. Not. R. Astr. Soc., 167, 63) found that, according to the general theory of relativity, when slowly rotating spheroids contract, conserving angular momentum, their eccentricity does not increase monotonically, as is the case for Newtonian gravity, but instead reaches a maximum (when the mean radius is a few times the Schwarzschild radius) and then decreases again. We show here that this can be explained within the framework of the recent discussion of rotational effects in a strong gravitational field. We suggest that it can be convenient to introduce a 'corrected' Newtonian theory, incorporating terms to approximate strong field effects, and that such a corrected theory could be useful for numerical studies. (author)

A gravitational entropy proposal

International Nuclear Information System (INIS)

Clifton, Timothy; Tavakol, Reza; Ellis, George F R

2013-01-01

We propose a thermodynamically motivated measure of gravitational entropy based on the Bel–Robinson tensor, which has a natural interpretation as the effective super-energy–momentum tensor of free gravitational fields. The specific form of this measure differs depending on whether the gravitational field is Coulomb-like or wave-like, and reduces to the Bekenstein–Hawking value when integrated over the interior of a Schwarzschild black hole. For scalar perturbations of a Robertson–Walker geometry we find that the entropy goes like the Hubble weighted anisotropy of the gravitational field, and therefore increases as structure formation occurs. This is in keeping with our expectations for the behaviour of gravitational entropy in cosmology, and provides a thermodynamically motivated arrow of time for cosmological solutions of Einstein’s field equations. It is also in keeping with Penrose’s Weyl curvature hypothesis. (paper)

Multiple shadows from distorted static black holes

Science.gov (United States)

Grover, Jai; Kunz, Jutta; Nedkova, Petya; Wittig, Alexander; Yazadjiev, Stoytcho

2018-04-01

We study the local shadow of the Schwarzschild black hole with a quadrupole distortion and the influence of the external gravitational field on the photon dynamics. The external matter sources modify the light ring structure and lead to the appearance of multiple shadow images. In the case of negative quadrupole moments we identify the most prominent mechanism causing multiple shadow formation. Furthermore, we obtain a condition under which this mechanism can be realized. This condition depends on the quadrupole moment, but also on the position of the observer and the celestial sphere.

Particle creation by a black hole as a consequence of the Casimir effect

International Nuclear Information System (INIS)

Nugayev, R.M.

1987-01-01

Particle creation by a blackhole is investigated in terms of temperature corrections to the Casimir effect. The reduction of the Hawking effect to more familiar effects observed in the laboratory enables us to reveal the mechanism of particle creation. The blackbody nature of the Hawking radiation is due to the interaction of virtual particles with the surface of a ''cavity'' formed by the Schwarzschild gravitational field potential barrier. These particles are ''squeezed out'' by the contraction of the potential barrier and appear to an observer at J + as the real blackbody ones. (orig.)

Three-dimensional Einstein-Klein-Gordon system in characteristic numerical relativity

International Nuclear Information System (INIS)

Barreto, W.; Silva, A. da; Lehner, L.; Gomez, R.; Rosales, L.; Winicour, J.

2005-01-01

We incorporate a massless scalar field into a three-dimensional code for the characteristic evolution of the gravitational field. The extended three-dimensional code for the Einstein-Klein-Gordon system is calibrated to be second-order convergent. It provides an accurate calculation of the gravitational and scalar radiation at infinity. As an application, we simulate the fully nonlinear evolution of an asymmetric scalar pulse of ingoing radiation propagating toward an interior Schwarzschild black hole and compute the backscattered scalar and gravitational outgoing radiation patterns. The amplitudes of the scalar and gravitational outgoing radiation modes exhibit the predicted power law scaling with respect to the amplitude of the initial data. For the scattering of an axisymmetric scalar field, the final ring down matches the complex frequency calculated perturbatively for the l=2 quasinormal mode

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.

Anomalous transport from holography. Part I

Energy Technology Data Exchange (ETDEWEB)

Bu, Yanyan [Department of Physics, Ben-Gurion University of the Negev,Beer-Sheva 84105 (Israel); Lublinsky, Michael [Department of Physics, Ben-Gurion University of the Negev,Beer-Sheva 84105 (Israel); Physics Department, University of Connecticut,2152 Hillside Road, Storrs, CT 06269-3046 (United States); Sharon, Amir [Department of Physics, Ben-Gurion University of the Negev,Beer-Sheva 84105 (Israel)

2016-11-17

We revisit the transport properties induced by the chiral anomaly in a charged plasma holographically dual to anomalous U(1){sub V}×U(1){sub A} Maxwell theory in Schwarzschild-AdS{sub 5}. Off-shell constitutive relations for vector and axial currents are derived using various approximations generalising most of known in the literature anomaly-induced phenomena and revealing some new ones. In a weak external field approximation, the constitutive relations have all-order derivatives resummed into six momenta-dependent transport coefficient functions: the diffusion, the electric/magnetic conductivity, and three anomaly induced functions. The latter generalise the chiral magnetic and chiral separation effects. Nonlinear transport is studied assuming presence of constant background external fields. The chiral magnetic effect, including all order nonlinearity in magnetic field, is proven to be exact when the magnetic field is the only external field that is turned on. Non-linear corrections to the constitutive relations due to electric and axial external fields are computed.

Anomalous transport from holography. Part I

International Nuclear Information System (INIS)

Bu, Yanyan; Lublinsky, Michael; Sharon, Amir

2016-01-01

We revisit the transport properties induced by the chiral anomaly in a charged plasma holographically dual to anomalous U(1)_V×U(1)_A Maxwell theory in Schwarzschild-AdS_5. Off-shell constitutive relations for vector and axial currents are derived using various approximations generalising most of known in the literature anomaly-induced phenomena and revealing some new ones. In a weak external field approximation, the constitutive relations have all-order derivatives resummed into six momenta-dependent transport coefficient functions: the diffusion, the electric/magnetic conductivity, and three anomaly induced functions. The latter generalise the chiral magnetic and chiral separation effects. Nonlinear transport is studied assuming presence of constant background external fields. The chiral magnetic effect, including all order nonlinearity in magnetic field, is proven to be exact when the magnetic field is the only external field that is turned on. Non-linear corrections to the constitutive relations due to electric and axial external fields are computed.

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.

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''.

On wormholes and black holes solutions of Einstein gravity coupled to a K-massless scalar field

International Nuclear Information System (INIS)

Estevez-Delgado, J; Zannias, T

2007-01-01

We investigate the nature of black holes and wormholes admitted by a K-essence model involving a massless scalar field φ, minimally coupled to gravity. Via Weyl's formalism, we show that any axial wormhole of the theory can be generated by a unique pair of harmonic functions: U(λ) = π/2 C + C arctan(λ/λ 0 ), φ(λ) = π/2 D + D arctan(λ/λ 0 ) where λ is one of the oblate coordinate, λ 0 > 0 and (C, D) real parameters. The properties of the wormholes depends crucially upon the values of the parameters (C, D). Whenever (C, D) are chosen so that 2C 2 - kD 2 = -2 the wormhole is spherical, while for the case where 2C 2 - kD 2 = -4 or 2C 2 - kD 2 = -6 the wormhole throat possesses toroidal topology. Those two families of wormholes exhaust all regular static and axisymmetric wormholes admitted by this theory. For completeness we add that whenever (C, D) satisfy 2C 2 - kD 2 = -2l with l ≥ 3/2 one still generates a spacetime possessing two asymptotically flat but the throat connecting the two ends contains a string like singularity. For the refined case where 2C 2 - kD 2 = -2l with l = 4,5, ... the resulting spacetime represents a multi-sheeted configuration which even though free of curvature singularities nevertheless the spacetime topology is distinct to so far accepted wormhole topology. Spacetimes generated by the pair (U(λ), φ(λ)) and parameters (C, D) subject to 2C 2 - kD 2 = -2l with l 2 bifurcating, regular Killing horizon necessary possesses a constant exterior scalar field. Under the assumption that the event horizon of any static black hole of this theory is a Killing horizon, the results show that the only static black hole admitted by this K-essence model, is the Schwarzschild black hole

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

Exponential fading to white of black holes in quantum gravity

International Nuclear Information System (INIS)

Barceló, Carlos; Carballo-Rubio, Raúl; Garay, Luis J

2017-01-01

Quantization of the gravitational field may allow the existence of a decay channel of black holes into white holes with an explicit time-reversal symmetry. The definition of a meaningful decay probability for this channel is studied in spherically symmetric situations. As a first nontrivial calculation, we present the functional integration over a set of geometries using a single-variable function to interpolate between black-hole and white-hole geometries in a bounded region of spacetime. This computation gives a finite result which depends only on the Schwarzschild mass and a parameter measuring the width of the interpolating region. The associated probability distribution displays an exponential decay law on the latter parameter, with a mean lifetime inversely proportional to the Schwarzschild mass. In physical terms this would imply that matter collapsing to a black hole from a finite radius bounces back elastically and instantaneously, with negligible time delay as measured by external observers. These results invite to reconsider the ultimate nature of astrophysical black holes, providing a possible mechanism for the formation of black stars instead of proper general relativistic black holes. The existence of both this decay channel and black stars can be tested in future observations of gravitational waves. (paper)

Relationship between five-dimensional black holes and de Sitter spaces

International Nuclear Information System (INIS)

Myung, Y S

2004-01-01

We study a close relationship between the topological anti-de Sitter (TAdS) black holes and topological de Sitter (TdS) spaces including the Schwarzschild-de Sitter (SdS) black hole in five dimensions. We show that all thermal properties of the TdS spaces can be found from those of the TAdS black holes by replacing k by -k. Also we find that all thermal information for the cosmological horizon of the SdS black hole is obtained from either the hyperbolic-AdS black hole or the Schwarzschild-TdS space by substituting m with -m. For this purpose we calculate thermal quantities of bulk (Euclidean) conformal field theory (ECFT) and moving domain wall by using the A(dS)/(E)CFT correspondences. Further, we compute logarithmic corrections to the Bekenstein-Hawking entropy, Cardy-Verlinde formula and Friedmann equation due to thermal fluctuations. It implies that in the thermal relation between the TdS spaces and TAdS black holes, the cosmological horizon plays the same role as the horizon of TAdS black holes. Finally we note that the dS/ECFT correspondence is valid for the TdS spaces in conjunction with the AdS/CFT correspondence for the TAdS black holes

New Massive Gravity and AdS4 Counterterms

International Nuclear Information System (INIS)

Jatkar, Dileep P.; Sinha, Aninda

2011-01-01

We show that the recently proposed Dirac-Born-Infeld extension of new massive gravity emerges naturally as a counterterm in four-dimensional anti-de Sitter space (AdS 4 ). The resulting on-shell Euclidean action is independent of the cutoff at zero temperature. We also find that the same choice of counterterm gives the usual area law for the AdS 4 Schwarzschild black hole entropy in a cutoff-independent manner. The parameter values of the resulting counterterm action correspond to a c=0 theory in the context of the duality between AdS 3 gravity and two-dimensional conformal field theory. We rewrite this theory in terms of the gauge field that is used to recast 3D gravity as a Chern-Simons theory.

Black holes in the gravity/gauge theory correspondence

International Nuclear Information System (INIS)

Gregory, J.P.

2002-06-01

The AdS/CFT correspondence provides a microscopic description of black hole thermodynamics. In this thesis, I study the relation between the classical physics of black holes and this microscopic description. I first consider the gauge theory's holographic encoding of non-trivial global causal structure, by studying various probes of the black hole. I study the charged black hole, so that the thermal scale is separated from the horizon scale, to demonstrate which relates to the field theory scale size. I find that, when probing the horizon, both Wilson loops and the duals of static supergravity probes have a scale size determined by the horizon, but the field theory scale size is divergent for a time-dependent probe. I also use the bulk black hole geometry to study the physics of the boundary theory. If we consider a dynamical boundary, a braneworld cosmology is induced from the bulk. However, the presence of matter on the brane introduces unconventional quadratic terms in the FRW equations of this braneworld. I find that bulk black holes induce identical unconventional terms on a matterless brane, therefore providing an alternative description of the same cosmology. A new conjecture relating classical and thermodynamic stability of black branes has emerged from the AdS/CFT correspondence. I make progress in proving this for the case of Schwarzschild black holes in a finite cavity. I also extend the conjecture to the supergravity backgrounds of the direct product form Schwarzschild-AdS x Sphere, which are relevant to my study of the AdS/CFT correspondence. (author)

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

Optical Design of the STAR-X Telescope

Science.gov (United States)

Saha, Timo T.; Zhang, William W.; McClelland, Ryan S.

