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
Gravitational collapse and topology change in spherically symmetric dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Csizmadia, Peter; Racz, Istvan, E-mail: cspeter@rmki.kfki.h, E-mail: iracz@rmki.kfki.h [RMKI H-1121 Budapest, Konkoly Thege Miklos ut 29-33 (Hungary)
2010-01-07
A new numerical framework, based on the use of a simple first-order strongly hyperbolic evolution equations, is introduced and tested in the case of four-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that our numerical method is capable of following the time evolution even after the appearance of trapped surfaces, more importantly, until the true physical singularities are reached. Using this framework, the gravitational collapse of various gravity-matter systems is investigated, with particular attention to the evolution in trapped regions. It is verified that, in advance of the formation of these curvature singularities, trapped regions develop in all cases, thereby supporting the validity of the weak cosmic censor hypothesis of Penrose. Various upper bounds on the rate of blow-up of the Ricci and Kretschmann scalars and the Misner-Sharp mass are provided. In spite of the unboundedness of the Ricci scalar, the Einstein-Hilbert action was found to remain finite in all the investigated cases. In addition, important conceptual issues related to the phenomenon of topology changes are discussed.
Spherically symmetric star model in the gravitational gauge theory
Energy Technology Data Exchange (ETDEWEB)
Tsou, C [Peking Observatory, China; Ch' en, S; Ho, T; Kuo, H
1976-12-01
It is shown that a star model, which is black hole-free and singularity-free, can be obtained naturally in the gravitational gauge theory, provided the space-time is torsion-free and the matter is spinless. The conclusion in a sense shows that the discussions about the black hole and the singularity based on general relativity may not describe nature correctly.
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)
Spherically Symmetric Geometries in f(T) and f(R) Gravitational Theories
International Nuclear Information System (INIS)
Nashed, Gamal G. L.
2015-01-01
Using the well know relation between Ricci scalar, R, and torsion scalar, T, that is, R=-T-2∇_αT"α, we show that, for any spherically symmetric spacetime whose (i) scalar torsion vanishing, that is, T=T_μ_ν"αS_α"μ"ν=0 or (ii) total derivative term, that is, ∇_αT"α with T"α is the contraction of the torsion, vanishing, or (iii) the combination of scalar torsion and total derivative term vanishing, could be solution for f(T) and f(R) gravitational theories.
Spherically Symmetric Gravitational Collapse of a Dust Cloud in Third-Order Lovelock Gravity
Zhou, Kang; Yang, Zhan-Ying; Zou, De-Cheng; Yue, Rui-Hong
We investigate the spherically symmetric gravitational collapse of an incoherent dust cloud by considering a LTB-type spacetime in third-order Lovelock Gravity without cosmological constant, and give three families of LTB-like solutions which separately corresponding to hyperbolic, parabolic and elliptic. Notice that the contribution of high-order curvature corrections have a profound influence on the nature of the singularity, and the global structure of spacetime changes drastically from the analogous general relativistic case. Interestingly, the presence of high order Lovelock terms leads to the formation of massive, naked and timelike singularities in the 7D spacetime, which is disallowed in general relativity. Moveover, we point out that the naked singularities in the 7D case may be gravitational weak therefore may not be a serious threat to the cosmic censorship hypothesis, while the naked singularities in the D ≥ 8 inhomogeneous collapse violate the cosmic censorship hypothesis seriously.
Herrera, L.
2018-02-01
We put forward a new definition of complexity, for static and spherically symmetric self-gravitating systems, based on a quantity, hereafter referred to as complexity factor, that appears in the orthogonal splitting of the Riemann tensor, in the context of general relativity. We start by assuming that the homogeneous (in the energy density) fluid, with isotropic pressure is endowed with minimal complexity. For this kind of fluid distribution, the value of complexity factor is zero. So, the rationale behind our proposal for the definition of complexity factor stems from the fact that it measures the departure, in the value of the active gravitational mass (Tolman mass), with respect to its value for a zero complexity system. Such departure is produced by a specific combination of energy density inhomogeneity and pressure anisotropy. Thus, zero complexity factor may also be found in self-gravitating systems with inhomogeneous energy density and anisotropic pressure, provided the effects of these two factors, on the complexity factor, cancel each other. Some exact interior solutions to the Einstein equations satisfying the zero complexity criterium are found, and prospective applications of this newly defined concept, to the study of the structure and evolution of compact objects, are discussed.
A Model of Dust-like Spherically Symmetric Gravitational Collapse without Event Horizon Formation
Directory of Open Access Journals (Sweden)
Piñol M.
2015-10-01
Full Text Available Some dynamical aspects of gravitational collapse are explored in this paper. A time- dependent spherically symmetric metric is proposed and the corresponding Einstein field equations are derived. An ultrarelativistic dust-like stress-momentum tensor is considered to obtain analytical solutions of these equations, with the perfect fluid con- sisting of two purely radial fluxes — the inwards flux of collapsing matter and the outwards flux of thermally emitted radiation. Thermal emission is calculated by means of a simplistic but illustrative model of uninteracting collapsing shells. Our results show an asymptotic approach to a maximal space-time deformation without the formation of event horizons. The size of the body is slightly larger than the Schwarzschild radius during most of its lifetime, so that there is no contradiction with either observations or previous theorems on black holes. The relation of the latter with our results is scruti- nized in detail.
Spherically symmetric conformal gravity and ''gravitational bubbles''
Energy Technology Data Exchange (ETDEWEB)
Berezin, V.A.; Dokuchaev, V.I.; Eroshenko, Yu.N., E-mail: berezin@inr.ac.ru, E-mail: dokuchaev@inr.ac.ru, E-mail: eroshenko@inr.ac.ru [Institute for Nuclear Research, Russian Academy of Sciences, 60th October Anniversary Prospect 7a, Moscow, 117312 (Russian Federation)
2016-01-01
The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the ''gravitational bubbles'', which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-times (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from ''nothing''. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics à la Vaidya, and the electrovacuum space-time metrics.
Holographic Spherically Symmetric Metrics
Petri, Michael
The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.
International Nuclear Information System (INIS)
Maeda, Hideki
2006-01-01
We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud including the perturbative effects of quantum gravity. The n(≥5)-dimensional action with the Gauss-Bonnet term for gravity is considered and a simple formulation of the basic equations is given for the spacetime M≅M 2 xK n-2 with a perfect fluid and a cosmological constant. This is a generalization of the Misner-Sharp formalism of the four-dimensional spherically symmetric spacetime with a perfect fluid in general relativity. The whole picture and the final fate of the gravitational collapse of a dust cloud differ greatly between the cases with n=5 and n≥6. There are two families of solutions, which we call plus-branch and the minus-branch solutions. A plus-branch solution can be attached to the outside vacuum region which is asymptotically anti-de Sitter in spite of the absence of a cosmological constant. Bounce inevitably occurs in the plus-branch solution for n≥6, and consequently singularities cannot be formed. Since there is no trapped surface in the plus-branch solution, the singularity formed in the case of n=5 must be naked. On the other hand, a minus-branch solution can be attached to the outside asymptotically flat vacuum region. We show that naked singularities are massless for n≥6, while massive naked singularities are possible for n=5. In the homogeneous collapse represented by the flat Friedmann-Robertson-Walker solution, the singularity formed is spacelike for n≥6, while it is ingoing-null for n=5. In the inhomogeneous collapse with smooth initial data, the strong cosmic censorship hypothesis holds for n≥10 and for n=9 depending on the parameters in the initial data, while a naked singularity is always formed for 5≤n≤8. These naked singularities can be globally naked when the initial surface radius of the dust cloud is fine-tuned, and then the weak cosmic censorship hypothesis is violated
How Spherical Is a Cube (Gravitationally)?
Sanny, Jeff; Smith, David
2015-01-01
An important concept that is presented in the discussion of Newton's law of universal gravitation is that the gravitational effect external to a spherically symmetric mass distribution is the same as if all of the mass of the distribution were concentrated at the center. By integrating over ring elements of a spherical shell, we show that the…
Averaging in spherically symmetric cosmology
International Nuclear Information System (INIS)
Coley, A. A.; Pelavas, N.
2007-01-01
The averaging problem in cosmology is of fundamental importance. When applied to study cosmological evolution, the theory of macroscopic gravity (MG) can be regarded as a long-distance modification of general relativity. In the MG approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We study the averaging problem within the class of spherically symmetric cosmological models. That is, we shall take the microscopic equations and effect the averaging procedure to determine the precise form of the correlation tensor in this case. In particular, by working in volume-preserving coordinates, we calculate the form of the correlation tensor under some reasonable assumptions on the form for the inhomogeneous gravitational field and matter distribution. We find that the correlation tensor in a Friedmann-Lemaitre-Robertson-Walker (FLRW) background must be of the form of a spatial curvature. Inhomogeneities and spatial averaging, through this spatial curvature correction term, can have a very significant dynamical effect on the dynamics of the Universe and cosmological observations; in particular, we discuss whether spatial averaging might lead to a more conservative explanation of the observed acceleration of the Universe (without the introduction of exotic dark matter fields). We also find that the correlation tensor for a non-FLRW background can be interpreted as the sum of a spatial curvature and an anisotropic fluid. This may lead to interesting effects of averaging on astrophysical scales. We also discuss the results of averaging an inhomogeneous Lemaitre-Tolman-Bondi solution as well as calculations of linear perturbations (that is, the backreaction) in an FLRW background, which support the main conclusions of the analysis
Relativistic fluids in spherically symmetric space
International Nuclear Information System (INIS)
Dipankar, R.
1977-12-01
Some of McVittie and Wiltshire's (1977) solutions of Walker's (1935) isotropy conditions for relativistic perfect fluid spheres are generalized. Solutions are spherically symmetric and conformally flat
Spherically symmetric charged compact stars
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Maurya, S.K. [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Gupta, Y.K. [Jaypee Institute of Information Technology University, Department of Mathematics, Noida, Uttar Pradesh (India); Ray, Saibal [Government College of Engineering and Ceramic Technology, Department of Physics, Kolkata, West Bengal (India); Chowdhury, Sourav Roy [Seth Anandaram Jaipuria College, Department of Physics, Kolkata, West Bengal (India)
2015-08-15
In this article we consider the static spherically symmetric metric of embedding class 1. When solving the Einstein-Maxwell field equations we take into account the presence of ordinary baryonic matter together with the electric charge. Specific new charged stellar models are obtained where the solutions are entirely dependent on the electromagnetic field, such that the physical parameters, like density, pressure etc. do vanish for the vanishing charge. We systematically analyze altogether the three sets of Solutions I, II, and III of the stellar models for a suitable functional relation of ν(r). However, it is observed that only the Solution I provides a physically valid and well-behaved situation, whereas the Solutions II and III are not well behaved and hence not included in the study. Thereafter it is exclusively shown that the Solution I can pass through several standard physical tests performed by us. To validate the solution set presented here a comparison has also been made with that of the compact stars, like RX J 1856 - 37, Her X - 1, PSR 1937+21, PSRJ 1614-2230, and PSRJ 0348+0432, and we have shown the feasibility of the models. (orig.)
Beig, Robert; Siddiqui, Azad A.
2007-11-01
It is known that spherically symmetric static spacetimes admit a foliation by flat hypersurfaces. Such foliations have explicitly been constructed for some spacetimes, using different approaches, but none of them have proved or even discussed the uniqueness of these foliations. The issue of uniqueness becomes more important due to suitability of flat foliations for studying black hole physics. Here, flat spherically symmetric spacelike hypersurfaces are obtained by a direct method. It is found that spherically symmetric static spacetimes admit flat spherically symmetric hypersurfaces, and that these hypersurfaces are unique up to translation under the timelike Killing vector. This result guarantees the uniqueness of flat spherically symmetric foliations for such spacetimes.