2017-01-01

Top-level science goals of the Survey and Time-domain Astrophysical Research eXplorer (STAR-X) include: investigations of most violent explosions in the universe, study of growth of black holes across cosmic time and mass scale, and measure how structure formation heats majority of baryons in the universe. To meet these goals, the field-of-view of the telescope should be about 1 square-degree, the angular resolution should be 5 arc-seconds or below across large part of the field-of-view. The on-axis effective area at 1 KeV should be about 2,000 sq cm. Payload cost and launch considerations limit the outer diameter, focal length, and mass to 1.3 meters, 5 meters, and 250 kilograms, respectively. Telescope design is based on a segmented meta-shell approach we have developed at Goddard Space Flight Center for the STAR-X telescope. The telescope shells are divided into 30-degree segments. Individual telescopes and meta-shells are nested inside each other to meet the effective area requirements in 0.5 - 6.0 KeV range. We consider Wolter-Schwarzschild, and Modified-Wolter-Schwarzschild telescope designs as basic building blocks of the nested STAR-X telescope. These designs offer an excellent resolution over a large field of views. Nested telescopes are vulnerable to stray light problems. We have designed a multi-component baffle system to eliminate direct and single-reflection light paths inside the telescopes. Large number of internal and external baffle vane structures are required to prevent stray rays from reaching the focal plane. We have developed a simple ray-trace based tool to determine the dimensions and locations of the baffles. In this paper, we present the results of our trade studies, baffle design studies, and optical performance analyses of the STAR-X telescope.

Determining the minimal length scale of the generalized uncertainty principle from the entropy-area relationship

International Nuclear Information System (INIS)

Kim, Wontae; Oh, John J.

2008-01-01

We derive the formula of the black hole entropy with a minimal length of the Planck size by counting quantum modes of scalar fields in the vicinity of the black hole horizon, taking into account the generalized uncertainty principle (GUP). This formula is applied to some intriguing examples of black holes - the Schwarzschild black hole, the Reissner-Nordstrom black hole, and the magnetically charged dilatonic black hole. As a result, it is shown that the GUP parameter can be determined by imposing the black hole entropy-area relationship, which has a Planck length scale and a universal form within the near-horizon expansion

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

Holography and Entanglement in Flat Spacetime

International Nuclear Information System (INIS)

Li Wei; Takayanagi, Tadashi

2011-01-01

We propose a holographic correspondence of the flat spacetime based on the behavior of the entanglement entropy and the correlation functions. The holographic dual theory turns out to be highly nonlocal. We argue that after most part of the space is traced out, the reduced density matrix gives the maximal entropy and the correlation functions become trivial. We present a toy model for this holographic dual using a nonlocal scalar field theory that reproduces the same property of the entanglement entropy. Our conjecture is consistent with the entropy of Schwarzschild black holes in asymptotically flat spacetimes.

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.

On the reduction of symmetry for static flat space-time in some general cylindrical-like coordinates

International Nuclear Information System (INIS)

Bokhari, A.H.; Bokhari, N.A.

1987-09-01

Flat static metric in terms of general cylindrical-like coordinates is considered and symmetry is reduced step by step. It turns out that the maximal and the minimal symmetry remains the same as that of the Minkowski or the Schwarzschild type. As soon as the dimensions of the metric are reduced, the symmetry turns out to be 6 or 3 in terms of independent Killing vector fields, respectively, not yet filling all the gaps between 10 to 8 to 4 or from 10 to 8 to 6 to 4 to 3 to 1. (author). 8 refs

Presenting Newtonian gravitation

International Nuclear Information System (INIS)

Counihan, Martin

2007-01-01

The basic principles of the Newtonian theory of gravitation are presented in a way which students may find more logically coherent, mathematically accessible and physically interesting than other approaches. After giving relatively simple derivations of the circular hodograph and the elliptical orbit from the inverse-square law, the concept of gravitational energy is developed from vector calculus. It is argued that the energy density of a gravitational field may reasonably be regarded as -g 2 /8πG, and that the inverse-square law may be replaced by a Schwarzschild-like force law without the need to invoke non-Euclidean geometry

2D Relativistic MHD simulations of the Kruskal-Schwarzschild instability in a relativistic striped wind

Science.gov (United States)

Gill, Ramandeep; Granot, Jonathan; Lyubarsky, Yuri

2018-03-01

We study the linear and non-linear development of the Kruskal-Schwarzchild instability in a relativisitically expanding striped wind. This instability is the generalization of Rayleigh-Taylor instability in the presence of a magnetic field. It has been suggested to produce a self-sustained acceleration mechanism in strongly magnetized outflows found in active galactic nuclei, gamma-ray bursts, and micro-quasars. The instability leads to magnetic reconnection, but in contrast with steady-state Sweet-Parker reconnection, the dissipation rate is not limited by the current layer's small aspect ratio. We performed two-dimensional (2D) relativistic magnetohydrodynamic (RMHD) simulations featuring two cold and highly magnetized (1 ≤ σ ≤ 103) plasma layers with an anti-parallel magnetic field separated by a thin layer of relativistically hot plasma with a local effective gravity induced by the outflow's acceleration. Our simulations show how the heavier relativistically hot plasma in the reconnecting layer drips out and allows oppositely oriented magnetic field lines to reconnect. The instability's growth rate in the linear regime matches the predictions of linear stability analysis. We find turbulence rather than an ordered bulk flow near the reconnection region, with turbulent velocities up to ˜0.1c, largely independent of model parameters. However, the magnetic energy dissipation rate is found to be much slower, corresponding to an effective ordered bulk velocity inflow into the reconnection region vin = βinc of 10-3 ≲ βin ≲ 5 × 10-3. This occurs due to the slow evacuation of hot plasma from the current layer, largely because of the Kelvin-Helmholtz instability experienced by the dripping plasma. 3D RMHD simulations are needed to further investigate the non-linear regime.

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.

Charged massive particle at rest in the field of a Reissner-Nordstroem black hole

International Nuclear Information System (INIS)

Bini, D.; Geralico, A.; Ruffini, R.

2007-01-01

The interaction of a Reissner-Nordstroem black hole and a charged massive particle is studied in the framework of perturbation theory. The particle backreaction is taken into account, studying the effect of general static perturbations of the hole following the approach of Zerilli. The solutions of the combined Einstein-Maxwell equations for both perturbed gravitational and electromagnetic fields to first order of the perturbation are exactly reconstructed by summing all multipoles, and are given explicit closed form expressions. The existence of a singularity-free solution of the Einstein-Maxwell system requires that the charge-to-mass ratios of the black hole and of the particle satisfy an equilibrium condition which is in general dependent on the separation between the two bodies. If the black hole is undercritically charged (i.e. its charge-to-mass ratio is less than one), the particle must be overcritically charged, in the sense that the particle must have a charge-to-mass ratio greater than one. If the charge-to-mass ratios of the black hole and of the particle are both equal to one (so that they are both critically charged, or 'extreme'), the equilibrium can exist for any separation distance, and the solution we find coincides with the linearization in the present context of the well-known Majumdar-Papapetrou solution for two extreme Reissner-Nordstroem black holes. In addition to these singularity-free solutions, we also analyze the corresponding solution for the problem of a massive particle at rest near a Schwarzschild black hole, exhibiting a strut singularity on the axis between the two bodies. The relations between our perturbative solutions and the corresponding exact two-body solutions belonging to the Weyl class are also discussed

Unbound motion on a Schwarzschild background: Practical approaches to frequency domain computations

Science.gov (United States)

Hopper, Seth

2018-03-01

Gravitational perturbations due to a point particle moving on a static black hole background are naturally described in Regge-Wheeler gauge. The first-order field equations reduce to a single master wave equation for each radiative mode. The master function satisfying this wave equation is a linear combination of the metric perturbation amplitudes with a source term arising from the stress-energy tensor of the point particle. The original master functions were found by Regge and Wheeler (odd parity) and Zerilli (even parity). Subsequent work by Moncrief and then Cunningham, Price and Moncrief introduced new master variables which allow time domain reconstruction of the metric perturbation amplitudes. Here, I explore the relationship between these different functions and develop a general procedure for deriving new higher-order master functions from ones already known. The benefit of higher-order functions is that their source terms always converge faster at large distance than their lower-order counterparts. This makes for a dramatic improvement in both the speed and accuracy of frequency domain codes when analyzing unbound motion.

Gravitational Contribution to the Heat Flux in a Simple Dilute Fluid: An Approach Based on General Relativistic Kinetic Theory to First Order in the Gradients

Directory of Open Access Journals (Sweden)

Dominique Brun-Battistini

2017-10-01

Full Text Available Richard C. Tolman analyzed the relation between a temperature gradient and a gravitational field in an equilibrium situation. In 2012, Tolman’s law was generalized to a non-equilibrium situation for a simple dilute relativistic fluid. The result in that scenario, obtained by introducing the gravitational force through the molecular acceleration, couples the heat flux with the metric coefficients and the gradients of the state variables. In the present paper it is shown, by explicitly describing the single particle orbits as geodesics in Boltzmann’s equation, that a gravitational field drives a heat flux in this type of system. The calculation is devoted solely to the gravitational field contribution to this heat flux in which a Newtonian limit to the Schwarzschild metric is assumed. The corresponding transport coefficient, which is obtained within a relaxation approximation, corresponds to the dilute fluid in a weak gravitational field. The effect is negligible in the non-relativistic regime, as evidenced by the direct evaluation of the corresponding limit.

Hawking radiation from AdS black holes

International Nuclear Information System (INIS)

Hubeny, Veronika E; Rangamani, Mukund; Marolf, Donald

2010-01-01

We study Hartle-Hawking-like states of quantum field theories on asymptotically AdS black hole backgrounds, with particular regard to the phase structure of interacting theories. By a suitable analytic continuation we show that the equilibrium dynamics of field theories on large asymptotically AdS black holes can be related to the low-temperature states of the same field theory on the AdS soliton (or pure AdS) background. This allows us to gain insight into Hartle-Hawking-like states on large-radius Schwarzschild- or rotating-AdS black holes. Furthermore, we exploit the AdS/CFT correspondence to explore the physics of strongly coupled large N theories on asymptotically AdS black holes. In particular, we exhibit a plausibly complete set of phases for the M2-brane world-volume superconformal field theory on a BTZ black hole background. Our analysis partially resolves puzzles previously raised in connection with Hawking radiation on large AdS black holes.

An analysis of Born–Infeld determinantal gravity in Weitzenböck spacetime

Directory of Open Access Journals (Sweden)

Franco Fiorini

2016-12-01

Full Text Available The Born–Infeld theory of the gravitational field formulated in Weitzenböck spacetime is studied in detail. The action, constructed quadratically upon the torsion two-form, reduces to Einstein gravity in the low field limit where the Born–Infeld constant λ goes to infinity, and it is described by second order field equations for the vielbein field in D spacetime dimensions. The equations of motion are derived, and a number of properties coming from them are discussed. In particular, we show that under fairly general circumstances, the equations of motion are those of Einstein's General Relativity plus an energy-momentum tensor of purely geometrical character. This tensor is obtained solely from the parallelization defining the spacetime structure, which is encoded in a set of D smooth, everywhere non-null, globally defined 1-forms ea. Spherical symmetry is studied as an example, and we comment on the emergence of the Schwarzschild geometry within this framework. Potential (regular extensions of it are envisioned.

Role of space--time topology in quantum phenomena: Superselection of charge and emergence of nontrivial vacua

International Nuclear Information System (INIS)

Ashtekar, A.; Sen, A.

1980-01-01

Schwarzschild--Kruskal space--time admits a two-parameter family of everywhere regular, static, source-free Maxwell fields. It is shown that there exists a corresponding two-parameter family of unitarily inequivalent representations of the canonical commutation relations. Elements of the underlying Hilbert space may be interpreted as ''quantum fluctuations of the Maxwell field off nontrivial classical vacua.'' The representation corresponding to the ''trivial'' sector: i.e., the zero classical solution: is the usual Fock representation. All others are ''non-Fock.'' In particular, in all other sectors, the Maxwell field develops a nonzero vacuum expectation value. The parameters labelling the family can be interpreted as electric and magnetic charges. Therefore, unitary inequivalence naturally leads to superselection rules for these charges. These features arise in spite of the linearity of field equations only because the space--time topology is ''nontrivial.'' Also, because of linearity, an exact analysis is possible at the quantum level; recourse to perturbation theory is unnecessary

Spontaneous excitation of a static multilevel atom coupled with electromagnetic vacuum fluctuations in Schwarzschild spacetime

International Nuclear Information System (INIS)

Zhou Wenting; Yu Hongwei

2012-01-01

We study the spontaneous excitation of a radially polarized static multilevel atom outside a spherically symmetric black hole in multipolar interaction with quantum electromagnetic fluctuations in the Boulware, Unruh and Hartle-Hawking vacuum states. We find that spontaneous excitation does not occur in the Boulware vacuum, and, in contrast to the scalar field case, the spontaneous emission rate is not well behaved at the event horizon as a result of the blow-up of the proper acceleration of the static atom. However, spontaneous excitation can take place both in the Unruh and the Hartle-Hawking vacua as if there were thermal radiation from the black hole. Distinctive features in contrast to the scalar field case are the existence of a term proportional to the proper acceleration squared in the rate of change of the mean atomic energy in the Unruh and the Hartle-Hawking vacua and the structural similarity in the spontaneous excitation rate between the static atoms outside a black hole and uniformly accelerated ones in a flat space with a reflecting boundary, which is particularly dramatic at the event horizon where a complete equivalence exists. (paper)

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

Gravitational perturbation theory and synchrotron radiation

Energy Technology Data Exchange (ETDEWEB)

Breuer, R A [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (F.R. Germany). Inst. fuer Astrophysik

1975-01-01

This article presents methods and results for a gravitational perturbation theory which treats massless fields as linearized perturbations of an arbitrary gravitational vacuum background spacetime. The formalism is outlined for perturbations of type (22) spacetimes. As an application, high-frequency radiation emitted by particles moving approximately on relativistic circular geodesic orbits is computed. More precisely, the test particle assumption is made; throughout it is therefore assumed that the reaction of the radiation on the particle motion is negligible. In particular, these orbits are studied in the gravitational field of a spherically symmetric (Schwarzschild-) black hole as well as of a rotating (Kerr-) black hole. In this model, the outgoing radiation is highly focussed and of much higher fequency than the orbital frequency, i.e. one is dealing with 'gravitational synchrotron radiation'.

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.

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.

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.

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

Compact objects in bimetric general relativity

International Nuclear Information System (INIS)

Harpaz, A.; Rosen, N.

1985-01-01

The field equations of the bimetric general relativity theory proposed by one of the authors (N. Rosen), in the static form, are solved in order to investigate the structure of a star. It is found that for an ordinary star the bimetric theory gives the same results as the Einstein general relativity theory. However, for a collapsed star the two theories give different results. In the bimetric theory a configuration in hydrostatic equilibrium exists for a collapsed star filling its Schwarzschild sphere. In general relativity no equilibrium configuration exists in this region, and the star shrinks to a point singularity to form a 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

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.

Internal structure of relativistic astrophysical objects in the wave approximation

International Nuclear Information System (INIS)

Bogdanov, I.V.; Demkov, Yu.N.

1987-01-01

Spherically symmetric inverse problems for the scattering of quantum particles by a static gravitational field are considered within the framework of general relativity theory. Methods are developed for determining the metric tensor on the basis of scattering data for a fixed energy or zero angular momentum for the Klein-Fock-Gordon equation in the Schwarzschild metric. The relation between the S-matrix and squared 4-momentum operator in curved space is investigated. The main elements of the algorithms developed are two definite nonlinear ordinary differential equations of the third and fourth order based on the scattering data. On the one hand, the inverse problems studied extend the classical inverse problems for the gravitational field, solved previously, to the quantum case. On the other hand, they extend the Marchenko and Regge-Newton methods familiar in quantum theory to the case of a gravitational field. An analogy is established between the motion of a scalar particle in a strong gravitational field and the motion in a field with a potential depending on the angular momentum or energy in nonrelativistic quantum mechanics

Macroscopic effects of the quantum trace anomaly

International Nuclear Information System (INIS)

Mottola, Emil; Vaulin, Ruslan

2006-01-01

The low energy effective action of gravity in any even dimension generally acquires nonlocal terms associated with the trace anomaly, generated by the quantum fluctuations of massless fields. The local auxiliary field description of this effective action in four dimensions requires two additional scalar fields, not contained in classical general relativity, which remain relevant at macroscopic distance scales. The auxiliary scalar fields depend upon boundary conditions for their complete specification, and therefore carry global information about the geometry and macroscopic quantum state of the gravitational field. The scalar potentials also provide coordinate invariant order parameters describing the conformal behavior and divergences of the stress tensor on event horizons. We compute the stress tensor due to the anomaly in terms of its auxiliary scalar potentials in a number of concrete examples, including the Rindler wedge, the Schwarzschild geometry, and de Sitter spacetime. In all of these cases, a small number of classical order parameters completely determine the divergent behaviors allowed on the horizon, and yield qualitatively correct global approximations to the renormalized expectation value of the quantum stress tensor

Spectrum of relativistic radiation from electric charges and dipoles as they fall freely into a black hole

Energy Technology Data Exchange (ETDEWEB)

Shatskiy, A. A., E-mail: shatskiy@asc.rssi.ru; Novikov, I. D.; Lipatova, L. N. [Russian Academy of Sciences, Astrospace Center, Lebedev Physical Institute (Russian Federation)

2013-06-15

The motion of electric charges and dipoles falling radially and freely into a Schwarzschild black hole is considered. The inverse effect of the electromagnetic fields on the black hole is neglected. Since the dipole is assumed to be a point particle, the deformation due to the action of tidal forces on it is neglected. According to the theorem stating that 'black holes have no hair', the multipole electromagnetic fields should be completely radiated as a multipole falls into a black hole. The electromagnetic radiation power spectrum for these multipoles (a monopole and a dipole) has been found. Differences have been found in the spectra for different orientations of the falling dipole. A general method has been developed to find the radiated multipole electromagnetic fields for multipoles (including higher-order multipoles-quadrupoles, etc.) falling freely into a black hole. The calculated electromagnetic spectra can be compared with observational data from stellar-mass and smaller black holes.

Foliation and the first law of black hole thermodynamics

International Nuclear Information System (INIS)

Siddiqui, Azad A.; Riaz, Syed Muhammad Jawwad; Akbar, M.

2011-01-01

There has been lots of interest in exploring the thermodynamic properties at the horizon of a black hole spacetime. It has been shown earlier that for different spacetimes, the Einstein field equations at the horizon can be expressed as the first law of black hole thermodynamics. Using the idea of foliation, we develop a simpler procedure to obtain such results. We consider r = constant slices, for the Schwarzschild and Reissner-Nordstrom black hole spacetimes. The Einstein field equations for the induced 3-dimensional metrics of the hypersurfaces are expressed in thermodynamic quantities under the virtual displacements of the hypersurfaces. As expected, it is found that the field equations of the induced metric corresponding to the horizon can be written as a first law of black hole thermodynamics. It is to be mentioned here that our procedure is much easier, to obtain such results, as here one has to essentially deal with (n - 1)-dimensional induced metric for an n-dimensional spacetime. (authors)

Foliation and the First Law of Black Hole Thermodynamics

International Nuclear Information System (INIS)

Siddiqui, Azad A.; Riaz, Syed Muhammad Jawwad; Akbar, M.

2011-01-01

There has been lots of interest in exploring the thermodynamic properties at the horizon of a black hole spacetime. It has been shown earlier that for different spacetimes, the Einstein field equations at the horizon can be expressed as the first law of black hole thermodynamics. Using the idea of foliation, we develop a simpler procedure to obtain such results. We consider r = constant slices, for the Schwarzschild and Reissner—Nordstrom black hole spacetimes. The Einstein field equations for the induced 3-dimensional metrics of the hypersurfaces are expressed in thermodynamic quantities under the virtual displacements of the hypersurfaces. As expected, it is found that the field equations of the induced metric corresponding to the horizon can be written as a first law of black hole thermodynamics. It is to be mentioned here that our procedure is much easier, to obtain such results, as here one has to essentially deal with (n — 1)-dimensional induced metric for an n-dimensional spacetime. (general)

Einstein black holes, free scalars, and AdS/CFT correspondence

International Nuclear Information System (INIS)

Louko, Jorma; Wisniewski, Jacek

2004-01-01

We investigate AdS/CFT correspondence for two families of Einstein black holes in d≥4 dimensions, modeling the boundary conformal field theory by a free conformal scalar field and evaluating the boundary two-point function in the bulk geodesic approximation. For the d≥4 counterpart of the nonrotating Banados-Teitelboim-Zanelli hole and for its Z 2 quotient, the boundary state is thermal in the expected sense, and its stress-energy reflects the properties of the bulk geometry and suggests a novel definition for the mass of the hole. For the generalized Schwarzschild-AdS hole with a flat horizon of topology R d-2 , the boundary stress-energy has a thermal form with energy density proportional to the hole Arnowitt-Deser-Misner mass, but stress-energy corrections from compactified horizon dimensions cannot be consistently included at least for d=5

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.

Hawking radiation from rotating black holes in anti-de Sitter spaces via gauge and gravitational anomalies

International Nuclear Information System (INIS)

Jiang Qingquan; Wu Shuangqing

2007-01-01

Robinson-Wilczek's recent work, which treats Hawking radiation as a compensating flux to cancel gravitational anomaly at the horizon of a Schwarzschild-type black hole, is extended to study Hawking radiation of rotating black holes in anti-de Sitter spaces, especially that in dragging coordinate system, via gauge and gravitational anomalies. The results show that in order to restore gauge invariance and general coordinate covariance at the quantum level in the effective field theory, the charge and energy flux by requiring to cancel gauge and gravitational anomalies at the horizon, must have a form equivalent to that of a (1+1)-dimensional blackbody radiation at Hawking temperature with an appropriate chemical potential

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.

Dark Candles of the Universe: Black Hole Observations

Science.gov (United States)

Aykutalp, Aycin

2016-03-01

In 1916, when Karl Schwarzschild solved the Einstein field equations of general relativity for a spherically symmetric, non-rotating mass no one anticipated the impact black holes would have on astrophysics. I will review the main formation channels for black hole seeds and their evolution through cosmic time. In this, emphasis will be placed on the observational diagnostics of astrophysical black holes and their role on the assembly of galaxy formation and evolution. I then review how these observations put constrain on the seed black hole formation theories. Finally, I present an outlook for how future observations can shed light on our understanding of black holes. This work is supported by NSF Grant AST-1333360.

Modified Dispersion Relations: from Black-Hole Entropy to the Cosmological Constant

Science.gov (United States)

Garattini, Remo

2012-07-01

Quantum Field Theory is plagued by divergences in the attempt to calculate physical quantities. Standard techniques of regularization and renormalization are used to keep under control such a problem. In this paper we would like to use a different scheme based on Modified Dispersion Relations (MDR) to remove infinities appearing in one loop approximation in contrast to what happens in conventional approaches. In particular, we apply the MDR regularization to the computation of the entropy of a Schwarzschild black hole from one side and the Zero Point Energy (ZPE) of the graviton from the other side. The graviton ZPE is connected to the cosmological constant by means of of the Wheeler-DeWitt equation.

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

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.

The electrodynamics of Ritz

International Nuclear Information System (INIS)

Waldron, R.A.

1979-01-01

An account is given of Ritz's electrodynamics. Ritz's paper is divided into two parts. In the first he criticises the Lorentz-Maxwell theory based on fields, and comments on alternative theories based on particle interactions. In the second he develops his own theory, also based on particle interactions. He starts from a force law which is analogous to a force law derived by Schwarzschild from the Lorentz theory. While the approach is interesting, it leads to results which do not agree with experimental results obtained several decades later, after Ritz's death. A similar approach is applied to gravitation and is shown to be capable of explaining the anomalous precession of the planet Mercury. (Auth.)