Theorem on axially symmetric gravitational vacuum configurations
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Papadopoulos, A; Le Denmat, G [Paris-6 Univ., 75 (France). Inst. Henri Poincare
1977-01-24
A theorem is proved which asserts the non-existence of axially symmetric gravitational vacuum configurations with non-stationary rotation only. The eventual consequences in black-hole physics are suggested.
Exact solutions of the spherically symmetric multidimensional ...
African Journals Online (AJOL)
The complete orthonormalised energy eigenfunctions and the energy eigenvalues of the spherically symmetric isotropic harmonic oscillator in N dimensions, are obtained through the methods of separation of variables. Also, the degeneracy of the energy levels are examined. KEY WORDS: - Schrödinger Equation, Isotropic ...
The theory of spherically symmetric thin shells in conformal gravity
Berezin, Victor; Dokuchaev, Vyacheslav; Eroshenko, Yury
The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy-momentum tensor of the thin shell is proportional to Diracs delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl-Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in detail the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless ( = massless) shell, it is shown that their dynamics cannot be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl-Einstein gravity, the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.
Spherically symmetric solution and a satisfactory energy-momentum complex
International Nuclear Information System (INIS)
Nashed, G.G.L.
2005-01-01
Mikhail et al. obtained two spherically symmetric solution in Moeller tetrad theory of gravitation. They calculated their energy content and obtained a strange value for the second solution, in spite that the associated metric of these solutions is the same (the Schwarzschild metric). We use another method given bu Gibbons and Hawking to calculate the energy content of these solutions. We also obtained a strange value of energy for the second solution. Studying the requirements of the satisfactory energy-momentum complex given by Moeller we find that the second solution which behaves as 1/√r does not transform as a four-vector under Lorentz transformation
Thermal properties of self-gravitating plane-symmetric configuration
Energy Technology Data Exchange (ETDEWEB)
Hara, T; Ikeuchi, S [Kyoto Univ. (Japan). Dept. of Physics; Sugimoto, D
1976-09-01
As a limiting case of rotating stars, thermal properties of infinite plane-symmetric self-gravitating gas are investigated. Such a configuration is characterized by surface density of the plane instead of stellar mass. In the Kelvin contraction, temperature of the interior decreases, if the surface density is kept constant. If the accretion of matter takes place, or if the angular momenta are transferred outward, the surface density will increase. In this case, the temperature of the interior may increase. When a nuclear burning is ignited, it is thermally unstable in most cases, even when electrons are non-degenerate. This thermal instability is one of the essential differences of the plane-symmetric configuration from the spherical star. Such instabilities are computed for different cases of nuclear fuels. This type of nuclear instability is the same phenomenon as thermal instability of a thin shell burning in a spherical star.
Spherically symmetric self-similar universe
Energy Technology Data Exchange (ETDEWEB)
Dyer, C C [Toronto Univ., Ontario (Canada)
1979-10-01
A spherically symmetric self-similar dust-filled universe is considered as a simple model of a hierarchical universe. Observable differences between the model in parabolic expansion and the corresponding homogeneous Einstein-de Sitter model are considered in detail. It is found that an observer at the centre of the distribution has a maximum observable redshift and can in principle see arbitrarily large blueshifts. It is found to yield an observed density-distance law different from that suggested by the observations of de Vaucouleurs. The use of these solutions as central objects for Swiss-cheese vacuoles is discussed.
Geometrodynamics of spherically symmetric Lovelock gravity
International Nuclear Information System (INIS)
Kunstatter, Gabor; Taves, Tim; Maeda, Hideki
2012-01-01
We derive the Hamiltonian for spherically symmetric Lovelock gravity using the geometrodynamics approach pioneered by Kuchar (1994 Phys. Rev. D 50 3961) in the context of four-dimensional general relativity. When written in terms of the areal radius, the generalized Misner-Sharp mass and their conjugate momenta, the generic Lovelock action and Hamiltonian take on precisely the same simple forms as in general relativity. This result supports the interpretation of Lovelock gravity as the natural higher dimensional extension of general relativity. It also provides an important first step towards the study of the quantum mechanics, Hamiltonian thermodynamics and formation of generic Lovelock black holes. (fast track communication)
The space-time outside a source of gravitational radiation: the axially symmetric null fluid
Energy Technology Data Exchange (ETDEWEB)
Herrera, L. [Universidad Central de Venezuela, Escuela de Fisica, Facultad de Ciencias, Caracas (Venezuela, Bolivarian Republic of); Universidad de Salamanca, Instituto Universitario de Fisica Fundamental y Matematicas, Salamanca (Spain); Di Prisco, A. [Universidad Central de Venezuela, Escuela de Fisica, Facultad de Ciencias, Caracas (Venezuela, Bolivarian Republic of); Ospino, J. [Universidad de Salamanca, Departamento de Matematica Aplicada and Instituto Universitario de Fisica Fundamental y Matematicas, Salamanca (Spain)
2016-11-15
We carry out a study of the exterior of an axially and reflection symmetric source of gravitational radiation. The exterior of such a source is filled with a null fluid produced by the dissipative processes inherent to the emission of gravitational radiation, thereby representing a generalization of the Vaidya metric for axially and reflection symmetric space-times. The role of the vorticity, and its relationship with the presence of gravitational radiation is put in evidence. The spherically symmetric case (Vaidya) is, asymptotically, recovered within the context of the 1 + 3 formalism. (orig.)
Canonical quantization of static spherically symmetric geometries
International Nuclear Information System (INIS)
Christodoulakis, T; Dimakis, N; Terzis, P A; Doulis, G; Grammenos, Th; Melas, E; Spanou, A
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''
Notes on entropy force in general spherically symmetric spacetimes
International Nuclear Information System (INIS)
Cai Ronggen; Cao Liming; Ohta, Nobuyoshi
2010-01-01
In a recent paper [arXiv:1001.0785], Verlinde has shown that the Newton gravity appears as an entropy force. In this paper we show how gravity appears as entropy force in Einstein's equation of gravitational field in a general spherically symmetric spacetime. We mainly focus on the trapping horizon of the spacetime. We find that when matter fields are absent, the change of entropy associated with the trapping horizon indeed can be identified with an entropy force. When matter fields are present, we see that heat flux of matter fields also leads to the change of entropy. Applying arguments made by Verlinde and Smolin, respectively, to the trapping horizon, we find that the entropy force is given by the surface gravity of the horizon. The cases in the untrapped region of the spacetime are also discussed.
Generalized transformations and coordinates for static spherically symmetric general relativity
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.
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.
New mathematical framework for spherical gravitational collapse
International Nuclear Information System (INIS)
Giambo, Roberto; Giannoni, Fabio; Magli, Giulio; Piccione, Paolo
2003-01-01
A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non-static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates the existence of singular null geodesics to the existence of regular curves which are supersolutions of the radial null geodesic equation, and allows us to treat all the known examples of naked singularities from a unified viewpoint. New examples are also found using this approach, and perspectives are discussed. (letter to the editor)
Stability of transparent spherically symmetric thin shells and wormholes
International Nuclear Information System (INIS)
Ishak, Mustapha; Lake, Kayll
2002-01-01
The stability of transparent spherically symmetric thin shells (and wormholes) to linearized spherically symmetric perturbations about static equilibrium is examined. This work generalizes and systematizes previous studies and explores the consequences of including the cosmological constant. The approach shows how the existence (or not) of a domain wall dominates the landscape of possible equilibrium configurations
Initial value formulation for the spherically symmetric dust solution
International Nuclear Information System (INIS)
Liu, H.
1990-01-01
An initial value formulation for the dust solution with spherical symmetry is given explicitly in which the initial distributions of dust and its velocity on an initial surface are chosen to be the initial data. As special cases, the Friedmann universe, the Schwarzschild solution in comoving coordinates, and a spherically symmetric and radially inhomogeneous cosmological model are derived
Non-Spherical Gravitational Collapse of Strange Quark Matter
Institute of Scientific and Technical Information of China (English)
Zade S S; Patil K D; Mulkalwar P N
2008-01-01
We study the non-spherical gravitational collapse of the strange quark null fluid.The interesting feature which emerges is that the non-spherical collapse of charged strange quark matter leads to a naked singularity whereas the gravitational collapse of neutral quark matter proceeds to form a black hole.We extend the earlier work of Harko and Cheng[Phys.Lett.A 266 (2000) 249]to the non-spherical case.
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.
Dynamics and entanglement in spherically symmetric quantum gravity
International Nuclear Information System (INIS)
Husain, Viqar; Terno, Daniel R.
2010-01-01
The gravity-scalar field system in spherical symmetry provides a natural setting for exploring gravitational collapse and its aftermath in quantum gravity. In a canonical approach, we give constructions of the Hamiltonian operator, and of semiclassical states peaked on constraint-free data. Such states provide explicit examples of physical states. We also show that matter-gravity entanglement is an inherent feature of physical states, whether or not there is a black hole.
Implications of the Cosmological Constant for Spherically Symmetric Mass Distributions
Zubairi, Omair; Weber, Fridolin
2013-04-01
In recent years, scientists have made the discovery that the expansion rate of the Universe is increasing rather than decreasing. This acceleration leads to an additional term in Albert Einstein's field equations which describe general relativity and is known as the cosmological constant. This work explores the aftermath of a non-vanishing cosmological constant for relativistic spherically symmetric mass distributions, which are susceptible to change against Einstein's field equations. We introduce a stellar structure equation known as the Tolman-Oppenhiemer-Volkoff (TOV) equation modified for a cosmological constant, which is derived from Einstein's modified field equations. We solve this modified TOV equation for these spherically symmetric mass distributions and obtain stellar properties such as mass and radius and investigate changes that may occur depending on the value of the cosmological constant.
The inverse spatial Laplacian of spherically symmetric spacetimes
International Nuclear Information System (INIS)
Fernandes, Karan; Lahiri, Amitabha
2017-01-01
We derive the inverse spatial Laplacian for static, spherically symmetric backgrounds by solving Poisson’s equation for a point source. This is different from the electrostatic Green function, which is defined on the four dimensional static spacetime, while the equation we consider is defined on the spatial hypersurface of such spacetimes. This Green function is relevant in the Hamiltonian dynamics of theories defined on spherically symmetric backgrounds, and closed form expressions for the solutions we find are absent in the literature. We derive an expression in terms of elementary functions for the Schwarzschild spacetime, and comment on the relation of this solution with the known Green function of the spacetime Laplacian operator. We also find an expression for the Green function on the static pure de-Sitter space in terms of hypergeometric functions. We conclude with a discussion of the constraints of the electromagnetic field. (paper)
R. Vlokh; M. Kostyrko
2006-01-01
Nonlinear effect of the gravitation field of spherically symmetric mass on the gravitational coefficient G has been analysed. In frame of the approaches of parametric optics and gravitation nonlinearity we have shown that the gravitation field of spherically symmetric mass can lead to changes in the gravitational coefficient G.
Internal structure of multicomponent static spherical gravitating fluids
International Nuclear Information System (INIS)
Olson, E.; Bailyn, M.
1975-01-01
The Maxwell--Einstein equations for a fluid comprised of more than one type of particle are not a determinate system even if an equation of state is added. The problem of what the charge distribution is in such fluids is therefore also not determinate. To complete the definition of the problem, more equations are needed. We obtain these for the simple case of a static spherically symmetric multicomponent system (imbedded in a Minkowskian background) by minimizing the energy of the fluid with respect to variations in the number densities of the constituents, with the side conditions that the total number of each constituent is constant during the variations. This procedure results in a determinate set of hydrostatic equilibrium equations, the sum of which is the familiar Tolman--Oppenheimer--Volkoff equation. Some general conclusions can be drawn. For example, the necessary and sufficient condition for charge neutrality is that the mass-energy density be some (arbitrary) function of some (arbitrary) linear combination of the number densities. Thus, since it is well known that the electrons in a white dwarf star at absolute zero form a degenerate gas, there must be a charge imbalance throughout such a star. This imbalance can then be computed self-consistently. An over-all physical interpretation of the new equations is that in equilibrium at any point in the fluid the sum of the non-gravitational forces per unit energy is the same for constituent 1 as for constituent 2 and so on. This is the analog of the corresponding (Galilean) statement for gravitational forces that is valid even without equilibrium
Classic tests of General Relativity described by brane-based spherically symmetric solutions
Energy Technology Data Exchange (ETDEWEB)
Cuzinatto, R.R. [Universidade Federal de Alfenas, Instituto de Ciencia e Tecnologia, Pocos de Caldas, MG (Brazil); Pompeia, P.J. [Departamento de Ciencia e Tecnologia Aeroespacial, Instituto de Fomento e Coordenacao Industrial, Sao Jose dos Campos, SP (Brazil); Departamento de Ciencia e Tecnologia Aeroespacial, Instituto Tecnologico de Aeronautica, Sao Jose dos Campos, SP (Brazil); De Montigny, M. [University of Alberta, Theoretical Physics Institute, Edmonton, AB (Canada); University of Alberta, Campus Saint-Jean, Edmonton, AB (Canada); Khanna, F.C. [University of Alberta, Theoretical Physics Institute, Edmonton, AB (Canada); TRIUMF, Vancouver, BC (Canada); University of Victoria, Department of Physics and Astronomy, PO box 1700, Victoria, BC (Canada); Silva, J.M.H. da [Universidade Estadual Paulista, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil)
2014-08-15
We discuss a way to obtain information about higher dimensions from observations by studying a brane-based spherically symmetric solution. The three classic tests of General Relativity are analyzed in detail: the perihelion shift of the planet Mercury, the deflection of light by the Sun, and the gravitational redshift of atomic spectral lines. The braneworld version of these tests exhibits an additional parameter b related to the fifth-coordinate. This constant b can be constrained by comparison with observational data for massive and massless particles. (orig.)
Spherically Symmetric Solutions of the Einstein-Bach Equations and a Consistent Spin-2 Field Theory
International Nuclear Information System (INIS)
Janda, A.
2006-01-01
We briefly present a relationship between General Relativity coupled to certain spin-0 and spin-2 field theories and higher derivatives metric theories of gravity. In a special case, described by the Einstein-Bach equations, the spin-0 field drops out from the theory and we obtain a consistent spin-two field theory interacting gravitationally, which overcomes a well known inconsistency of the theory for a linear spin-two field coupled to the Einstein's gravity. Then we discuss basic properties of static spherically symmetric solutions of the Einstein-Bach equations. (author)
Spherically symmetric analysis on open FLRW solution in non-linear massive gravity
Energy Technology Data Exchange (ETDEWEB)
Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin, E-mail: chienichiang@berkeley.edu, E-mail: izumi@phys.ntu.edu.tw, E-mail: chen@slac.stanford.edu [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China)
2012-12-01
We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity from general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.
Spherically symmetric static spacetimes in vacuum f(T) gravity
International Nuclear Information System (INIS)
Ferraro, Rafael; Fiorini, Franco
2011-01-01
We show that Schwarzschild geometry remains as a vacuum solution for those four-dimensional f(T) gravitational theories behaving as ultraviolet deformations of general relativity. In the gentler context of three-dimensional gravity, we also find that the infrared-deformed f(T) gravities, like the ones used to describe the late cosmic speed up of the Universe, have as the circularly symmetric vacuum solution a Deser-de Sitter or a Banados, Teitelboim and Zanelli-like spacetime with an effective cosmological constant depending on the infrared scale present in the function f(T).
Finster, Felix; Smoller, Joel; Yau, Shing-Tung
We consider for j=1/2, 3/2,... a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field. The Einstein-Dirac-Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner-Nordstrom solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a "cloud" of spin-1/2-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon.
Maximal slicing of D-dimensional spherically symmetric vacuum spacetime
International Nuclear Information System (INIS)
Nakao, Ken-ichi; Abe, Hiroyuki; Yoshino, Hirotaka; Shibata, Masaru
2009-01-01
We study the foliation of a D-dimensional spherically symmetric black-hole spacetime with D≥5 by two kinds of one-parameter families of maximal hypersurfaces: a reflection-symmetric foliation with respect to the wormhole slot and a stationary foliation that has an infinitely long trumpetlike shape. As in the four-dimensional case, the foliations by the maximal hypersurfaces avoid the singularity irrespective of the dimensionality. This indicates that the maximal slicing condition will be useful for simulating higher-dimensional black-hole spacetimes in numerical relativity. For the case of D=5, we present analytic solutions of the intrinsic metric, the extrinsic curvature, the lapse function, and the shift vector for the foliation by the stationary maximal hypersurfaces. These data will be useful for checking five-dimensional numerical-relativity codes based on the moving puncture approach.
Spherically symmetric near-critical accretion onto neutron stars
International Nuclear Information System (INIS)
Miller, G.S.
1990-01-01
Numerical and approximate analytic solutions for time-independent, spherically symmetric, radiation pressure-dominated accretion flows are presented. For flows with luminosities at infinity, L-infinity, sufficiently close to the Eddington limit L-crit, the flow velocity profile is qualitatively different from the modified free-fall profile v(r) = (1 - L-infinity/L-crit)exp 1/2 (2GM/r)exp 1/2. Advective contributions to the comoving radiation flux decelerate the flow within a criical radius, and, in this settling region, the velocity of the flow decreases linearly with decreasing radius. 14 refs
Minimal Length Effects on Tunnelling from Spherically Symmetric Black Holes
Directory of Open Access Journals (Sweden)
Benrong Mu
2015-01-01
Full Text Available We investigate effects of the minimal length on quantum tunnelling from spherically symmetric black holes using the Hamilton-Jacobi method incorporating the minimal length. We first derive the deformed Hamilton-Jacobi equations for scalars and fermions, both of which have the same expressions. The minimal length correction to the Hawking temperature is found to depend on the black hole’s mass and the mass and angular momentum of emitted particles. Finally, we calculate a Schwarzschild black hole's luminosity and find the black hole evaporates to zero mass in infinite time.
All spherically symmetric charged anisotropic solutions for compact stars
Energy Technology Data Exchange (ETDEWEB)
Maurya, S.K. [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Gupta, Y.K. [Raj Kumar Goel Institute of Technology, Department of Mathematics, Ghaziabad, UP (India); Ray, Saibal [Government College of Engineering and Ceramic Technology, Department of Physics, Kolkata, West Bengal (India)
2017-06-15
In the present paper we develop an algorithm for all spherically symmetric anisotropic charged fluid distributions. Considering a new source function ν(r) we find a set of solutions which is physically well behaved and represents compact stellar models. A detailed study specifically shows that the models actually correspond to strange stars in terms of their mass and radius. In this connection we investigate several physical properties like energy conditions, stability, mass-radius ratio, electric charge content, anisotropic nature and surface redshift through graphical plots and mathematical calculations. All the features from these studies are in excellent agreement with the already available evidence in theory as well as observations. (orig.)
Integral solution for the spherically symmetric Fokker-Planck equation
International Nuclear Information System (INIS)
Donoso, J.M.; Soler, M.
1993-01-01
We propose an integral method to deal with the spherically symmetric non-linear Fokker-Planck equation appearing in plasma physics. A probability transition expression is obtained, which takes into account the proper domain for the radial velocity component. The analytical and computational results are new, and the time evolution is completely satisfactory. The main achievement of the method is conservation of both the initial norm and energy for unlimited times, which has not been attained in the differential approach to the problem. (orig.)
Static axially symmetric gravitational fields with shell sources
International Nuclear Information System (INIS)
McCrea, J.D.
1976-01-01
Israel's (Israel, W., 1966, Nuovo Cim., vol.44, 1-14) method for treating surface layers in general relativity is applied to construct shell sources for exterior static axially symmetric gravitational fields. Consideration is restricted to cases in which the 3-cylinder representing the history of the shell is an equipotential surface of the exterior field and consequently the space-time inside this 3-cylinder is flat. (author)
Gravitational field of spherical domain wall in higher dimension
Indian Academy of Sciences (India)
An exact solution of Einstein's equations is found describing the gravitational ﬁeld of a spherical domain wall with nonvanishing stress component in the direction perpendicular to the plane of the wall. Also we have studied the motion of test particle around the domain wall.
Canonical theory of spherically symmetric spacetimes with cross-streaming null dusts
Bičák, Jiří; Hájíček, Petr
2003-11-01
The Hamiltonian dynamics of two-component spherically symmetric null dust is studied with regard to the quantum theory of gravitational collapse. The components—the ingoing and outgoing dusts—are assumed to interact only through gravitation. Different kinds of singularities, naked or “clothed,” which can form during collapse processes are described. The general canonical formulation of the one-component null-dust dynamics by Bičák and Kuchař is restricted to the spherically symmetric case and used to construct an action for the two components. The transformation from a metric variable to the quasilocal mass is shown to simplify the mathematics. The action is reduced by a choice of gauge and the corresponding true Hamiltonian is written down. Asymptotic coordinates and energy densities of dust shells are shown to form a complete set of Dirac observables. The action of the asymptotic time translation on the observables is defined but it has been calculated explicitly only in the case of one-component dust (Vaidya metric).
Spherically symmetric solutions of general second-order gravity
International Nuclear Information System (INIS)
Whitt, B.
1988-01-01
The general second-order gravity theory, whose Lagrangian includes higher powers of the curvature, is considered in arbitrary dimensions. It is shown that spherically symmetric solutions are static, except in certain, special, unphysical cases. Spherically symmetric solutions are found and classified. Each theory's solutions fall into a number of distinct branches, which may represent finite space with two singular boundaries, or an asymptotically either flat or (anti--)de Sitter space with one singular boundary. A theory may contain at most one branch of solutions in which all singularities are hidden by event horizons. Such horizons generally emit Hawking radiation, though in certain cases the horizon may have zero temperature. Black holes do not necessarily radiate away all their mass: they may terminate in a zero-temperature black hole, a naked singularity, or a hot black hole in equilibrium with a ''cosmological'' event horizon. The thermodynamics of black-hole solutions is discussed; entropy is found to be an increasing function of horizon area, and the first law is shown to hold
Spherical aberration correction with threefold symmetric line currents.
Hoque, Shahedul; Ito, Hiroyuki; Nishi, Ryuji; Takaoka, Akio; Munro, Eric
2016-02-01
It has been shown that N-fold symmetric line current (henceforth denoted as N-SYLC) produces 2N-pole magnetic fields. In this paper, a threefold symmetric line current (N3-SYLC in short) is proposed for correcting 3rd order spherical aberration of round lenses. N3-SYLC can be realized without using magnetic materials, which makes it free of the problems of hysteresis, inhomogeneity and saturation. We investigate theoretically the basic properties of an N3-SYLC configuration which can in principle be realized by simple wires. By optimizing the parameters of a system with beam energy of 5.5keV, the required excitation current for correcting 3rd order spherical aberration coefficient of 400 mm is less than 1AT, and the residual higher order aberrations can be kept sufficiently small to obtain beam size of less than 1 nm for initial slopes up to 5 mrad. Copyright © 2015 Elsevier B.V. All rights reserved.
Gravitational entropy of nonstationary black holes and spherical shells
International Nuclear Information System (INIS)
Hiscock, W.A.
1989-01-01
The problem of defining the gravitational entropy of a nonstationary black hole is considered in a simple model consisting of a spherical shell which collapses into a preexisting black hole. The second law of black-hole mechanics strongly suggests identifying one-quarter of the area of the event horizon as the gravitational entropy of the system. It is, however, impossible to accurately locate the position of the global event horizon using only local measurements. In order to maintain a local thermodynamics, it is suggested that the entropy of the black hole be identified with one-quarter the area of the apparent horizon. The difference between the event-horizon entropy (to the extent it can be determined) and the apparent-horizon entropy may then be interpreted as the gravitational entropy of the collapsing shell. The total (event-horizon) gravitational entropy evolves in a smooth (C 0 ) fashion, even in the presence of δ-functional shells of matter
Information entropy for static spherically symmetric black holes
Institute of Scientific and Technical Information of China (English)
Jiang Ji-Jian; Li Chuan-An
2009-01-01
By using the new equation of state density derived from the generalized uncertainty relation, the number of the quantum states near event horizon is obtained, with which then the information entropy of static spherically symmetric black holes has been discussed. It is found that the divergent integral of quantum states near the event horizon can be naturally avoided if using the new equation of state density without introducing the ultraviolet cut-off. The information entropy of black holes can be obtained precisely by the residue theorem, which is shown to be proportional to the horizon area. The information entropy of black holes obtained agrees with the Bechenstein-Hawking entropy when the suitable cutoff factor is adopted.