The EDGE-CALIFA survey: validating stellar dynamical mass models with CO kinematics

Science.gov (United States)

Leung, Gigi Y. C.; Leaman, Ryan; van de Ven, Glenn; Lyubenova, Mariya; Zhu, Ling; Bolatto, Alberto D.; Falcón-Barroso, Jesus; Blitz, Leo; Dannerbauer, Helmut; Fisher, David B.; Levy, Rebecca C.; Sanchez, Sebastian F.; Utomo, Dyas; Vogel, Stuart; Wong, Tony; Ziegler, Bodo

2018-06-01

Deriving circular velocities of galaxies from stellar kinematics can provide an estimate of their total dynamical mass, provided a contribution from the velocity dispersion of the stars is taken into account. Molecular gas (e.g. CO), on the other hand, is a dynamically cold tracer and hence acts as an independent circular velocity estimate without needing such a correction. In this paper, we test the underlying assumptions of three commonly used dynamical models, deriving circular velocities from stellar kinematics of 54 galaxies (S0-Sd) that have observations of both stellar kinematics from the Calar Alto Legacy Integral Field Area (CALIFA) survey, and CO kinematics from the Extragalactic Database for Galaxy Evolution (EDGE) survey. We test the asymmetric drift correction (ADC) method, as well as Jeans, and Schwarzschild models. The three methods each reproduce the CO circular velocity at 1Re to within 10 per cent. All three methods show larger scatter (up to 20 per cent) in the inner regions (R < 0.4Re) that may be due to an increasingly spherical mass distribution (which is not captured by the thin disc assumption in ADC), or non-constant stellar M/L ratios (for both the JAM and Schwarzschild models). This homogeneous analysis of stellar and gaseous kinematics validates that all three models can recover Mdyn at 1Re to better than 20 per cent, but users should be mindful of scatter in the inner regions where some assumptions may break down.

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

Lorentz violation and black-hole thermodynamics: Compton scattering process

International Nuclear Information System (INIS)

Kant, E.; Klinkhamer, F.R.; Schreck, M.

2009-01-01

A Lorentz-noninvariant modification of quantum electrodynamics (QED) is considered, which has photons described by the nonbirefringent sector of modified Maxwell theory and electrons described by the standard Dirac theory. These photons and electrons are taken to propagate and interact in a Schwarzschild spacetime background. For appropriate Lorentz-violating parameters, the photons have an effective horizon lying outside the Schwarzschild horizon. A particular type of Compton scattering event, taking place between these two horizons (in the photonic ergoregion) and ultimately decreasing the mass of the black hole, is found to have a nonzero probability. These events perhaps allow for a violation of the generalized second law of thermodynamics in the Lorentz-noninvariant theory considered.

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)

New view about black holes. [Tachyon--bradyon transformation at horizon

Energy Technology Data Exchange (ETDEWEB)

De Sabbata, V; Pavsic, M; Recami, E

1977-01-01

For a Schwarzschild black-hole, as reference frame is chosen the frame sigma at rest with respect to the Schwarzschild metric. In this locally non-inertial frame, a freely falling body is shown to reach the speed of light on the horizon and then to travel faster than light inside the horizon. The usual Szekeres--Kruskal (SK) coordinates represent themselves frames that (with respect to the frames sigma) travel at subluminal speed outside, at luminal speed on, and at superluminal speed inside the horizon (so that SK frames always describe any free falling body as a standard, slower-than-light object). Finally, black-holes are shown to be possible sources of tachyons.

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

Understanding Hawking radiation in the framework of open quantum systems

International Nuclear Information System (INIS)

Yu Hongwei; Zhang Jialin

2008-01-01

We study the Hawking radiation in the framework of open quantum systems by examining the time evolution of a detector (modeled by a two-level atom) interacting with vacuum massless scalar fields. The dynamics of the detector is governed by a master equation obtained by tracing over the field degrees of freedom from the complete system. The nonunitary effects are studied by analyzing the time behavior of a particular observable of the detector, i.e., its admissible state, in the Unruh, Hartle-Hawking, as well as Boulware vacua outside a Schwarzschild black hole. We find that the detector in both the Unruh and Hartle-Hawking vacua would spontaneously excite with a nonvanishing probability the same as what one would obtain if there is thermal radiation at the Hawking temperature from the black hole, thus reproducing the basic results concerning the Hawking effect in the framework of open quantum systems

Weyl curvature tensor in static spherical sources

International Nuclear Information System (INIS)

Ponce de Leon, J.

1988-01-01

The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ''purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed

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)

Eikonal Approximation in AdS/CFT From Shock Waves to Four-Point Functions

CERN Document Server

Cornalba, L; Costa, Miguel S; Penedones, Joao; Cornalba, Lorenzo; Costa, M S; Penedones, J; Schiappa, Ricardo

2007-01-01

We initiate a program to generalize the standard eikonal approximation to compute amplitudes in Anti-de Sitter spacetimes. Inspired by the shock wave derivation of the eikonal amplitude in flat space, we study the two-point function E ~ _{shock} in the presence of a shock wave in Anti-de Sitter, where O_1 is a scalar primary operator in the dual conformal field theory. At tree level in the gravitational coupling, we relate the shock two-point function E to the discontinuity across a kinematical branch cut of the conformal field theory four-point function A ~ , where O_2 creates the shock geometry in Anti-de Sitter. Finally, we extend the above results by computing E in the presence of shock waves along the horizon of Schwarzschild BTZ black holes. This work gives new tools for the study of Planckian physics in Anti-de Sitter spacetimes.

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

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.

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

Spectral features of radiation from Nordstroem and Kerr-Newman white holes. [Kinetics

Energy Technology Data Exchange (ETDEWEB)

Dadhich, N [Poona Univ. (India). Dept. of Mathematics and Statistics

1977-01-01

Unlike the Schwarzschild white hole, Nordstroem and Kerr-Newman white holes cannot explode right down from the space time singularity R = 0. For example a charged white hole has to commence explosion (i.e., comes into existence) with a radius Rsub(o)=Rsub(c)(2-Rsub(c)/Rsub(b))sup(-1) where Rsub(c) is the 'classical radius' and Rsub(b) is the final radius attained when the stationary state is reached. That means charged and rotating black holes also cannot hit the singularity R = 0 and perish. Here the explosion is decelerated by the presence of charge and rotation and hence the radiation emitted would be not as energetic as in the Schwarzschild case where its energy is infinitely large for emission from R = 0.

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.)

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)

A new class of relativistic stellar models

Science.gov (United States)

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.

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.

Intrinsic and extrinsic geometries of a tidally deformed black hole

International Nuclear Information System (INIS)

Vega, Ian; Poisson, Eric; Massey, Ryan

2011-01-01

A description of the event horizon of a perturbed Schwarzschild black hole is provided in terms of the intrinsic and extrinsic geometries of the null hypersurface. This description relies on a Gauss-Codazzi theory of null hypersurfaces embedded in spacetime, which extends the standard theory of spacelike and timelike hypersurfaces involving the first and second fundamental forms. We show that the intrinsic geometry of the event horizon is invariant under a reparameterization of the null generators, and that the extrinsic geometry depends on the parameterization. Stated differently, we show that while the extrinsic geometry depends on the choice of gauge, the intrinsic geometry is gauge invariant. We apply the formalism to solutions to the vacuum field equations that describe a tidally deformed black hole. In a first instance, we consider a slowly varying, quadrupolar tidal field imposed on the black hole, and in a second instance, we examine the tide raised during a close parabolic encounter between the black hole and a small orbiting body.

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

The Weak Gravity Conjecture and the axionic black hole paradox

Science.gov (United States)

Hebecker, Arthur; Soler, Pablo

2017-09-01

In theories with a perturbatively massless 2-form (dual to an axion), a paradox may arise in the process of black hole evaporation. Schwarzschild black holes can support a non-trivial Wilson-line-type field, the integral of the 2-form around their horizon. After such an `axionic black hole' evaporates, the Wilson line must be supported by the corresponding 3-form field strength in the region formerly occupied by the black hole. In the limit of small axion decay-constant f, the energy required for this field configuration is too large. Thus, energy cannot be conserved in the process of black hole evaporation. The natural resolution of this paradox is through the presence of light strings, which allow the black hole to "shed" its axionic hair sufficiently early. This gives rise to a new Weak-Gravity-type argument in the 2-form context: small coupling, in this case f , enforces the presence of light strings or a low cutoff. We also discuss how this argument may be modified in situations where the weak coupling regime is achieved in the low-energy effective theory through an appropriate gauging of a model with a vector field and two 2-forms.

Einstein and the history of general relativity

International Nuclear Information System (INIS)

Howard, D.; Stachel, J.

1989-01-01

This book is a collection of essays by the authors and other people that deal with scientific opinions that led Einstein and his contemporaries to their views of general relativity. Some of the essays explore Einstein's passage from the special theory through a sequence of gravitational theories to the discovery of the field equations of the grand theory in November 1915. Two other essays discuss Einstein's public and private exchanges with Max Abraham and Tullio Levi-Civita in 1913 and 1914. A sympathetic picture of H.A. Lorentz's reaction to the general theory of relativity is included, and a careful and insightful essay on the early understanding of the Schwarzschild-Droste solution to the field equations of general relativity is presented. One paper presents a discussion on the state of the enterprise of general relativity between 1925 and 1928, and a short essay details the history of steps toward quantum gravitational through canonical quantization. A discussion of the history of derivations of the geodesic equation of motion from the field equation and conservation laws of the general theory is presented. The early history of geometrical unified field theories is included

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)

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.

Optical Analysis of an Ultra-High resolution Two-Mirror Soft X-Ray Microscope

Science.gov (United States)

Shealy, David L.; Wang, Cheng; Hoover, Richard B.

1994-01-01

This work has summarized for a Schwarzschild microscope some relationships between numerical aperture (NA), magnification, diameter of the primary mirror, radius of curvature of the secondary mirror, and the total length of the microscope. To achieve resolutions better than a spherical Schwarzschild microscope of 3.3 Lambda for a perfectly aligned and fabricated system. it is necessary to use aspherical surfaces to control higher-order aberrations. For an NA of 0.35, the aspherical Head microscope provides diffraction limited resolution of 1.4 Lambda where the aspherical surfaces differ from the best fit spherical surface by approximately 1 micrometer. However, the angle of incidence varies significantly over the primary and the secondary mirrors, which will require graded multilayer coatings to operate near peak reflectivities. For higher numerical apertures, the variation of the angle of incidence over the secondary mirror surface becomes a serious problem which must be solved before multilayer coatings can be used for this application. Tolerance analysis of the spherical Schwarzschild microscope has shown that water window operations will require 2-3 times tighter tolerances to achieve a similar performance for operations with 130 A radiation. Surface contour errors have been shown to have a significant impact on the MTF and must be controlled to a peak-to-valley variation of 50-100 A and a frequency of 8 periods over the surface of a mirror.

Journal of Astrophysics and Astronomy | Indian Academy of Sciences

Indian Academy of Sciences (India)

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 depend on the quantum ...

Orbits in general relativity: the Jacobian elliptic function

Energy Technology Data Exchange (ETDEWEB)

Miro Rodriguez, C

1987-03-11

The Jacobian elliptic functions are applied to the motion of nonzero-rest-mass particles in the Schwarzschild geometry. The bound and unbound trajectories are analysed together with their classical and special-relativity limits.

2T Physics, Weyl Symmetry and the Geodesic Completion of Black Hole Backgrounds

Science.gov (United States)

Araya Quezada, Ignacio Jesus

behavior of fields, interpreted as the first quantized particle wavefunctions in the backgrounds is discussed for the 2D stringy BH case. It is shown that the geodesic completion also carries through at the quantum level, by examining the effective potential of the corresponding Schwarzschild problem. Also, in the case of the 2D stringy BH, it is explicitly shown that the spacetime has a multi-sheeted structure, which resolves possible issues like the presence of closed timelike curves. This multi-sheeted structure is conjectured to exist also for the 4D Schwarzschild BH (and perhaps for all BH backgrounds). The main new results of this thesis are the extended network of dualities, in the form of canonical transformations including time and energy, between the 1T dynamical systems, presented in Chapter 2 and the construction of the geodesically complete 4D Schwarzschild and 2D stringy black hole backgrounds, presented in Chapter 3.