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.)
Static spherically symmetric wormholes in f(R, T) gravity
Energy Technology Data Exchange (ETDEWEB)
Zubair, M.; Ahmad, Yasir [Institute Of Information Technology, Department of Mathematics, COMSATS, Lahore (Pakistan); Waheed, Saira [Prince Mohammad Bin Fahd University, Al Khobar (Saudi Arabia)
2016-08-15
In this work, we explore wormhole solutions in f(R, T) theory of gravity, where R is the scalar curvature and T is the trace of stress-energy tensor of matter. To investigate this, we consider a static spherically symmetric geometry with matter contents as anisotropic, isotropic, and barotropic fluids in three separate cases. By taking into account the Starobinsky f(R) model, we analyze the behavior of energy conditions for these different kinds of fluids. It is shown that the wormhole solutions can be constructed without exotic matter in few regions of space-time. We also give the graphical illustration of the results obtained and discuss the equilibrium picture for the anisotropic case only. It is concluded that the wormhole solutions with anisotropic matter are realistic and stable in this theory of gravity. (orig.)
Timelike geodesics around a charged spherically symmetric dilaton black hole
Directory of Open Access Journals (Sweden)
Blaga C.
2015-01-01
Full Text Available In this paper we study the timelike geodesics around a spherically symmetric charged dilaton black hole. The trajectories around the black hole are classified using the effective potential of a free test particle. This qualitative approach enables us to determine the type of orbit described by test particle without solving the equations of motion, if the parameters of the black hole and the particle are known. The connections between these parameters and the type of orbit described by the particle are obtained. To visualize the orbits we solve numerically the equation of motion for different values of parameters envolved in our analysis. The effective potential of a free test particle looks different for a non-extremal and an extremal black hole, therefore we have examined separately these two types of black holes.
Information entropy for static spherically symmetric black holes
International Nuclear Information System (INIS)
Ji-Jian, Jiang; Chuan-An, Li
2009-01-01
By using the new equation of state density derived from the generalized uncertainty relation, the number of the quantum states near event horizon is obtained, with which then the information entropy of static spherically symmetric black holes has been discussed. It is found that the divergent integral of quantum states near the event horizon can be naturally avoided if using the new equation of state density without introducing the ultraviolet cut-off. The information entropy of black holes can be obtained precisely by the residue theorem, which is shown to be proportional to the horizon area. The information entropy of black holes obtained agrees with the Bechenstein–Hawking entropy when the suitable cutoff factor is adopted. (general)
Absorbed dose from traversing spherically symmetric, Gaussian radioactive clouds
International Nuclear Information System (INIS)
Thompson, J.M.; Poston, J.W.
1999-01-01
If a large radioactive cloud is produced, sampling may require that an airplane traverse the cloud. A method to predict the absorbed dose to the aircrew from penetrating the radioactive cloud is needed. Dose rates throughout spherically symmetric Gaussian clouds of various sizes, and the absorbed doses from traversing the clouds, were calculated. Cloud size is a dominant parameter causing dose to vary by orders of magnitude for a given dose rate measured at some distance. A method to determine cloud size, based on dose rate readings at two or more distances from the cloud center, was developed. This method, however, failed to resolve the smallest cloud sizes from measurements made at 1,000 m to 2,000 m from the cloud center
Observational signatures of spherically-symmetric black hole spacetimes
De Laurentis, Mariafelicia; Younsi, Ziri; Porth, Oliver; Mizuno, Yosuke; Fromm, Christian; Rezzolla, Luciano; Olivares, Hector
2017-12-01
A binary system composed of a supermassive black hole and a pulsar orbiting around it is studied. The motivation for this study arises from the fact that pulsar timing observations have proven to be a powerful tool in identifying physical features of the orbiting companion. In this study, taking into account a general spherically-symmetric metric, we present analytic calculations of the geodesic motion, and the possible deviations with respect to the standard Schwarzschild case of General Relativity. In particular, the advance at periastron is studied with the aim of identifying corrections to General Relativity. A discussion of the motion of a pulsar very close the supermassive central black hole in our Galaxy (Sgr A*) is reported.
Energy Technology Data Exchange (ETDEWEB)
Hod, Shahar [The Ruppin Academic Center, Emeq Hefer (Israel); The Hadassah Academic College, Jerusalem (Israel)
2017-12-15
It has recently been demonstrated that asymptotically flat neutral reflecting stars are characterized by an intriguing no-hair property. In particular, it has been proved that these horizonless compact objects cannot support spatially regular static matter configurations made of scalar (spin-0) fields, vector (spin-1) fields and tensor (spin-2) fields. In the present paper we shall explicitly prove that spherically symmetric compact reflecting stars can support stationary (rather than static) bound-state massive scalar fields in their exterior spacetime regions. To this end, we solve analytically the Klein-Gordon wave equation for a linearized scalar field of mass μ and proper frequency ω in the curved background of a spherically symmetric compact reflecting star of mass M and radius R{sub s}. It is proved that the regime of existence of these stationary composed star-field configurations is characterized by the simple inequalities 1 - 2M/R{sub s} < (ω/μ){sup 2} < 1. Interestingly, in the regime M/R{sub s} << 1 of weakly self-gravitating stars we derive a remarkably compact analytical equation for the discrete spectrum {ω(M,R_s, μ)}{sup n=∞}{sub n=1} of resonant oscillation frequencies which characterize the stationary composed compact-reflecting-star-linearized-massive-scalar-field configurations. Finally, we verify the accuracy of the analytically derived resonance formula of the composed star-field configurations with direct numerical computations. (orig.)
Spherically symmetric Einstein-aether perfect fluid models
Energy Technology Data Exchange (ETDEWEB)
Coley, Alan A.; Latta, Joey [Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 3J5 (Canada); Leon, Genly [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4950, Valparaíso (Chile); Sandin, Patrik, E-mail: aac@mathstat.dal.ca, E-mail: genly.leon@ucv.cl, E-mail: patrik.sandin@aei.mpg.de, E-mail: lattaj@mathstat.dal.ca [Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Am Mühlenberg 1, D-14476 Potsdam (Germany)
2015-12-01
We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic inhomogeneous cosmological models and astrophysical objects with values for the parameters which are consistent with current constraints. In particular, we consider dust models in (β−) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs models using appropriate bounded normalized variables. We then analyse these models, with special emphasis on the future asymptotic behaviour for different values of the parameters. Finally, we investigate static models for a mixture of a (necessarily non-tilted) perfect fluid with a barotropic equations of state and a scalar field.
Generation of spherically symmetric metrics in f(R) gravity
Energy Technology Data Exchange (ETDEWEB)
Amirabi, Z.; Halilsoy, M.; Mazharimousavi, S.H. [Eastern Mediterranean University, Department of Physics, Gazimagusa (Turkey)
2016-06-15
In D-dimensional spherically symmetric f(R) gravity there are three unknown functions to be determined from the fourth order differential equations. It is shown that the system remarkably may be integrated to relate two functions through the third one to provide a reduction to second order equations accompanied with a large class of potential solutions. The third function, which acts as the generator of the process, is F(R) = (df(R))/(dR). We recall that our generating function has been employed as a scalar field with an accompanying self-interacting potential previously, which is entirely different from our approach. Reduction of f(R) theory into a system of equations seems to be efficient enough to generate a solution corresponding to each generating function. As particular examples, besides the known ones, we obtain new black hole solutions in any dimension D. We further extend our analysis to cover non-zero energy-momentum tensors. Global monopole and Maxwell sources are given as examples. (orig.)
Rovibrational states of Wigner molecules in spherically symmetric confining potentials
Energy Technology Data Exchange (ETDEWEB)
Cioslowski, Jerzy [Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden (Germany)
2016-08-07
The strong-localization limit of three-dimensional Wigner molecules, in which repulsively interacting particles are confined by a weak spherically symmetric potential, is investigated. An explicit prescription for computation of rovibrational wavefunctions and energies that are asymptotically exact at this limit is presented. The prescription is valid for systems with arbitrary angularly-independent interparticle and confining potentials, including those involving Coulombic and screened (i.e., Yukawa/Debye) interactions. The necessary derivations are greatly simplified by explicit constructions of the Eckart frame and the parity-adapted primitive wavefunctions. The performance of the new formalism is illustrated with the three- and four-electron harmonium atoms at their strong-correlation limits. In particular, the involvement of vibrational modes with the E symmetry is readily pinpointed as the origin of the “anomalous” weak-confinement behavior of the {sup 1}S{sub +} state of the four-electron species that is absent in its {sup 1}D{sub +} companion of the strong-confinement regime.
International Nuclear Information System (INIS)
Nariai, Hidekazu.
1986-06-01
In similar to Misner and Sharp's formalism in general relativity for a spherical gravitational collapse, a formalism for the spherical gravitational collapse is presented on the basis of a generalized theory of gravitation in the sense of Utiyama-DeWitt (which was later extended by Parker's school and Zel'dovich's one). The resulted formalism is somewhat similar to that developed by me in 1972 based on the scalar-tensor theory of gravity. (author)
International Nuclear Information System (INIS)
Nyambuya, Golden Gadzirayi
2010-01-01
This paper is part of a series on the Azimuthally Symmetric Theory of Gravitation (ASTG). This theory is built on Laplace-Poisson's well known equation and it has been shown that the ASTG is capable of explaining, from a purely classical physics standpoint, the precession of the perihelion of solar planets as a consequence of the azimuthal symmetry emerging from the spin of the Sun. This symmetry has and must have an influence on the emergent gravitational field. We show herein that the emergent equations from the ASTG, under some critical conditions determined by the spin, do possess repulsive gravitational fields in the polar regions of the gravitating body in question. This places the ASTG on an interesting pedestal to infer the origins of outflows as a repulsive gravitational phenomenon. Outflows are a ubiquitous phenomenon found in star forming systems and their true origin is a question yet to be settled. Given the current thinking on their origin, the direction that the present paper takes is nothing short of an asymptotic break from conventional wisdom; at the very least, it is a complete paradigm shift because gravitation is not at all associated with this process, but rather it is thought to be an all-attractive force that only tries to squash matter together onto a single point. Additionally, we show that the emergent Azimuthally Symmetric Gravitational Field from the ASTG strongly suggests a solution to the supposed Radiation Problem that is thought to be faced by massive stars in their process of formation. That is, at ∼ 8-10 M sun , radiation from the nascent star is expected to halt the accretion of matter. We show that in-falling material will fall onto the equatorial disk and from there, this material will be channeled onto the forming star via the equatorial plane, thus accretion of mass continues well past the value of ∼ 8-10 M sun , albeit via the disk. Along the equatorial plane, the net force (with the radiation force included) on any
Energy Technology Data Exchange (ETDEWEB)
Akbar, M.M., E-mail: akbar@utdallas.edu
2017-06-10
It is well known that static spherically symmetric spacetimes can admit foliations by flat spacelike hypersurfaces, which are best described in terms of the Painlevè–Gullstrand coordinates. The uniqueness and existence of such foliations were addressed earlier. In this paper, we prove, purely geometrically, that any possible foliation of a static spherically symmetric spacetime by an arbitrary codimension-one spherical spacelike geometry, up to time translation and rotation, is unique, and we find the algebraic condition under which it exists. This leads us to what can be considered as the most natural generalization of the Painlevè–Gullstrand coordinate system for static spherically symmetric metrics, which, in turn, makes it easy to derive generic conclusions on foliation and to study specific cases as well as to easily reproduce previously obtained generalizations as special cases. In particular, we note that the existence of foliation by flat hypersurfaces guarantees the existence of foliation by hypersurfaces whose Ricci curvature tensor is everywhere non-positive (constant negative curvature is a special case). The study of uniqueness and the existence concurrently solves the question of embeddability of a spherical spacelike geometry in one-dimensional higher static spherically symmetric spacetimes, and this produces known and new results geometrically, without having to go through the momentum and Hamiltonian constraints.