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

Noncommutative geometry inspired black holes in Rastall gravity

Energy Technology Data Exchange (ETDEWEB)

Ma, Meng-Sen [Shanxi Datong University, Institute of Theoretical Physics, Datong (China); Shanxi Datong University, Department of Physics, Datong (China); Zhao, Ren [Shanxi Datong University, Institute of Theoretical Physics, Datong (China)

2017-09-15

Under two different metric ansatzes, the noncommutative geometry inspired black holes (NCBH) in the framework of Rastall gravity are derived and analyzed. We consider the fluid-type matter with the Gaussian-distribution smeared mass density. Taking a Schwarzschild-like metric ansatz, it is shown that the noncommutative geometry inspired Schwarzschild black hole (NCSBH) in Rastall gravity, unlike its counterpart in general relativity (GR), is not a regular black hole. It has at most one event horizon. After showing a finite maximal temperature, the black hole will leave behind a point-like massive remnant at zero temperature. Considering a more general metric ansatz and a special equation of state of the matter, we also find a regular NCBH in Rastall gravity, which has a similar geometric structure and temperature to that of NCSBH in GR. (orig.)

Field transformations to multivalued fields

Energy Technology Data Exchange (ETDEWEB)

Kleinert, H [Institut fuer Theoretische Physik, Arnimallee 14, D-14195 Berlin (Germany)

2007-05-15

Changes of field variables may lead to multivalued fields which do not satisfy the Schwarz integrability conditions. Their quantum field theory needs special care as is shown in an application to the superfluid and superconducting phase transitions.

Hawking Radiation from a (4+n)-dimensional Black Hole Exact Results for the Schwarzschild Phase

CERN Document Server

Harris, C M; Harris, Chris M.; Kanti, Panagiota

2003-01-01

We start our analysis by deriving a master equation that describes the motion of a field with arbitrary spin $s$ on a 3-brane embedded in a non-rotating, uncharged (4+n)-dimensional black hole background. By numerical analysis, we derive exact results for the greybody factors and emission rates for scalars, fermions and gauge bosons emitted directly on the brane, for all energy regimes and for an arbitrary number $n$ of extra dimensions. The relative emissivities on the brane for different types of particles are computed and their dependence on the dimensionality of spacetime is demonstrated -- we therefore conclude that both the amount and the type of radiation emitted can be used for the determination of $n$ if the Hawking radiation from these black holes is observed. The emission of scalar modes in the bulk from the same black holes is also studied and the relative bulk-to-brane energy emissivity is accurately computed. We demonstrate that this quantity varies considerably with $n$ but always remains small...

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)

Spherically symmetric radiation in gravitational collapse

International Nuclear Information System (INIS)

Bridy, D.J.

1983-01-01

This paper investigates a previously neglected mode by which a star may lose energy in the late stages of gravitational collapse to the black hole state. A model consisting of a Schwarzschild exterior matched to a Friedman interior of collapsing pressureless dust is studied. The matter of the collapsing star is taken as the source of a massive vector boson field and a detailed boundary value problem is carried out. Vector mesons are strongly coupled to all nucleons and will be radiated by ordinary matter during the collapse. The time dependent coupling between interior and exterior modes matched across the moving boundary of the collapsing star and the presence of the gravitational fields and their gradients in the field equations may give rise to a parametric amplification mechanism and permit the gravitational field to pump energy into the boson field, greatly enhancing the amount of boson radiation. The significance of a radiative mechanism driven by collapse is that it can react back upon the collapsing source and deprive it of some of the very mass that drives the collapse via its self gravitation. If the mass loss is great enough, this may provide a mechanism to slow or even halt gravitational collapse in some cases

Anomalous transport from holography. Pt. II

Energy Technology Data Exchange (ETDEWEB)

Bu, Yanyan; Sharon, Amir [Ben-Gurion University of the Negev, Department of Physics, Beersheba (Israel); Lublinsky, Michael [Ben-Gurion University of the Negev, Department of Physics, Beersheba (Israel); University of Connecticut, Physics Department, Storrs, CT (United States)

2017-03-15

This is a second study of chiral anomaly-induced transport within a holographic model consisting of anomalous U(1){sub V} x U(1){sub A} Maxwell theory in Schwarzschild-AdS{sub 5} spacetime. In the first part, chiral magnetic/separation effects (CME/CSE) are considered in the presence of a static spatially inhomogeneous external magnetic field. Gradient corrections to CME/CSE are analytically evaluated up to third order in the derivative expansion. Some of the third order gradient corrections lead to an anomaly-induced negative B{sup 2}-correction to the diffusion constant. We also find modifications to the chiral magnetic wave nonlinear in B. In the second part, we focus on the experimentally interesting case of the axial chemical potential being induced dynamically by a constant magnetic and time-dependent electric fields. Constitutive relations for the vector/axial currents are computed employing two different approximations: (a) derivative expansion (up to third order) but fully nonlinear in the external fields, and (b) weak electric field limit but resuming all orders in the derivative expansion. A non-vanishing nonlinear axial current (CSE) is found in the first case. The dependence on magnetic field and frequency of linear transport coefficient functions is explored in the second. (orig.)

Anomalous transport from holography. Pt. II

International Nuclear Information System (INIS)

Bu, Yanyan; Sharon, Amir; Lublinsky, Michael

2017-01-01

This is a second study of chiral anomaly-induced transport within a holographic model consisting of anomalous U(1)_V x U(1)_A Maxwell theory in Schwarzschild-AdS_5 spacetime. In the first part, chiral magnetic/separation effects (CME/CSE) are considered in the presence of a static spatially inhomogeneous external magnetic field. Gradient corrections to CME/CSE are analytically evaluated up to third order in the derivative expansion. Some of the third order gradient corrections lead to an anomaly-induced negative B"2-correction to the diffusion constant. We also find modifications to the chiral magnetic wave nonlinear in B. In the second part, we focus on the experimentally interesting case of the axial chemical potential being induced dynamically by a constant magnetic and time-dependent electric fields. Constitutive relations for the vector/axial currents are computed employing two different approximations: (a) derivative expansion (up to third order) but fully nonlinear in the external fields, and (b) weak electric field limit but resuming all orders in the derivative expansion. A non-vanishing nonlinear axial current (CSE) is found in the first case. The dependence on magnetic field and frequency of linear transport coefficient functions is explored in the second. (orig.)

Black holes and quantum mechanics

CERN Document Server

Wilczek, Frank

1995-01-01

1. Qualitative introduction to black holes : classical, quantum2. Model black holes and model collapse process: The Schwarzschild and Reissner-Nordstrom metrics, The Oppenheimer-Volkov collapse scenario3. Mode mixing4. From mode mixing to radiance.

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.)

The generalized second law of thermodynamics in generalized gravity theories

International Nuclear Information System (INIS)

Wu Shaofeng; Yang Guohong; Wang Bin; Zhang Pengming

2008-01-01

We investigate the generalized second law of thermodynamics (GSL) in generalized theories of gravity. We examine the total entropy evolution with time including the horizon entropy, the non-equilibrium entropy production, and the entropy of all matter, field and energy components. We derive a universal condition to protect the generalized second law and study its validity in different gravity theories. In Einstein gravity (even in the phantom-dominated universe with a Schwarzschild black hole), Lovelock gravity and braneworld gravity, we show that the condition to keep the GSL can always be satisfied. In f(R) gravity and scalar-tensor gravity, the condition to protect the GSL can also hold because the temperature should be positive, gravity is always attractive and the effective Newton constant should be an approximate constant satisfying the experimental bounds

On smoothness-asymmetric null infinities

International Nuclear Information System (INIS)

Valiente Kroon, Juan Antonio

2006-01-01

We discuss the existence of asymptotically Euclidean initial data sets for the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past and a future null infinity of different smoothness. For simplicity, the analysis is restricted to the class of conformally flat, axially symmetric initial data sets. It is shown how the free parameters in the second fundamental form of the data can be used to satisfy certain obstructions to the smoothness of null infinity. The resulting initial data sets could be interpreted as those of some sort of (nonlinearly) distorted Schwarzschild black hole. Their developments would be that they admit a peeling future null infinity, but at the same time have a polyhomogeneous (non-peeling) past null infinity

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

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.

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.

X-ray emission characteristics of foam target plasmas

International Nuclear Information System (INIS)

Fronya, A.A.; Borisenko, N.G.; Chernodub, M.L.; Merkuliev, Yu.A.; Osipov, M.V.; Puzyrev, V.N.; Sahakyan, A.T.; Starodub, A.N.; Vasin, B.L.; Yakushev, O.F.

2010-01-01

Complete text of publication follows. Experimental results of laser radiation interaction with a foam targets are presented. The spatial, temporal and energy characteristics of x-ray plasma radiation have been investigated. The pinhole-camera and Schwarzschild objective have been used for the plasma image formation in different spectral ranges. The plasma image is registered by the Schwarzschild objective in a narrow spectral range 180 - 200 A. Spectral characteristics of x-ray radiation registered by pinhole-camera have been defined by means outer filters. The use of the filters with different transmission curves allowed one the determine the localization of x-ray radiation with fixed wavelength. Spatial resolution accounts 16 μm in the pinhole-camera diagnostic channel and 2.5 μm in the Schwarzschild objective diagnostic channel. The plasma images in the intrinsic x-ray radiation show that the emission area in the transverse direction with respect to the direction of the propagating heating radiation exceeds the focal spot size. This fact indicates that the target heating in the transverse direction is due to internal energy of the created plasma. The average value of plasma electron temperature is ∼ 0.4 - 1.4 keV. Acknowledgements. The work is partly supported by the Russian Foundation for Basic Researches, grant no. 10-02-00113 and by Federal Target Program 'Research and scientific-pedagogical cadres of Innovative Russia' (grant 2009-1.1-122-052-025).

Proč je obvod Slunce menší než 2pi r?

Czech Academy of Sciences Publication Activity Database

Křížek, Michal

2017-01-01

Roč. 46, č. 3 (2017), s. 7-18 ISSN 1335-4981 Institutional support: RVO:67985840 Keywords : interior Schwarzschild metrie * proper radius * coordinate radius Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics OBOR OECD: Astronomy (including astrophysics,space science)

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.)

No Hawking-Page phase transition in three dimensions

International Nuclear Information System (INIS)

Myung, Y.S.

2005-01-01

We investigate whether or not the Hawking-Page phase transition is possible to occur in three dimensions. Starting with the simplest class of Lanczos-Lovelock action, thermodynamic behavior of all AdS-type black holes without charge falls into two classes: Schwarzschild-AdS black holes in even dimensions and Chern-Simons black holes in odd dimensions. The former class can provide the Hawking-Page transition between Schwarzschild-AdS black holes and thermal AdS space. On the other hand, the latter class is exceptional and thus the Hawking-Page transition is hard to occur. In three dimensions, a second-order phase transition might occur between the non-rotating BTZ black hole and the massless BTZ black hole (thermal AdS space), instead of the first-order Hawking-Page transition between the non-rotating BTZ black hole and thermal AdS space

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

Discontinuous Galerkin method for computing gravitational waveforms from extreme mass ratio binaries

International Nuclear Information System (INIS)

Field, Scott E; Hesthaven, Jan S; Lau, Stephen R

2009-01-01

Gravitational wave emission from extreme mass ratio binaries (EMRBs) should be detectable by the joint NASA-ESA LISA project, spurring interest in analytical and numerical methods for investigating EMRBs. We describe a discontinuous Galerkin (dG) method for solving the distributionally forced 1+1 wave equations which arise when modeling EMRBs via the perturbation theory of Schwarzschild black holes. Despite the presence of jump discontinuities in the relevant polar and axial gravitational 'master functions', our dG method achieves global spectral accuracy, provided that we know the instantaneous position, velocity and acceleration of the small particle. Here these variables are known, since we assume that the particle follows a timelike geodesic of the Schwarzschild geometry. We document the results of several numerical experiments testing our method, and in our concluding section discuss the possible inclusion of gravitational self-force effects.