Spectral combination of spherical gravitational curvature boundary-value problems
PitoÅák, Martin; Eshagh, Mehdi; Šprlák, Michal; Tenzer, Robert; Novák, Pavel
2018-04-01
Four solutions of the spherical gravitational curvature boundary-value problems can be exploited for the determination of the Earth's gravitational potential. In this article we discuss the combination of simulated satellite gravitational curvatures, i.e., components of the third-order gravitational tensor, by merging these solutions using the spectral combination method. For this purpose, integral estimators of biased- and unbiased-types are derived. In numerical studies, we investigate the performance of the developed mathematical models for the gravitational field modelling in the area of Central Europe based on simulated satellite measurements. Firstly, we verify the correctness of the integral estimators for the spectral downward continuation by a closed-loop test. Estimated errors of the combined solution are about eight orders smaller than those from the individual solutions. Secondly, we perform a numerical experiment by considering the Gaussian noise with the standard deviation of 6.5× 10-17 m-1s-2 in the input data at the satellite altitude of 250 km above the mean Earth sphere. This value of standard deviation is equivalent to a signal-to-noise ratio of 10. Superior results with respect to the global geopotential model TIM-r5 are obtained by the spectral downward continuation of the vertical-vertical-vertical component with the standard deviation of 2.104 m2s-2, but the root mean square error is the largest and reaches 9.734 m2s-2. Using the spectral combination of all gravitational curvatures the root mean square error is more than 400 times smaller but the standard deviation reaches 17.234 m2s-2. The combination of more components decreases the root mean square error of the corresponding solutions while the standard deviations of the combined solutions do not improve as compared to the solution from the vertical-vertical-vertical component. The presented method represents a weight mean in the spectral domain that minimizes the root mean square error
International Nuclear Information System (INIS)
Bruckman, W.
1986-01-01
The inverse scattering method of Belinsky and Zakharov is used to investigate axially symmetric stationary vacuum soliton solutions in the five-dimensional representation of the Brans-Dicke-Jordan theory of gravitation, where the scalar field of the theory is an element of a five-dimensional metric. The resulting equations for the spacetime metric are similar to those of solitons in general relativity, while the scalar field generated is the product of a simple function of the coordinates and an already known scalar field solution. A family of solutions is considered that reduce, in the absence of rotation, to the five-dimensional form of a well-known Weyl-Levi Civita axially symmetric static vacuum solution. With a suitable choice of parameters, this static limit becomes equivalent to the spherically symmetric solution of the Brans-Dicke theory. An exact metric, in which the Kerr-scalar McIntosh solution is a special case, is given explicitly
Plane symmetric cosmological model with thick domain walls in Brans-Dicke theory of gravitation
International Nuclear Information System (INIS)
Pawar, D.; Bayaskar, S.; Patil, V.
2009-01-01
We have investigated plane symmetric cosmological model in presence of thick domain walls in Brans-Dicke theory of gravitation, some geometrical and physical behavior of the model are discussed. (authors)
Energy Technology Data Exchange (ETDEWEB)
Zhuk, Alexander [The International Center of Future Science of the Jilin University, Changchun City (China); Odessa National University, Astronomical Observatory, Odessa (Ukraine); Chopovsky, Alexey; Fakhr, Seyed Hossein [Odessa National University, Astronomical Observatory, Odessa (Ukraine); Shulga, Valerii [The International Center of Future Science of the Jilin University, Changchun City (China); Institut of Radio Astronomy of National Academy of Sciences of Ukraine, Kharkov (Ukraine); Wei, Han [The International Center of Future Science of the Jilin University, Changchun City (China)
2017-11-15
In a multidimensional Kaluza-Klein model with Ricci-flat internal space, we study the gravitational field in the weak-field limit. This field is created by two coupled sources. First, this is a point-like massive body which has a dust-like equation of state in the external space and an arbitrary parameter Ω of equation of state in the internal space. The second source is a static spherically symmetric massive scalar field centered at the origin where the point-like massive body is. The found perturbed metric coefficients are used to calculate the parameterized post-Newtonian (PPN) parameter γ. We define under which conditions γ can be very close to unity in accordance with the relativistic gravitational tests in the solar system. This can take place for both massive or massless scalar fields. For example, to have γ ∼ 1 in the solar system, the mass of scalar field should be μ >or similar 5.05 x 10{sup -49} g ∝ 2.83 x 10{sup -16} eV. In all cases, we arrive at the same conclusion that to be in agreement with the relativistic gravitational tests, the gravitating mass should have tension: Ω = -1/2. (orig.)
Spherically symmetric relativistic model for spiral galaxies and dense stars
International Nuclear Information System (INIS)
Hojman, R.; Rodrigues, L.M.C.; Sasse, F.D.
1990-01-01
The behaviour of the pressure and the density as well as the gravitational field of a dense star are studied in some detail. For such a purpose and to take into account relativistic effects, we find a family of exact solutions of the Tolman-Oppenheimer-Volkov equation, which contains as a particular case solutions corresponding to a γ-law equation of state. The mentioned family can also be used to model the (luminous or dark) matter content of spiral galaxies, as it fits the observed data for their orbital velocities profiles. (author)
Dyons in presence of gravitation and symmetrized field equations
International Nuclear Information System (INIS)
Rawat, A.S.; Negi, O.P.S.
1999-01-01
Combined theory of gravitation and electromagnetism associated with particles carrying electric and magnetic charges has been established from an invariant action principle. Corresponding field equations, equation of motion and Einstein Maxwell's equations are obtained in unique and consistent way. It is shown that weak field approximation of slowly moving particle in gravitational field leads the symmetry between electromagnetic and linear gravitational fields. Postulation of the existence of gravimagnetic monopole leads structural symmetry between generalized electromagnetic and gravielectromagnetic fields. Corresponding quantization conditions and angular momentum are also analysed. (author)
Invariant identification of naked singularities in spherically symmetric spacetimes
International Nuclear Information System (INIS)
Torres, R
2012-01-01
The study of generic naked singularities and their implications for the cosmic censorship conjecture is still an open issue in the framework of general relativity. One of the obstacles can be traced to the procedures for identifying naked singularities. Usually, the methods applied are not only model and coordinate dependent, but they very often rely in some strong assumptions on the degree of differentiability of the physical magnitudes of the model (such as the mass, density, etc) in the singularity. In this paper, we present a coordinate independent framework for identifying naked singularities based on invariants which is also devoid of strong differentiability requirements. The approach is intended to analyse whole families of models and to provide general results related to the cosmic censorship conjecture. Moreover, since the framework has a strict geometrical nature it can be used with alternative theories of gravitation as long as they assume the existence of a Lorentzian manifold. We exemplify its strength by applying it to the study of the collapse of radiation in radiative coordinates and the collapse of dust in comoving coordinates. (paper)
No nonminimally coupled massless scalar hair for spherically symmetric neutral black holes
Directory of Open Access Journals (Sweden)
Shahar Hod
2017-08-01
Full Text Available We provide a remarkably compact proof that spherically symmetric neutral black holes cannot support static nonminimally coupled massless scalar fields. The theorem is based on causality restrictions imposed on the energy-momentum tensor of the fields near the regular black-hole horizon.
Non-integrability of time-dependent spherically symmetric Yang-Mills equations
International Nuclear Information System (INIS)
Matinyan, S.G.; Prokhorenko, E.V.; Savvidy, G.K.
1986-01-01
The integrability of time-dependent spherically symmetric Yang-Mills equations is studied using the Fermi-Pasta-Ulam method. The phase space of this system is shown to have no quasi-periodic motion specific for integrable systems. In particular, the well-known Wu-Yang static solution is unstable, so its vicinity in phase is the stochasticity region
The general class of the vacuum spherically symmetric equations of the general relativity theory
International Nuclear Information System (INIS)
Karbanovski, V. V.; Sorokin, O. M.; Nesterova, M. I.; Bolotnyaya, V. A.; Markov, V. N.; Kairov, T. V.; Lyash, A. A.; Tarasyuk, O. R.
2012-01-01
The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g 00 and g 22 is obtained. The properties of the found solutions are analyzed.
Non-integrability of time-dependent spherically symmetric Yang-Mills equations
Energy Technology Data Exchange (ETDEWEB)
Matinyan, S G; Prokhorenko, E B; Savvidy, G K
1988-03-07
The integrability of time-dependent spherically symmetric Yang-Mills equations is studied using the Fermi-Pasta-Ulam method. It is shown that the motion of this system is ergodic, while the system itself is non-integrable, i.e. manifests dynamical chaos.
Brito, Irene; Mena, Filipe C
2017-08-01
We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial space-like hypersurface with a time-like boundary, there exists a unique, local in time solution to the Einstein equations in a neighbourhood of the boundary. As an application, we consider a particular elastic fluid interior matched to a vacuum exterior.
Gravitational Waves in Locally Rotationally Symmetric (LRS Class II Cosmologies
Directory of Open Access Journals (Sweden)
Michael Bradley
2017-10-01
Full Text Available In this work we consider perturbations of homogeneous and hypersurface orthogonal cosmological backgrounds with local rotational symmetry (LRS, using a method based on the 1 + 1 + 2 covariant split of spacetime. The backgrounds, of LRS class II, are characterised by that the vorticity, the twist of the 2-sheets, and the magnetic part of the Weyl tensor all vanish. They include the flat Friedmann universe as a special case. The matter contents of the perturbed spacetimes are given by vorticity-free perfect fluids, but otherwise the perturbations are arbitrary and describe gravitational, shear, and density waves. All the perturbation variables can be given in terms of the time evolution of a set of six harmonic coefficients. This set decouples into one set of four coefficients with the density perturbations acting as source terms, and another set of two coefficients describing damped source-free gravitational waves with odd parity. We also consider the flat Friedmann universe, which has been considered by several others using the 1 + 3 covariant split, as a check of the isotropic limit. In agreement with earlier results we find a second-order wavelike equation for the magnetic part of the Weyl tensor which decouples from the density gradient for the flat Friedmann universes. Assuming vanishing vector perturbations, including the density gradient, we find a similar equation for the electric part of the Weyl tensor, which was previously unnoticed.
Lee, Myoung-Jae; Jung, Young-Dae
2018-05-01
The dispersion properties of surface dust ion-acoustic waves in a self-gravitating magnetized dusty plasma layer with the (r, q) distribution are investigated. The result shows that the wave frequency of the symmetric mode in the plasma layer decreases with an increase in the wave number. It is also shown that the wave frequency of the symmetric mode decreases with an increase in the spectral index r. However, the wave frequency of the anti-symmetric mode increases with an increase in the wave number. It is also found that the anti-symmetric mode wave frequency increases with an increase in the spectral index r. In addition, it is found that the influence of the self-gravitation on the symmetric mode wave frequency decreases with increasing scaled Jeans frequency. Moreover, it is found that the wave frequency of the symmetric mode increases with an increase in the dust charge; however, the anti-symmetric mode shows opposite behavior.