How massive is the black hole at the centre of our Galaxy?

Czech Academy of Sciences Publication Activity Database

Křížek, Filip; Křížek, Michal; Šolc, Jakub

2007-01-01

Roč. 36, č. 1 (2007), s. 43-51 ISSN 1335-4981 Institutional research plan: CEZ:AV0Z10190503; CEZ:AV0Z10480505 Keywords : Schwarzschild radius * Kepler´s laws * numerical excentricity Subject RIV: BA - General Mathematics

Late-time tails of wave propagation in higher dimensional spacetimes

International Nuclear Information System (INIS)

Cardoso, Vitor; Yoshida, Shijun; Dias, Oscar J.C.; Lemos, Jose P.S.

2003-01-01

We study the late-time tails appearing in the propagation of massless fields (scalar, electromagnetic, and gravitational) in the vicinities of a D-dimensional Schwarzschild black hole. We find that at late times the fields always exhibit a power-law falloff, but the power law is highly sensitive to the dimensionality of the spacetime. Accordingly, for odd D>3 we find that the field behaves as t -(2l+D-2) at late times, where l is the angular index determining the angular dependence of the field. This behavior is entirely due to D being odd; it does not depend on the presence of a black hole in the spacetime. Indeed this tail is already present in the flat space Green's function. On the other hand, for even D>4 the field decays as t -(2l+3D-8) , and this time there is no contribution from the flat background. This power law is entirely due to the presence of the black hole. The D=4 case is special and exhibits, as is well known, t -(2l+3) behavior. In the extra dimensional scenario for our Universe, our results are strictly correct if the extra dimensions are infinite, but also give a good description of the late-time behavior of any field if the large extra dimensions are large enough

An electric field in a gravitational field

International Nuclear Information System (INIS)

Harpaz, Amos

2005-01-01

The behaviour of an electric field in a gravitational field is analysed. It is found that due to the mass (energy) of the electric field, it is subjected to gravity and it falls in the gravitational field. This fall curves the electric field, a stress force (a reaction force) is created, and the interaction of this reaction force with the static charge gives rise to the creation of radiation

Discrete Torsion, (Anti) de Sitter D4-Brane and Tunneling

Science.gov (United States)

Singh, Abhishek K.; Pandey, P. K.; Singh, Sunita; Kar, Supriya

2014-06-01

We obtain quantum geometries on a vacuum created pair of a (DDbar)3-brane, at a Big Bang singularity, by a local two form on a D4-brane. In fact our analysis is provoked by an established phenomenon leading to a pair creation by a gauge field at a black hole horizon by Stephen Hawking in 1975. Importantly, the five dimensional microscopic black holes are described by an effective non-perturbative curvature underlying a discrete torsion in a second order formalism. In the case for a non-propagating torsion, the effective curvature reduces to Riemannian, which in a low energy limit may describe Einstein vacuum in the formalism. In particular, our analysis suggests that a non-trivial space begin with a hot de Sitter brane-Universe underlying a nucleation of a vacuum pair of (DDbar)-instanton at a Big Bang. A pair of instanton nucleats a D-particle which in turn combines with an anti D-particle to describe a D-string and so on. The nucleation of a pair of higher dimensional pair of brane/anti-brane from a lower dimensional pair may be viewed via an expansion of the brane-Universe upon time. It is in conformity with the conjecture of a branes within a brane presumably in presence of the non-zero modes of two form. Interestingly, we perform a thermal analysis underlying various emergent quantum de Sitter vacua on a D4-brane and argue for the plausible tunneling geometries underlying a thermal equilibrium. It is argued that a de Sitter Schwarzschild undergoes quantum tunneling to an AdS-brane Schwarzschild via Nariai and de Sitter topological black hole.

Stimulated-emission effects in particle creation near black holes

International Nuclear Information System (INIS)

Wald, R.M.

1976-01-01

It has recently been shown that if a black hole is formed by gravitational collapse, spontaneous particle creation will occur and a thermal spectrum of all species of particles will be emitted to infinity if the quantum matter was initially in the vacuum state. In this paper we investigate the stimulated-emission effects which occur if particles are present initially. We show in general that for a Hermitian scalar field in an external potential or in curved, asymptotically flat spacetime, stimulated-emission effects can occur precisely in those modes for which there is spontaneous particle creation from the vacuum. For the case of a Schwarzschild black hole, this result appears paradoxical, since spontaneous emission occurs at late times but there is no classical analog of stimulated emission at late times. The resolution of this paradox is that in order to induce emission of particles which emerge at late times one must send in particles at early times, so that they reach the black hole very near the instant of its formation. However, enormous energy is required of these incoming particles in order to stimulate emission of particles which emerge at late times. Thus, for a Schwarzschild black hole, even if particles are initially present (with limited energy) they will induce emission only at early times; at late times one will see only the spontaneously emitted blackbody thermal radiation. For the case of a Kerr black hole stimulated emission can be induced by particles sent in at late times with the appropriate frequencies and angular dependence. If the number of incoming particles is large, this quantum stimulated emission just gives the classical superradiant scattering

Skyrmion black hole hair: Conservation of baryon number by black holes and observable manifestations

Energy Technology Data Exchange (ETDEWEB)

Dvali, Gia [Arnold Sommerfeld Center, Ludwig-Maximilians-Universität, 80333 München (Germany); Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München (Germany); Center for Cosmology and Particle Physics, Department of Physics, New York University, 4 Washington Place, New York, NY 10003 (United States); Gußmann, Alexander, E-mail: alexander.gussmann@physik.uni-muenchen.de [Arnold Sommerfeld Center, Ludwig-Maximilians-Universität, 80333 München (Germany)

2016-12-15

We show that the existence of black holes with classical skyrmion hair invalidates standard proofs that global charges, such as the baryon number, cannot be conserved by a black hole. By carefully analyzing the standard arguments based on a Gedankenexperiment in which a black hole is seemingly-unable to return the baryon number that it swallowed, we identify inconsistencies in this reasoning, which does not take into the account neither the existence of skyrmion black holes nor the baryon/skyrmion correspondence. We then perform a refined Gedankenexperiment by incorporating the new knowledge and show that no contradiction with conservation of baryon number takes place at any stage of black hole evolution. Our analysis also indicates no conflict between semi-classical black holes and the existence of baryonic gauge interaction arbitrarily-weaker than gravity. Next, we study classical cross sections of a minimally-coupled massless probe scalar field scattered by a skyrmion black hole. We investigate how the skyrmion hair manifests itself by comparing this cross section with the analogous cross section caused by a Schwarzschild black hole which has the same ADM mass as the skyrmion black hole. Here we find an order-one difference in the positions of the characteristic peaks in the cross sections. The peaks are shifted to smaller scattering angles when the skyrmion hair is present. This comes from the fact that the skyrmion hair changes the near horizon geometry of the black hole when compared to a Schwarzschild black hole with same ADM mass. We keep the study of this second aspect general so that the qualitative results which we obtain can also be applied to black holes with classical hair of different kind.

Compact stars with a small electric charge: the limiting radius to mass relation and the maximum mass for incompressible matter

Energy Technology Data Exchange (ETDEWEB)

Lemos, Jose P.S.; Lopes, Francisco J.; Quinta, Goncalo [Universidade de Lisboa, UL, Departamento de Fisica, Centro Multidisciplinar de Astrofisica, CENTRA, Instituto Superior Tecnico, IST, Lisbon (Portugal); Zanchin, Vilson T. [Universidade Federal do ABC, Centro de Ciencias Naturais e Humanas, Santo Andre, SP (Brazil)

2015-02-01

One of the stiffest equations of state for matter in a compact star is constant energy density and this generates the interior Schwarzschild radius to mass relation and the Misner maximum mass for relativistic compact stars. If dark matter populates the interior of stars, and this matter is supersymmetric or of some other type, some of it possessing a tiny electric charge, there is the possibility that highly compact stars can trap a small but non-negligible electric charge. In this case the radius to mass relation for such compact stars should get modifications. We use an analytical scheme to investigate the limiting radius to mass relation and the maximum mass of relativistic stars made of an incompressible fluid with a small electric charge. The investigation is carried out by using the hydrostatic equilibrium equation, i.e., the Tolman-Oppenheimer-Volkoff (TOV) equation, together with the other equations of structure, with the further hypothesis that the charge distribution is proportional to the energy density. The approach relies on Volkoff and Misner's method to solve the TOV equation. For zero charge one gets the interior Schwarzschild limit, and supposing incompressible boson or fermion matter with constituents with masses of the order of the neutron mass one finds that the maximum mass is the Misner mass. For a small electric charge, our analytical approximating scheme, valid in first order in the star's electric charge, shows that the maximum mass increases relatively to the uncharged case, whereas the minimum possible radius decreases, an expected effect since the new field is repulsive, aiding the pressure to sustain the star against gravitational collapse. (orig.)

Discrete Torsion, (Anti) de Sitter D4-Brane and Tunneling

International Nuclear Information System (INIS)

Singh, Abhishek K.; Pandey, P.K.; Singh, Sunita; Kar, Supriya

2014-01-01

We obtain quantum geometries on a vacuum created pair of a (DD ¯ ) 3 -brane, at a Big Bang singularity, by a local two form on a D 4 -brane. In fact our analysis is provoked by an established phenomenon leading to a pair creation by a gauge field at a black hole horizon by Stephen Hawking in 1975. Importantly, the five dimensional microscopic black holes are described by an effective non-perturbative curvature underlying a discrete torsion in a second order formalism. In the case for a non-propagating torsion, the effective curvature reduces to Riemannian, which in a low energy limit may describe Einstein vacuum in the formalism. In particular, our analysis suggests that a non-trivial space begin with a hot de Sitter brane-Universe underlying a nucleation of a vacuum pair of (DD ¯ )-instanton at a Big Bang. A pair of instanton nucleats a D-particle which in turn combines with an anti D-particle to describe a D-string and so on. The nucleation of a pair of higher dimensional pair of brane/anti-brane from a lower dimensional pair may be viewed via an expansion of the brane-Universe upon time. It is in conformity with the conjecture of a branes within a brane presumably in presence of the non-zero modes of two form. Interestingly, we perform a thermal analysis underlying various emergent quantum de Sitter vacua on a D 4 -brane and argue for the plausible tunneling geometries underlying a thermal equilibrium. It is argued that a de Sitter Schwarzschild undergoes quantum tunneling to an AdS-brane Schwarzschild via Nariai and de Sitter topological black hole

Liouville's equation and radiative acceleration in general relativity

International Nuclear Information System (INIS)

Keane, A.J.

1999-01-01

This thesis examines thoroughly the general motion of a material charged particle in the intense radiation field of a static spherically symmetric compact object with spherical emitting surface outside the Schwarzschild radius. Such a test particle will be pulled in by the gravitational attraction of the compact object and pushed out by the radiation pressure force, therefore the types of trajectory admitted will depend the gravitational field, the radiation field and the particle cross-section. The presence of a strong gravitational field demands a fully general relativistic treatment of the problem. This type of calculation is interesting not only as a formal problem in general relativity but also since it has important astrophysical implications, for example, application to astrophysical discs and jets. In chapter 1 we review the classical radiation force problem and outline the transition to a fully general relativistic scenario. We discuss the method for obtaining the radiation pressure force and calculating the particle trajectories. We review previous work in this area and outline the aims of the thesis. Then we consider some astrophysical applications and discuss how realistic our calculations are. In chapter 2 we give an introduction and overview of differential geometry as this is necessary for an accurate description of tensors on a curved manifold. Then we review the general theory of relativity and in particular obtain the Schwarzschild metric describing a static spherically symmetric vacuum spacetime. Chapter 3 deals with test particle motion through a curved spacetime. Liouville's equation describes the statistical distribution in phase space of a collection of test particles and is based upon a Hamiltonian formulation of the dynamical system - this material also relies heavily upon the concepts of differential geometry introduced in chapter 2. In particular we are interested in photon transport and find the general solutions for some symmetric

Tripolar electric field Structure in guide field magnetic reconnection

Science.gov (United States)

Fu, Song; Huang, Shiyong; Zhou, Meng; Ni, Binbin; Deng, Xiaohua

2018-03-01

It has been shown that the guide field substantially modifies the structure of the reconnection layer. For instance, the Hall magnetic and electric fields are distorted in guide field reconnection compared to reconnection without guide fields (i.e., anti-parallel reconnection). In this paper, we performed 2.5-D electromagnetic full particle simulation to study the electric field structures in magnetic reconnection under different initial guide fields (Bg). Once the amplitude of a guide field exceeds 0.3 times the asymptotic magnetic field B0, the traditional bipolar Hall electric field is clearly replaced by a tripolar electric field, which consists of a newly emerged electric field and the bipolar Hall electric field. The newly emerged electric field is a convective electric field about one ion inertial length away from the neutral sheet. It arises from the disappearance of the Hall electric field due to the substantial modification of the magnetic field and electric current by the imposed guide field. The peak magnitude of this new electric field increases linearly with the increment of guide field strength. Possible applications of these results to space observations are also discussed.