Static spherically symmetric solutions in mimetic gravity: rotation curves and wormholes
International Nuclear Information System (INIS)
Myrzakulov, Ratbay; Sebastiani, Lorenzo; Vagnozzi, Sunny; Zerbini, Sergio
2016-01-01
In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension of general relativity where the conformal degree of freedom of gravity is isolated in a covariant fashion. Here we extend previous works by considering, in addition, a potential for the mimetic field. An appropriate choice of such a potential allows for the reconstruction of a number of interesting cosmological and astrophysical scenarios. We explicitly show how to reconstruct such a potential for a general static spherically symmetric space-time. A number of applications and scenarios are then explored, among which are traversable wormholes. Finally, we analytically reconstruct potentials, which leads to solutions to the equations of motion featuring polynomial corrections to the Schwarzschild space-time. Accurate choices for such corrections could provide an explanation for the inferred flat rotation curves of spiral galaxies within the mimetic gravity framework, without the need for particle dark matter. (paper)
All static spherically symmetric perfect-fluid solutions of Einstein's equations
International Nuclear Information System (INIS)
Lake, Kayll
2003-01-01
An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect-fluid solutions of Einstein's equations. For physically relevant solutions the generating functions must be restricted by nontrivial integral-differential inequalities. Nonetheless, the algorithm is demonstrated here by the construction of an infinite number of previously unknown physically interesting exact solutions
Unified Treatment of a Class of Spherically Symmetric Potentials: Quasi-Exact Solution
International Nuclear Information System (INIS)
Baradaran, M.; Panahi, H.
2016-01-01
We investigate the Schrödinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all models give rise to the same basic differential equation, which is expressible as an element of the universal enveloping algebra of sl(2). Then, we obtain the general exact solutions of the problem by employing the representation theory of sl(2) Lie algebra.
Gravitational field of spherical domain wall in higher dimension
Indian Academy of Sciences (India)
and examine whether bound orbits are possible or not. This study will be of relevance to the structure formation because it gives some idea about the behaviour of the particles. (created at the early universe) in the gravitational field of the domain walls. Our paper is organized as follows: The basic equations are constructed ...
Response of spherical gravitational wave antenna modes to high-energy cosmic ray particles
International Nuclear Information System (INIS)
Jr, R M Marinho; Magalhaes, N S; Aguiar, O D; Frajuca, C
2002-01-01
High-energy cosmic ray particles are expected to be a significant source of noise in resonant mass gravitational wave detectors close to the quantum limit. The spherical, fourth generation antennas have been designed to attain such a limit. In this work we will show how the energy of a cosmic ray particle interacting with such an antenna is distributed over its eigenmodes. We will then make some comments on the relevant consequences of such a distribution for gravitational wave detection
Response of spherical gravitational wave antenna modes to high-energy cosmic ray particles
Marinho, R M; Aguiar, O D; Frajuca, C
2002-01-01
High-energy cosmic ray particles are expected to be a significant source of noise in resonant mass gravitational wave detectors close to the quantum limit. The spherical, fourth generation antennas have been designed to attain such a limit. In this work we will show how the energy of a cosmic ray particle interacting with such an antenna is distributed over its eigenmodes. We will then make some comments on the relevant consequences of such a distribution for gravitational wave detection.
A new approach to spherically symmetric junction surfaces and the matching of FLRW regions
International Nuclear Information System (INIS)
Kirchner, U
2004-01-01
We investigate timelike junctions (with surface layer) between spherically symmetric solutions of the Einstein-field equation. In contrast to previous investigations, this is done in a coordinate system in which the junction surface motion is absorbed in the metric, while all coordinates are continuous at the junction surface. The evolution equations for all relevant quantities are derived. We discuss the no-surface layer case (boundary surface) and study the behaviour for small surface energies. It is shown that one should expect cases in which the speed of light is reached within a finite proper time. We carefully discuss necessary and sufficient conditions for a possible matching of spherically symmetric sections. For timelike junctions between spherically symmetric spacetime sections we show explicitly that the time component of the Lanczos equation always reduces to an identity (independent of the surface equation of state). The results are applied to the matching of Friedmann-LemaItre-Robertson-Walker (FLRW) models. We discuss 'vacuum bubbles' and closed-open junctions in detail. As illustrations several numerical integration results are presented, some of them indicate that (observers comoving with) the junction surface can reach the speed of light within a finite time
Naked singularities in self-similar spherical gravitational collapse
International Nuclear Information System (INIS)
Ori, A.; Piran, T.
1987-01-01
We present general-relativistic solutions of self-similar spherical collapse of an adiabatic perfect fluid. We show that if the equation of state is soft enough (Γ-1<<1), a naked singularity forms. The singularity resembles the shell-focusing naked singularities that arise in dust collapse. This solution increases significantly the range of matter fields that should be ruled out in order that the cosmic-censorship hypothesis will hold
Sufficient condition for black-hole formation in spherical gravitational collapse
International Nuclear Information System (INIS)
Giambo, Roberto; Giannoni, Fabio; Magli, Giulio
2002-01-01
A sufficient condition for the validity of cosmic censorship in spherical gravitational collapse is formulated and proved. The condition relies on an attractive mathematical property of the apparent horizon, which holds if 'minimal' requirements of physical reasonableness are satisfied by the matter model. (letter to the editor)
Gravitational sedimentation of cloud of solid spherical particles at small Reynolds numbers
Directory of Open Access Journals (Sweden)
Arkhipov Vladimir
2015-01-01
Full Text Available The experimental results of study of gravitational sedimentation of highly-concentrated systems of solid spherical particles at small Reynolds numbers Re<1 are presented. Empirical equation for drag coefficient of the particle assembly has been obtained. The influence of initial particle concentration in the cloud on its dynamics and velocity has been analysed.
Sufficient condition for black-hole formation in spherical gravitational collapse
Energy Technology Data Exchange (ETDEWEB)
Giambo, Roberto [Dipartimento di Matematica e Fisica, Universita di Camerino (Italy); Giannoni, Fabio [Dipartimento di Matematica e Fisica, Universita di Camerino (Italy); Magli, Giulio [Dipartimento di Matematica, Politecnico di Milano (Italy)
2002-01-21
A sufficient condition for the validity of cosmic censorship in spherical gravitational collapse is formulated and proved. The condition relies on an attractive mathematical property of the apparent horizon, which holds if 'minimal' requirements of physical reasonableness are satisfied by the matter model. (letter to the editor)
Directory of Open Access Journals (Sweden)
Chifu E. N.
2009-07-01
Full Text Available General Relativistic metric tensors for gravitational fields exterior to homogeneous spherical mass distributions rotating with constant angular velocity about a fixed di- ameter are constructed. The coeffcients of affine connection for the gravitational field are used to derive equations of motion for test particles. The laws of conservation of energy and angular momentum are deduced using the generalized Lagrangian. The law of conservation of angular momentum is found to be equal to that in Schwarzschild’s gravitational field. The planetary equation of motion and the equation of motion for a photon in the vicinity of the rotating spherical mass distribution have rotational terms not found in Schwarzschild’s field.
On the use of the Kodama vector field in spherically symmetric dynamical problems
Energy Technology Data Exchange (ETDEWEB)
Racz, Istvan [MTA KFKI, Reszecske- es Magfizikai Kutatointezet, H-1121 Budapest, Konkoly Thege Miklos ut 29-33, (Hungary)
2006-01-07
It is shown that by making use of the Kodama vector field, as a preferred time evolution vector field, in spherically symmetric dynamical systems unexpected simplifications arise. In particular, the evolution equations relevant for the case of a massless scalar field minimally coupled to gravity are investigated. The simplest form of these equations in the 'canonical gauge' is known to possess the character of a mixed first-order elliptic-hyperbolic system. The advantages related to the use of the Kodama vector field are twofold although they show up simultaneously. First, it is found that the true degrees of freedom separate. Second, a subset of the field equations possessing the form of a first-order symmetric hyperbolic system for these preferred degrees of freedom is singled out. It is also demonstrated, in the appendix, that the above results generalize straightforwardly to the case of a generic self-interacting scalar field.
Spherical aberration correction with an in-lens N-fold symmetric line currents model.
Hoque, Shahedul; Ito, Hiroyuki; Nishi, Ryuji
2018-04-01
In our previous works, we have proposed N-SYLC (N-fold symmetric line currents) models for aberration correction. In this paper, we propose "in-lens N-SYLC" model, where N-SYLC overlaps rotationally symmetric lens. Such overlap is possible because N-SYLC is free of magnetic materials. We analytically prove that, if certain parameters of the model are optimized, an in-lens 3-SYLC (N = 3) doublet can correct 3rd order spherical aberration. By computer simulation, we show that the required excitation current for correction is less than 0.25 AT for beam energy 5 keV, and the beam size after correction is smaller than 1 nm at the corrector image plane for initial slope less than 4 mrad. Copyright © 2018 Elsevier B.V. All rights reserved.
Beyond Extreme Ultra Violet (BEUV) Radiation from Spherically symmetrical High-Z plasmas
Yoshida, Kensuke; Fujioka, Shinsuke; Higashiguchi, Takeshi; Ugomori, Teruyuki; Tanaka, Nozomi; Kawasaki, Masato; Suzuki, Yuhei; Suzuki, Chihiro; Tomita, Kentaro; Hirose, Ryouichi; Eshima, Takeo; Ohashi, Hayato; Nishikino, Masaharu; Scally, Enda; Nshimura, Hiroaki; Azechi, Hiroshi; O'Sullivan, Gerard
2016-03-01
Photo-lithography is a key technology for volume manufacture of high performance and compact semiconductor devices. Smaller and more complex structures can be fabricated by using shorter wavelength light in the photolithography. One of the most critical issues in development of the next generation photo-lithography is to increase energy conversion efficiency (CE) from laser to shorter wavelength light. Experimental database of beyond extreme ultraviolet (BEUV) radiation was obtained by using spherically symmetrical high-Z plasmas generated with spherically allocated laser beams. Absolute energy and spectra of BEUV light emitted from Tb, Gd, and Mo plasmas were measured with a absolutely calibrated BEUV calorimeter and a transmission grating spectrometer. 1.0 x 1012 W/cm2 is the optimal laser intensity to produced efficient BEUV light source plasmas with Tb and Gd targets. Maximum CE is achieved at 0.8% that is two times higher than the published CEs obtained with planar targets.
Solutions for the conductivity of multi-coated spheres and spherically symmetric inclusion problems
Pham, Duc Chinh
2018-02-01
Variational results on the macroscopic conductivity (thermal, electrical, etc.) of the multi-coated sphere assemblage have been used to derive the explicit expression of the respective field (thermal, electrical, etc.) within the spheres in d dimensions (d=2,3). A differential substitution approach has been developed to construct various explicit expressions or determining equations for the effective spherically symmetric inclusion problems, which include those with radially variable conductivity, different radially variable transverse and normal conductivities, and those involving imperfect interfaces, in d dimensions. When the volume proportion of the outermost spherical shell increases toward 1, one obtains the respective exact results for the most important specific cases: the dilute solutions for the compound inhomogeneities suspended in a major matrix phase. Those dilute solution results are also needed for other effective medium approximation schemes.
On spherically symmetric motions of a viscous compressible barotropic and selfgravitating gas
Czech Academy of Sciences Publication Activity Database
Ducomet, B.; Nečasová, Šárka; Vasseur, A.
2011-01-01
Roč. 13, č. 2 (2011), s. 191-211 ISSN 1422-6928 R&D Projects: GA ČR GA201/08/0012; GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : spherically symmetric motion * selfgravitating gas * non monotone pressure law * density-dependent viscosities Subject RIV: BA - General Mathematics Impact factor: 0.768, year: 2011 http://link.springer.com/article/10.1007%2Fs00021-009-0010-5
Energy Technology Data Exchange (ETDEWEB)
Kafka, P; Meszaros, P [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (Germany, F.R.)
1976-11-01
Stationary spherically symmetric solutions of the equations for accretion of large mass flows onto a black hole, including the interaction of matter and radiation due to Thomson scattering in diffusion approximation are constructed. The relevance of these solutions is discussed with respect to the question of whether the limitation of the luminosity (Eddington limit) also implies an upper bound to the possible rate of mass flow. The question remains open until all instabilities have been studied. At the moment a negative answer is favoured.
de Hoop, Maarten V.; Ilmavirta, Joonas
2017-12-01
We study ray transforms on spherically symmetric manifolds with a piecewise C1, 1 metric. Assuming the Herglotz condition, the x-ray transform is injective on the space of L 2 functions on such manifolds. We also prove injectivity results for broken ray transforms (with and without periodicity) on such manifolds with a C1, 1 metric. To make these problems tractable in low regularity, we introduce and study a class of generalized Abel transforms and study their properties. This low regularity setting is relevant for geophysical applications.
Axi-symmetric patterns of active polar filaments on spherical and composite surfaces
Srivastava, Pragya; Rao, Madan
2014-03-01
Experiments performed on Fission Yeast cells of cylindrical and spherical shapes, rod-shaped bacteria and reconstituted cylindrical liposomes suggest the influence of cell geometry on patterning of cortical actin. A theoretical model based on active hydrodynamic description of cortical actin that includes curvature-orientation coupling predicts spontaneous formation of acto-myosin rings, cables and nodes on cylindrical and spherical geometries [P. Srivastava et al, PRL 110, 168104(2013)]. Stability and dynamics of these patterns is also affected by the cellular shape and has been observed in experiments performed on Fission Yeast cells of spherical shape. Motivated by this, we study the stability and dynamics of axi-symmetric patterns of active polar filaments on the surfaces of spherical, saddle shaped and conical geometry and classify the stable steady state patterns on these surfaces. Based on the analysis of the fluorescence images of Myosin-II during ring slippage we propose a simple mechanical model for ring-sliding based on force balance and make quantitative comparison with the experiments performed on Fission Yeast cells. NSF Grant DMR-1004789 and Syracuse Soft Matter Program.
International Nuclear Information System (INIS)
Clarisse, J.M.
2007-01-01
A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)
Fake signals caused by heavy-mass motions near a sensitive spherical gravitational wave antenna
International Nuclear Information System (INIS)
Lobo, Alberto; Cerdonio, Massimo; Montero, Alvaro
2002-01-01
In this paper we analyse in quantitative detail the effect of a moving mass on a spherical gravitational wave detector. This applies to situations where heavy traffic or similar disturbances occur near the GW antenna. Such disturbances result in quadrupole tidal stresses in the antenna mass, and they therefore precisely fake a real gravitational signal. The study shows that there are always characteristic frequencies, depending on the motion of the external masses, at which the fake signals are most intense. It however appears that, even at those frequencies, fake signals should be orders of magnitude below the sensitivity curve of an optimized detector, in likely realistic situations
International Nuclear Information System (INIS)
Burikham, Piyabut; Cheamsawat, Krai; Harko, Tiberiu; Lake, Matthew J.
2016-01-01
We obtain bounds for the minimum and maximum mass/radius ratio of a stable, charged, spherically symmetric compact object in a D-dimensional space-time in the framework of general relativity, and in the presence of dark energy. The total energy, including the gravitational component, and the stability of objects with minimum mass/radius ratio is also investigated. The minimum energy condition leads to a representation of the mass and radius of the charged objects with minimum mass/radius ratio in terms of the charge and vacuum energy only. As applied to the electron in the four-dimensional case, this procedure allows one to re-obtain the classical electron radius from purely general relativistic considerations. By combining the lower mass bound, in four space-time dimensions, with minimum length uncertainty relations (MLUR) motivated by quantum gravity, we obtain an alternative bound for the maximum charge/mass ratio of a stable, gravitating, charged quantum mechanical object, expressed in terms of fundamental constants. Evaluating this limit numerically, we obtain again the correct order of magnitude value for the charge/mass ratio of the electron, as required by the stability conditions. This suggests that, if the electron were either less massive (with the same charge) or if its charge were any higher (for fixed mass), a combination of electrostatic and dark energy repulsion would destabilize the Compton radius. In other words, the electron would blow itself apart. Our results suggest the existence of a deep connection between gravity, the presence of the cosmological constant, and the stability of fundamental particles. (orig.)
Do cosmic rays perturb the operation of a large resonant spherical detector of gravitational waves?
International Nuclear Information System (INIS)
Pizzella, G.
1999-01-01
The sensitivity of resonant gravitational wave detectors is reviewed. The effect of cosmic rays on a large spherical detector is considered. It is shown that the sensibility to short bursts, to monochromatic and to stochastic GW is not significantly degraded by cosmic rays. For a two-detector experiment, only one detector needs to be installed in an underground laboratory. This supports the idea to install a resonant detector at sea-level near a GW interferometer
Do cosmic rays perturb the operation of a large resonant spherical detector of gravitational waves?
Energy Technology Data Exchange (ETDEWEB)
Pizzella, G. [Rome Univ. Tor Vergata, Rome (Italy). Physics Dept.; Inst. for Nuclear Physics, Frascati, RM (Italy)
1999-07-01
The sensitivity of resonant gravitational wave detectors is reviewed. The effect of cosmic rays on a large spherical detector is considered. It is shown that the sensibility to short bursts, to monochromatic and to stochastic GW is not significantly degraded by cosmic rays. For a two-detector experiment, only one detector needs to be installed in an underground laboratory. This supports the idea to install a resonant detector at sea-level near a GW interferometer.
The effect of the equatorially symmetric zonal winds of Saturn on its gravitational field
Kong, Dali; Zhang, Keke; Schubert, Gerald; Anderson, John D.
2018-04-01
The penetration depth of Saturn’s cloud-level winds into its interior is unknown. A possible way of estimating the depth is through measurement of the effect of the winds on the planet’s gravitational field. We use a self-consistent perturbation approach to study how the equatorially symmetric zonal winds of Saturn contribute to its gravitational field. An important advantage of this approach is that the variation of its gravitational field solely caused by the winds can be isolated and identified because the leading-order problem accounts exactly for rotational distortion, thereby determining the irregular shape and internal structure of the hydrostatic Saturn. We assume that (i) the zonal winds are maintained by thermal convection in the form of non-axisymmetric columnar rolls and (ii) the internal structure of the winds, because of the Taylor-Proundman theorem, can be uniquely determined by the observed cloud-level winds. We calculate both the variation ΔJn , n = 2, 4, 6 … of the axisymmetric gravitational coefficients Jn caused by the zonal winds and the non-axisymmetric gravitational coefficients ΔJnm produced by the columnar rolls, where m is the azimuthal wavenumber of the rolls. We consider three different cases characterized by the penetration depth 0.36, R S, 0.2, R S and 0.1, R S, where R S is the equatorial radius of Saturn at the 1-bar pressure level. We find that the high-degree gravitational coefficient (J 12 + ΔJ 12) is dominated, in all the three cases, by the effect of the zonal flow with |ΔJ 12/J 12| > 100% and that the size of the non-axisymmetric coefficients ΔJ mn directly reflects the depth and scale of the flow taking place in the Saturnian interior.
Self-gravitating axially symmetric disks in general-relativistic rotation
Karkowski, Janusz; Kulczycki, Wojciech; Mach, Patryk; Malec, Edward; Odrzywołek, Andrzej; Piróg, Michał
2018-05-01
We integrate numerically axially symmetric stationary Einstein equations describing self-gravitating disks around spinless black holes. The numerical scheme is based on a method developed by Shibata, but contains important new ingredients. We derive a new general-relativistic Keplerian rotation law for self-gravitating disks around spinning black holes. Former results concerning rotation around spinless black holes emerge in the limit of a vanishing spin parameter. These rotation curves might be used for the description of rotating stars, after appropriate modification around the symmetry axis. They can be applied to the description of compact torus-black hole configurations, including active galactic nuclei or products of coalescences of two neutron stars.
Cylindrically symmetric solutions of a scalar--tensor theory of gravitation
International Nuclear Information System (INIS)
Singh, T.
1975-01-01
The cylindrically symmetric solutions for the Einstein--Rosen metric of a scalar--tensor theory proposed by Dunn have been obtained. A method has been given by which one can obtain, under certain conditions, solutions of this scalar--tensor theory from known solutions of the empty space field equations of Einstein's theory of gravitation. It is also found that one of the solutions of the scalar--tensor theory is nonsingular in the sense of Bonnor. Further some special solutions are obtained which reduce to the well-known solution of Levi-Civita and a time dependent solution obtained by Misra and Radhakrishna
Odd-parity pertubations of spherically symmetric star clusters in general relativity
International Nuclear Information System (INIS)
Semenzato, R.; Ipser, J.R.
1981-01-01
The theory of odd-parity nonspherical peturbations of collisionless, isotropic, spherically symmetric star clusters is developed within general relativity for l> or =2. A variational principle is derived for the associated normal modes of oscillation. The variational expression reveals that an unstable normal mode has a pure exponentially growing time dependence--the corresponding complex ''eigenfrequency'' is purely imaginary--and hence that a normal mode can become unstable in a smooth fashion only thorugh zero frequency. Further, it is shown that no instabilities can set in through zero-frequency modes along smooth sequences of models with fewer high-energy stars than low-energy stars. Unless unstable normal modes suddenly appear in a nonsmooth fashion, the implications is that these models possess no unstable normal modes
Spherically symmetric cosmological spacetimes with dust and radiation — numerical implementation
International Nuclear Information System (INIS)
Lim, Woei Chet; Regis, Marco; Clarkson, Chris
2013-01-01
We present new numerical cosmological solutions of the Einstein Field Equations. The spacetime is spherically symmetric with a source of dust and radiation approximated as a perfect fluid. The dust and radiation are necessarily non-comoving due to the inhomogeneity of the spacetime. Such a model can be used to investigate non-linear general relativistic effects present during decoupling or big-bang nucleosynthesis, as well as for investigating void models of dark energy with isocurvature degrees of freedom. We describe the full evolution of the spacetime as well as the redshift and luminosity distance for a central observer. After demonstrating accuracy of the code, we consider a few example models, and demonstrate the sensitivity of the late time model to the degree of inhomogeneity of the initial radiation contrast
Spherically symmetric cosmological spacetimes with dust and radiation — numerical implementation
Lim, Woei Chet; Regis, Marco; Clarkson, Chris
2013-10-01
We present new numerical cosmological solutions of the Einstein Field Equations. The spacetime is spherically symmetric with a source of dust and radiation approximated as a perfect fluid. The dust and radiation are necessarily non-comoving due to the inhomogeneity of the spacetime. Such a model can be used to investigate non-linear general relativistic effects present during decoupling or big-bang nucleosynthesis, as well as for investigating void models of dark energy with isocurvature degrees of freedom. We describe the full evolution of the spacetime as well as the redshift and luminosity distance for a central observer. After demonstrating accuracy of the code, we consider a few example models, and demonstrate the sensitivity of the late time model to the degree of inhomogeneity of the initial radiation contrast.
Calculation of the fast ion tail distribution for a spherically symmetric hot spot
McDevitt, C. J.; Tang, X.-Z.; Guo, Z.; Berk, H. L.
2014-10-01
The fast ion tail for a spherically symmetric hot spot is computed via the solution of a simplified Fokker-Planck collision operator. Emphasis is placed on describing the energy scaling of the fast ion distribution function in the hot spot as well as the surrounding cold plasma throughout a broad range of collisionalities and temperatures. It is found that while the fast ion tail inside the hot spot is significantly depleted, leading to a reduction of the fusion yield in this region, a surplus of fast ions is observed in the neighboring cold plasma region. The presence of this surplus of fast ions in the neighboring cold region is shown to result in a partial recovery of the fusion yield lost in the hot spot.
Calculation of the fast ion tail distribution for a spherically symmetric hot spot
Energy Technology Data Exchange (ETDEWEB)
McDevitt, C. J.; Tang, X.-Z.; Guo, Z. [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Berk, H. L. [Department of Physics, University of Texas, Austin, Texas 78712 (United States)
2014-10-15
The fast ion tail for a spherically symmetric hot spot is computed via the solution of a simplified Fokker-Planck collision operator. Emphasis is placed on describing the energy scaling of the fast ion distribution function in the hot spot as well as the surrounding cold plasma throughout a broad range of collisionalities and temperatures. It is found that while the fast ion tail inside the hot spot is significantly depleted, leading to a reduction of the fusion yield in this region, a surplus of fast ions is observed in the neighboring cold plasma region. The presence of this surplus of fast ions in the neighboring cold region is shown to result in a partial recovery of the fusion yield lost in the hot spot.