Tripolar electric field Structure in guide field magnetic reconnection

Directory of Open Access Journals (Sweden)

S. Fu

2018-03-01

Full Text Available It has been shown that the guide field substantially modifies the structure of the reconnection layer. For instance, the Hall magnetic and electric fields are distorted in guide field reconnection compared to reconnection without guide fields (i.e., anti-parallel reconnection. In this paper, we performed 2.5-D electromagnetic full particle simulation to study the electric field structures in magnetic reconnection under different initial guide fields (Bg. Once the amplitude of a guide field exceeds 0.3 times the asymptotic magnetic field B0, the traditional bipolar Hall electric field is clearly replaced by a tripolar electric field, which consists of a newly emerged electric field and the bipolar Hall electric field. The newly emerged electric field is a convective electric field about one ion inertial length away from the neutral sheet. It arises from the disappearance of the Hall electric field due to the substantial modification of the magnetic field and electric current by the imposed guide field. The peak magnitude of this new electric field increases linearly with the increment of guide field strength. Possible applications of these results to space observations are also discussed.

Possible observational manifestations of wormholes in the Brans-Dicke theory

Energy Technology Data Exchange (ETDEWEB)

Alexeyev, S. O., E-mail: alexeyev@sai.msu.ru; Rannu, K. A., E-mail: rannu@xray.sai.msu.ru [Sternberg Astronomical Institute (Russian Federation); Gareeva, D. V., E-mail: 4elesta@mail.ru [Moscow State University (Russian Federation)

2011-10-15

The energy flux emitted during the accretion of matter onto a wormhole in the Brans-Dicke theory has been calculated. This characteristic is compared with its values calculated previously for wormholes in general relativity and for a Schwarzschild black hole.

Logarithmic corrections to entropy and AdS/CFT

Indian Academy of Sciences (India)

Abstract. We calculate the correction to the Bekenstein-Hawking entropy formula for five-dimensional AdS-Schwarzschild black holes due to thermodynamic fluctuations. The result is then compared with the boundary gauge theory entropy corrections via AdS/CFT correspondence.

Gauge fields in a torsion field

International Nuclear Information System (INIS)

Rosu, Ion

2004-01-01

In this paper we analyse the motion and the field equations in a non-null curvature and torsion space. In this 4-n dimensional space, the connection coefficients are γ bc a = 1/2S bc a + 1/2T bc a, where S bc a is the symmetrical part and T bc a are the components of the torsion tensor. We will consider that all the fields depend on x = x α , α = 1,2,3,4 and do not depend on y = y k , k=1,2,...,n. The factor S bc a depends on the components of the metric tensor g αβ (x) and on the gauge fields A ν s 0 (x) and the components of the torsion depend only on the gauge fields A ν s 0 (x). We take into consideration the particular case for which the geodesic equations coincide with the motion equations in the presence of the gravitational and the gauge fields. In this case the field equations are Einstein equations in a 4-n dimensional space. We show that both the geodesic equations and the field equations can be obtained from a variational principle. (author)

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.

Black holes in the presence of dark energy

International Nuclear Information System (INIS)

Babichev, E O; Dokuchaev, V I; Eroshenko, Yu N

2013-01-01

The new, rapidly developing field of theoretical research—studies of dark energy interacting with black holes (and, in particular, accreting onto black holes)–—is reviewed. The term 'dark energy' is meant to cover a wide range of field theory models, as well as perfect fluids with various equations of state, including cosmological dark energy. Various accretion models are analyzed in terms of the simplest test field approximation or by allowing back reaction on the black-hole metric. The behavior of various types of dark energy in the vicinity of Schwarzschild and electrically charged black holes is examined. Nontrivial effects due to the presence of dark energy in the black hole vicinity are discussed. In particular, a physical explanation is given of why the black hole mass decreases when phantom energy is being accreted, a process in which the basic energy conditions of the famous theorem of nondecreasing horizon area in classical black holes are violated. The theoretical possibility of a signal escaping from beneath the black hole event horizon is discussed for a number of dark energy models. Finally, the violation of the laws of thermodynamics by black holes in the presence of noncanonical fields is considered. (reviews of topical problems)

Quantized fields in external field. Pt. 2

International Nuclear Information System (INIS)

Bellissard, J.

1976-01-01

The case of a charged scalar field is considered first. The existence of the corresponding Green's functions is proved. For weak fields, as well as pure electric or scalar external fields, the Bogoliubov S-operator is shown to be unitary, covariant, causal up-to-a-phase. These results are generalised to a class of higher spin quantized fields, 'nicely' coupled to external fields, which includes the Dirac theory, and in the case of minimal and magnetic dipole coupling, the spin one Petiau-Duffin-Kemmer theory. (orig.) [de

Wake fields and wake field acceleration

International Nuclear Information System (INIS)

Bane, K.L.F.; Wilson, P.B.; Weiland, T.

1984-12-01

In this lecture we introduce the concepts of wake fields and wake potentials, examine some basic properties of these functions, show how they can be calculated, and look briefly at a few important applications. One such application is wake field acceleration. The wake field accelerator is capable of producing the high gradients required for future very high energy e + e - linear colliders. The principles of wake field acceleration, and a brief description of experiments in progress in this area, are presented in the concluding section. 40 references, 27 figures

Comment on 'Hawking radiation from fluctuating black holes'

NARCIS (Netherlands)

Khavkine, I.

2010-01-01

Takahashi and Soda (2010 Class. Quantum Grav. 27 175008) have recently considered the effect (at lowest non-trivial order) of dynamical, quantized gravitational fluctuations on the spectrum of scalar Hawking radiation from a collapsing Schwarzschild black hole. However, due to an unfortunate choice

Snippets of Physics

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 4. Snippets of Physics - Schwarzschild Metric at a Discounted Price. T Padmanabhan. Series Article Volume 13 Issue 4 April 2008 pp 312-318. Fulltext. Click here to view fulltext PDF. Permanent link:

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)

ICO Topical Meeting on Atmospheric, Volume and Surface Scattering and Propagation Held in Florence, Italy on 27-30 August 1991

Science.gov (United States)

1991-01-01

noises occurring in optoelectronic system as a whole. 60 ADAPTIVE OPTICS AND ITS APPLICATION IN ASTRONOMY FRITZ MERKLE European Southern Observatory Karl ... Schwarzschild -Str.2, 8046 Garching bei Mijuchen Federal Republic of Germany Telephone: +49-89-32006.341 (DWITED) Introduction The image quality

The Weak-Line T Tauri Star V410 Tau

Science.gov (United States)

2003-01-01

700052 Tashkent, Uzbekistan 7 USRA/USNO Flagstaff Station, PO Box 1149, Flagstaff, AZ 86002-1149, USA 8 Thüringer Landessternwarte, Karl ... Schwarzschild -Observatorium, Sternwarte 5, 07778 Tautenburg, Germany 9 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA 10

Mass density of the Earth from a Gravito-Electro-Magnetic 5D vacuum

OpenAIRE

Musmarra, Juan Ignacio; Anabitarte, Mariano; Bellini, Mauricio

2016-01-01

We calculate the mass density of the Earth using a Gravito-Electro-Magnetic theory on an extended 5D Schwarzschild-de Sitter metric, in which we define the vacuum. Our results are in very good agreement with that of the Dziewonski-Anderson model.

Ring wormholes via duality rotations

Directory of Open Access Journals (Sweden)

Gary W. Gibbons

2016-09-01

Full Text Available We apply duality rotations and complex transformations to the Schwarzschild metric to obtain wormhole geometries with two asymptotically flat regions connected by a throat. In the simplest case these are the well-known wormholes supported by phantom scalar field. Further duality rotations remove the scalar field to yield less well known vacuum metrics of the oblate Zipoy–Voorhees–Weyl class, which describe ring wormholes. The ring encircles the wormhole throat and can have any radius, whereas its tension is always negative and should be less than −c4/4G. If the tension reaches the maximal value, the geometry becomes exactly flat, but the topology remains non-trivial and corresponds to two copies of Minkowski space glued together along the disk encircled by the ring. The geodesics are straight lines, and those which traverse the ring get to the other universe. The ring therefore literally produces a hole in space. Such wormholes could perhaps be created by negative energies concentrated in toroidal volumes, for example by vacuum fluctuations.

Lessons on black holes from the elliptic genus

Energy Technology Data Exchange (ETDEWEB)

Giveon, Amit [Racah Institute of Physics, The Hebrew University,Jerusalem, 91904 (Israel); Itzhaki, Nissan [Physics Department, Tel-Aviv University,Ramat-Aviv, 69978 (Israel); Troost, Jan [Laboratoire de Physique Théorique, Unité Mixte du CNRS et de l’École Normale Supérieure associée à l’Université Pierre et Marie Curie 6, École Normale Supérieure, Rue Lhomond Paris (France)

2014-04-28

We further study the elliptic genus of the cigar SL(2,ℝ){sub k}/U(1) coset superconformal field theory. We find that, even in the small curvature, infinite level limit, there are holomorphic and non-holomorphic parts that are due to the discrete states and a mismatch in the spectral densities of the continuum, respectively. The mismatch in the continuum is universal, in the sense that it is fully determined by the asymptotic cylindrical topology of the cigar’s throat. Since modularity of the elliptic genus requires both the holomorphic and non-holomorphic parts, the holomorphic term is universal as well. The contribution of the discrete states is thus present even for perturbative strings propagating in the background of large Schwarzschild black holes. We argue that the discrete states live at a stringy distance from the tip of the cigar both from the conformal field theory wave-function analysis and from a holonomy space perspective. Thus, the way string theory takes care of its self-consistency seems to have important consequences for the physics near horizons, even for parametrically large black holes.

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)

General Relativity Exactly Described by Use of Newton's Laws within a Curved Geometry

Science.gov (United States)

Savickas, David

2014-03-01

The connection between general relativity and Newtonian mechanics is shown to be much closer than generally recognized. When Newton's second law is written in a curved geometry by using the physical components of a vector as defined in tensor calculus, and by replacing distance within the momentum's velocity by the vector metric ds in a curved geometry, the second law can then be easily shown to be exactly identical to the geodesic equation of motion occurring in general relativity. By using a time whose vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be separated into two equations one of which is a curved three-dimensional equation of motion and the other is an equation for energy. For the gravitational field of an isolated particle, they yield the Schwarzschild equations. They can be used to describe gravitation for any array of masses for which the Newtonian gravitational potential is known, and is applied here to describe motion in the gravitational field of a thin mass-rod.

Convective instabilities in SN 1987A

Science.gov (United States)

Benz, Willy; Thielemann, Friedrich-Karl

1990-01-01

Following Bandiera (1984), it is shown that the relevant criterion to determine the stability of a blast wave, propagating through the layers of a massive star in a supernova explosion, is the Schwarzschild (or Ledoux) criterion rather than the Rayleigh-Taylor criterion. Both criteria coincide only in the incompressible limit. Results of a linear stability analysis are presented for a one-dimensional (spherical) explosion in a realistic model for the progenitor of SN 1987A. When applying the Schwarzschild criterion, unstable regions get extended considerably. Convection is found to develop behind the shock, with a characteristic growth rate corresponding to a time scale much smaller than the shock traversal time. This ensures that efficient mixing will take place. Since the entire ejected mass is found to be convectively unstable, Ni can be transported outward, even into the hydrogen envelope, while hydrogen can be mixed deep into the helium core.

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

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

Charge loss (or the lack thereof) for AdS black holes

International Nuclear Information System (INIS)

Ong, Yen Chin; Chen, Pisin

2014-01-01

The evolution of evaporating charged black holes is complicated to model in general, but is nevertheless important since the hints to the Information Loss Paradox and its recent firewall incarnation may lie in understanding more generic geometries than that of Schwarzschild spacetime. Fortunately, for sufficiently large asymptotically flat Reissner-Nordström black holes, the evaporation process can be modeled via a system of coupled linear ordinary differential equations, with charge loss rate governed by Schwinger pair-production process. The same model can be generalized to study the evaporation of AdS Reissner-Nordström black holes with flat horizon. It was recently found that such black holes always evolve towards extremality since charge loss is inefficient. This property is completely opposite to the asymptotically flat case in which the black hole eventually loses its charges and tends towards Schwarzschild limit. We clarify the underlying reason for this different behavior.

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

Pseudo-Newtonian Equations for Evolution of Particles and Fluids in Stationary Space-times

Energy Technology Data Exchange (ETDEWEB)

Witzany, Vojtěch; Lämmerzahl, Claus, E-mail: vojtech.witzany@zarm.uni-bremen.de, E-mail: claus.laemmerzahl@zarm.uni-bremen.de [ZARM, Universität Bremen, Am Fallturm, D-28359 Bremen (Germany)

2017-06-01

Pseudo-Newtonian potentials are a tool often used in theoretical astrophysics to capture some key features of a black hole space-time in a Newtonian framework. As a result, one can use Newtonian numerical codes, and Newtonian formalism, in general, in an effective description of important astrophysical processes such as accretion onto black holes. In this paper, we develop a general pseudo-Newtonian formalism, which pertains to the motion of particles, light, and fluids in stationary space-times. In return, we are able to assess the applicability of the pseudo-Newtonian scheme. The simplest and most elegant formulas are obtained in space-times without gravitomagnetic effects, such as the Schwarzschild rather than the Kerr space-time; the quantitative errors are smallest for motion with low binding energy. Included is a ready-to-use set of fluid equations in Schwarzschild space-time in Cartesian and radial coordinates.

A field-sweep/field-lock system for superconducting magnets--Application to high-field EPR.

Science.gov (United States)

Maly, Thorsten; Bryant, Jeff; Ruben, David; Griffin, Robert G

2006-12-01

We describe a field-lock/field-sweep system for the use in superconducting magnets. The system is based on a commercially available field mapping unit and a custom designed broad-band 1H NMR probe. The NMR signal of a small water sample is used in a feedback loop to set and control the magnetic field to high accuracy. The current instrumental configuration allows field sweeps of +/-0.4 T and a resolution of up to 10(-5) T (0.1 G) and the performance of the system is demonstrated in a high-field electron paramagnetic resonance (EPR) application. The system should also be of utility in other experiments requiring precise and reproducible sweeps of the magnetic field such as DNP, ENDOR or PELDOR.

A Field-Sweep/Field-Lock System for Superconducting Magnets-Application to High-Field EPR

Science.gov (United States)

Maly, Thorsten; Bryant, Jeff; Ruben, David; Griffin, Robert G.

2007-01-01

We describe a field-lock/field-sweep system for the use in superconducting magnets. The system is based on a commercially available field mapping unit and a custom designed broad-band 1H-NMR probe. The NMR signal of a small water sample is used in a feedback loop to set and control the magnetic field to high accuracy. The current instrumental configuration allows field sweeps of ± 0.4 T and a resolution of up to 10-5 T (0.1 G) and the performance of the system is demonstrated in a high-field electron paramagnetic resonance (EPR) application. The system should also be of utility in other experiments requiring precise and reproducible sweeps of the magnetic field such as DNP, ENDOR or PELDOR. PMID:17027306

Matching tomographic IMRT fields with static photon fields

International Nuclear Information System (INIS)

Sethi, A.; Leybovich, L.; Dogan, N.; Emami, B.

2001-01-01

The matching of abutting radiation fields presents a challenging problem in radiation therapy. Due to sharp penumbra of linear accelerator beams, small (1-2 mm) errors in field positioning can lead to large (>30%) hot or cold spots in the abutment region. With head and neck immobilization devices (thermoplastic mask/aquaplast) an average setup error of 3 mm has been reported. Therefore hot or cold spots approaching 50% of the prescription dose may occur along the matchline. Although abutting radiation fields have been investigated for static fields, there is no reported study regarding matching of tomographic IMRT and static fields. Compared to static fields, the matching of tomographic IMRT fields with static fields is more complicated. Since IMRT and static fields are planned on separate treatment planning computers, the dose in the abutment region is not specified. In addition, commonly used techniques for matching fields, such as feathering of junctions, are not practical. We have developed a method that substantially reduces dose inhomogeneity in the abutment region. In this method, a 'buffer zone' around the matchline was created and was included as part of the target for both IMRT and static field plans. In both fields, a small dose gradient (≤3%/mm) in the buffer zone was created. In the IMRT plan, the buffer zone was divided into three sections with dose varying from 83% to 25% of prescription dose. The static field dose profile was modified using either a specially designed physical (hard) or a dynamic (soft) wedge. When these modified fields were matched, the combined dose in the abutment region varied by ≤10% in the presence of setup errors spanning 4 mm (±2 mm) when the hard wedge was used and 10 mm (±5 mm) with the soft wedge

Topics in black-hole physics: geometric constraints on noncollapsing, gravitating systems, and tidal distortions of a Schwarzschild black hole

International Nuclear Information System (INIS)

Redmount, I.H.

1984-01-01

This dissertation consists of two studies on the general-relativistic theory of black holes. The first work concerns the fundamental issue of black-hole formation: in it geometric constraints are sought on gravitating matter systems, in the special case of axial symmetry, which determine whether or not those systems undergo gravitational collapse to form black holes. The second project deals with mechanical behavior of a black hole: specifically, the tidal deformation of a static black hole is studied by the gravitational fields of external bodies

The effects of massive graviton on the equilibrium between the black hole and radiation gas in an isolated box

Directory of Open Access Journals (Sweden)

Ya-Peng Hu

2017-09-01

Full Text Available It is well known that the black hole can have temperature and radiate the particles with black body spectrum, i.e. Hawking radiation. Therefore, if the black hole is surrounded by an isolated box, there is a thermal equilibrium between the black hole and radiation gas. A simple case considering the thermal equilibrium between the Schwarzschild black hole and radiation gas in an isolated box has been well investigated previously in detail, i.e. taking the conservation of energy and principle of maximal entropy for the isolated system into account. In this paper, following the above spirit, the effects of massive graviton on the thermal equilibrium will be investigated. For the gravity with massive graviton, we will use the de Rham–Gabadadze–Tolley (dRGT massive gravity which has been proven to be ghost free. Because the graviton mass depends on two parameters in the dRGT massive gravity, here we just investigate two simple cases related to the two parameters, respectively. Our results show that in the first case the massive graviton can suppress or increase the condensation of black hole in the radiation gas although the T–E diagram is similar as the Schwarzschild black hole case. For the second case, a new T–E diagram has been obtained. Moreover, an interesting and important prediction is that the condensation of black hole just increases from the zero radius of horizon in this case, which is very different from the Schwarzschild black hole case.

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.

The Science and Design of the AGIS Observatory

Science.gov (United States)

Schroedter, Martin

2010-02-01

The AGIS observatory is a next-generation array of imaging atmospheric Cherenkov telescopes (IACTs) for gamma-ray astronomy between 100 GeV and 100 TeV. The AGIS observatory is the next logical step in high energy gamma-ray astronomy, offering improved angular resolution and sensitivity compared to FERMI, and overlapping the high energy end of FERMI's sensitivity band. The baseline AGIS observatory will employ an array of 36 Schwarzschild-Couder IACTs in combination with a highly pixelated (0.05^o diameter) camera. The instrument is designed to provide millicrab sensitivity over a wide (8^o diameter) field of view, allowing both deep studies of faint point sources as well as efficient mapping of the Galactic plane and extended sources. I will describe science drivers behind the AGIS observatory and the design and status of the project. )

Researching on Hawking Effect in a Kerr Space Time via Open Quantum System Approach

International Nuclear Information System (INIS)

Liu, Wen-Biao; Liu, Xian-Ming

2014-01-01

It has been proposed that Hawking radiation from a Schwarzschild or a de Sitter spacetime can be understood as the manifestation of thermalization phenomena in the framework of an open quantum system. Through examining the time evolution of a detector interacting with vacuum massless scalar fields, it is found that the detector would spontaneously excite with a probability the same as the thermal radiation at Hawking temperature. Following the proposals, the Hawking effect in a Kerr space time is investigated in the framework of an open quantum systems. It is shown that Hawking effect of the Kerr space time can also be understood as the the manifestation of thermalization phenomena via open quantum system approach. Furthermore, it is found that near horizon local conformal symmetry plays the key role in the quantum effect of the Kerr space time

The Magnetic Rayleigh-Taylor Instability in Astrophysical Discs

Science.gov (United States)

Contopoulos, I.; Kazanas, D.; Papadopoulos, D. B.

2016-01-01

This is our first study of the magnetic Rayleigh-Taylor instability at the inner edge of an astrophysical disc around a central back hole. We derive the equations governing small-amplitude oscillations in general relativistic ideal magnetodydrodynamics and obtain a criterion for the onset of the instability. We suggest that static disc configurations where magnetic field is held by the disc material are unstable around a Schwarzschild black hole. On the other hand, we find that such configurations are stabilized by the space-time rotation around a Kerr black hole. We obtain a crude estimate of the maximum amount of poloidal magnetic flux that can be accumulated around the centre, and suggest that it is proportional to the black hole spin. Finally, we discuss the astrophysical implications of our result for the theoretical and observational estimations of the black hole jet power.

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.

Buchdahl compactness limit for a pure Lovelock static fluid star

Science.gov (United States)

Dadhich, Naresh; Chakraborty, Sumanta

2017-03-01

We obtain the Buchdahl compactness limit for a pure Lovelock static fluid star and verify that the limit following from the uniform-density Schwarzschild's interior solution, which is universal irrespective of the gravitational theory (Einstein or Lovelock), is true in general. In terms of surface potential Φ (r ) , it means at the surface of the star r =r0, Φ (r0)Lovelock order, respectively. For a given N , Φ (r0) is maximum for d =2 N +2 , while it is always 4 /9 , Buchdahl's limit, for d =3 N +1 . It is also remarkable that for N =1 Einstein gravity, or for pure Lovelock in d =3 N +1 , Buchdahl's limit is equivalent to the criterion that gravitational field energy exterior to the star must be less than half its gravitational mass, having no reference to the interior at all.

Contribution of the cosmological constant to the relativistic bending of light revisited

International Nuclear Information System (INIS)

Rindler, Wolfgang; Ishak, Mustapha

2007-01-01

We study the effect of the cosmological constant Λ on the bending of light by a concentrated spherically symmetric mass. Contrarily to previous claims, we show that, when the Schwarzschild-de Sitter geometry is taken into account, Λ does indeed contribute to the bending

Field theories with subcanonical fields

International Nuclear Information System (INIS)

Bigi, I.I.Y.

1976-01-01

The properties of quantum field theories with spinor fields of dimension less than the canonical value of 3/2 are studied. As a starting point for the application of common perturbation theory we look for the linear version of these theories. A gange-interaction is introduced and with the aid of power counting the renormalizability of the theory is shown. It follows that in the case of a spinor-field with negative dimension renormalization can only be attained if the interaction has a further symmetry. By this symmetry the theory is determined in an unequivocal way. The gange-interaction introduced in the theory leads to a spontaneous breakdown of scale invariance whereby masses are produced. At the same time the spinor-field operators can now be separated in two orthogonal sections with opposite norm. It is proposed to use the section with negative (positive) norm to describe hadrons (leptons) respectively. (orig./WL) [de