Higher spins tunneling from a time dependent and spherically symmetric black hole
International Nuclear Information System (INIS)
Siahaan, Haryanto M.
2016-01-01
The discussions of Hawking radiation via tunneling method have been performed extensively in the case of scalar particles. Moreover, there are also several works in discussing the tunneling method for Hawking radiation by using higher spins, e.g. neutrino, photon, and gravitino, in the background of static black holes. Interestingly, it is found that the Hawking temperature for static black holes using the higher spins particles has no difference compared to the one computed using scalars. In this paper, we study the Hawking radiation for a spherically symmetric and time dependent black holes using the tunneling of Dirac particles, photon, and gravitino. We find that the obtained Hawking temperature is similar to the one derived in the tunneling method by using scalars. (orig.)
Higher spins tunneling from a time dependent and spherically symmetric black hole
Energy Technology Data Exchange (ETDEWEB)
Siahaan, Haryanto M. [Parahyangan Catholic University, Physics Department, Bandung (Indonesia)
2016-03-15
The discussions of Hawking radiation via tunneling method have been performed extensively in the case of scalar particles. Moreover, there are also several works in discussing the tunneling method for Hawking radiation by using higher spins, e.g. neutrino, photon, and gravitino, in the background of static black holes. Interestingly, it is found that the Hawking temperature for static black holes using the higher spins particles has no difference compared to the one computed using scalars. In this paper, we study the Hawking radiation for a spherically symmetric and time dependent black holes using the tunneling of Dirac particles, photon, and gravitino. We find that the obtained Hawking temperature is similar to the one derived in the tunneling method by using scalars. (orig.)
Compact invariant sets of the static spherically symmetric Einstein-Yang-Mills equations
International Nuclear Information System (INIS)
Starkov, Konstantin E.
2010-01-01
In this Letter we obtain results concerning compact invariant sets of the static spherically symmetric Einstein-Yang-Mills (EYM) equations with help of studies of its localization. Let a be a cosmological constant and s be another parameter entering into these equations which is used for considering the physical time as a temporal variable, with s=1, while s=-1 is used for considering the physical time as a spatial variable. We show that in case s=1; a 0 the set of all compact invariant sets consists of two equilibrium points only. Further, we state that in cases s=-1; a 0 there are only two equilibrium points and there are no periodic orbits. In addition, we prove that in the last two cases there are neither homoclinic orbits nor heteroclinic orbits as well.
A new model for spherically symmetric charged compact stars of embedding class 1
Energy Technology Data Exchange (ETDEWEB)
Maurya, S.K. [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Gupta, Y.K. [Raj Kumar Goel Institute of Technology, Department of Mathematics, Ghaziabad, U.P. (India); Ray, Saibal [Government College of Engineering and Ceramic Technology, Department of Physics, Kolkata, West Bengal (India); Deb, Debabrata [Indian Institute of Engineering Science and Technology, Department of Physics, Howrah, West Bengal (India)
2017-01-15
In the present study we search for a new stellar model with spherically symmetric matter and a charged distribution in a general relativistic framework. The model represents a compact star of embedding class 1. The solutions obtained here are general in nature, having the following two features: first of all, the metric becomes flat and also the expressions for the pressure, energy density, and electric charge become zero in all the cases if we consider the constant A = 0, which shows that our solutions represent the so-called 'electromagnetic mass model' [17], and, secondly, the metric function ν(r), for the limit n tending to infinity, converts to ν(r) = Cr{sup 2}+ ln B, which is the same as considered by Maurya et al. [11]. We have investigated several physical aspects of the model and find that all the features are acceptable within the requirements of contemporary theoretical studies and observational evidence. (orig.)
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
Mimoso, José Pedro; Mena, Filipe C
2010-01-01
We investigate spherically symmetric perfect fluid spacetimes and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We perform a 3+1 splitting and obtain gauge invariant conditions relating the intrinsic spatial curvature of the shells to the ADM mass and to a function of the pressure which we introduce and that generalises the Tolman-Oppenheimer-Volkoff equilibrium condition. We analyse the particular cases of the Lema\\^itre-Tolman-Bondi dust models with a cosmological constant as an example of a $\\Lambda$-CDM model and its generalization to contain a central perfect fluid core. These models provide simple, but physically interesting illustrations of our results.
Santa Vélez, Camilo; Enea Romano, Antonio
2018-05-01
Static coordinates can be convenient to solve the vacuum Einstein's equations in presence of spherical symmetry, but for cosmological applications comoving coordinates are more suitable to describe an expanding Universe, especially in the framework of cosmological perturbation theory (CPT). Using CPT we develop a method to transform static spherically symmetric (SSS) modifications of the de Sitter solution from static coordinates to the Newton gauge. We test the method with the Schwarzschild de Sitter (SDS) metric and then derive general expressions for the Bardeen's potentials for a class of SSS metrics obtained by adding to the de Sitter metric a term linear in the mass and proportional to a general function of the radius. Using the gauge invariance of the Bardeen's potentials we then obtain a gauge invariant definition of the turn around radius. We apply the method to an SSS solution of the Brans-Dicke theory, confirming the results obtained independently by solving the perturbation equations in the Newton gauge. The Bardeen's potentials are then derived for new SSS metrics involving logarithmic, power law and exponential modifications of the de Sitter metric. We also apply the method to SSS metrics which give flat rotation curves, computing the radial energy density profile in comoving coordinates in presence of a cosmological constant.
Directory of Open Access Journals (Sweden)
Matsui Toshinori
2018-01-01
Full Text Available Among various scenarios of baryon asymmetry of the Universe, electroweak baryogenesis is directly connected with physics of the Higgs sector. We discuss spectra of gravitational waves which are originated by the strongly first order phase transition at the electroweak symmetry breaking, which is required for a successful scenario of electroweak baryogenesis. In the Z3 symmetric singlet scalar model, the significant gravitational waves are caused by the multi-step phase transition. We show that the model can be tested by measuring the characteristic spectra of the gravitational waves at future interferometers such as LISA and DECIGO.
Axially symmetric stationary black-hole states of the Einstein gravitational theory
International Nuclear Information System (INIS)
Meinhardt, R.
1976-01-01
Some aspects of the thepry of black-hole states of the Einstein gravitational theory are reviewed in this paper. First explicit vacuum solutions of Einstein's field equations are searched for when the space-time admits 2 isometries (axially symmetric and stationary), which could be considered as candidates for black holes. Then the Liapounov stability of these solutions is studied. A generalization of the Ernst potential is introduced for solutions of Einstein's vacuum field equations with axial symmetry only, and this allows to construct a dynamical system. Using the theory of ''multiple integrals in the calculus of variations'' it is possible to show that the weakest casuality condition (chronology) is a necessary condition for the Liapounov stability. Finally, it is shown that the Kerr solution is Liapounov stable under a given topology
Axially symmetric stationary black-hole states of the Einstein gravitational theory
Energy Technology Data Exchange (ETDEWEB)
Meinhardt, R [Chile Univ., Santiago. Departamento de Fisica
1976-01-01
Some aspects of the theory of black-hole states of the Einstein gravitational theory are reviewed in this paper. First explicit vacuum solutions of Einstein's field equations are searched for when the space-time admits 2 isometries (axially symmetric and stationary), which could be considered as candidates for black holes. Then the Liapounov stability of these solutions is studied. A generalization of the Ernst potential is introduced for solutions of Einstein's vacuum field equations with axial symmetry only, and this allows to construct a dynamical system. Using the theory of ''multiple integrals in the calculus of variations'' it is possible to show that the weakest casuality condition (chronology) is a necessary condition for the Liapounov stability. Finally, it is shown that the Kerr solution is Liapounov stable under a given topology.
Wang, Rongjiang; Heimann, Sebastian; Zhang, Yong; Wang, Hansheng; Dahm, Torsten
2017-09-01
A hybrid method is proposed to calculate complete synthetic seismograms based on a spherically symmetric and self-gravitating Earth with a multilayered structure of atmosphere, ocean, mantle, liquid core and solid core. For large wavelengths, a numerical scheme is used to solve the geodynamic boundary-value problem without any approximation on the deformation and gravity coupling. With decreasing wavelength, the gravity effect on the deformation becomes negligible and the analytical propagator scheme can be used. Many useful approaches are used to overcome the numerical problems that may arise in both analytical and numerical schemes. Some of these approaches have been established in the seismological community and the others are developed for the first time. Based on the stable and efficient hybrid algorithm, an all-in-one code QSSP is implemented to cover the complete spectrum of seismological interests. The performance of the code is demonstrated by various tests including the curvature effect on teleseismic body and surface waves, the appearance of multiple reflected, teleseismic core phases, the gravity effect on long period surface waves and free oscillations, the simulation of near-field displacement seismograms with the static offset, the coupling of tsunami and infrasound waves, and free oscillations of the solid Earth, the atmosphere and the ocean. QSSP is open source software that can be used as a stand-alone FORTRAN code or may be applied in combination with a Python toolbox to calculate and handle Green's function databases for efficient coding of source inversion problems.
Chen, Gui-Qiang G.; Schrecker, Matthew R. I.
2018-04-01
We are concerned with globally defined entropy solutions to the Euler equations for compressible fluid flows in transonic nozzles with general cross-sectional areas. Such nozzles include the de Laval nozzles and other more general nozzles whose cross-sectional area functions are allowed at the nozzle ends to be either zero (closed ends) or infinity (unbounded ends). To achieve this, in this paper, we develop a vanishing viscosity method to construct globally defined approximate solutions and then establish essential uniform estimates in weighted L p norms for the whole range of physical adiabatic exponents γ\\in (1, ∞) , so that the viscosity approximate solutions satisfy the general L p compensated compactness framework. The viscosity method is designed to incorporate artificial viscosity terms with the natural Dirichlet boundary conditions to ensure the uniform estimates. Then such estimates lead to both the convergence of the approximate solutions and the existence theory of globally defined finite-energy entropy solutions to the Euler equations for transonic flows that may have different end-states in the class of nozzles with general cross-sectional areas for all γ\\in (1, ∞) . The approach and techniques developed here apply to other problems with similar difficulties. In particular, we successfully apply them to construct globally defined spherically symmetric entropy solutions to the Euler equations for all γ\\in (1, ∞).
Asymptotic properties of spherically symmetric, regular and static solutions to Yang-Mills equations
International Nuclear Information System (INIS)
Cronstrom, C.
1987-01-01
In this paper the author discusses the asymptotic properties of solutions to Yang-Mills equations with the gauge group SU(2), for spherically symmetric, regular and static potentials. It is known, that the pure Yang-Mills equations cannot have nontrivial regular solutions which vanish rapidly at space infinity (socalled finite energy solutions). So, if regular solutions exist, they must have non-trivial asymptotic properties. However, if the asymptotic behaviour of the solutions is non-trivial, then the fact must be explicitly taken into account in constructing the proper action (and energy) for the theory. The elucidation of the appropriate surface correction to the Yang-Mills action (and hence the energy-momentum tensor density) is one of the main motivations behind the present study. In this paper the author restricts to the asymptotic behaviour of the static solutions. It is shown that this asymptotic behaviour is such that surface corrections (at space-infinity) are needed in order to obtain a well-defined (classical) theory. This is of relevance in formulating a quantum Yang-Mills theory
Cyclic and heteroclinic flows near general static spherically symmetric black holes
Energy Technology Data Exchange (ETDEWEB)
Ahmed, Ayyesha K.; Jamil, Mubasher [National University of Sciences and Technology(NUST), Department of Mathematics, School of Natural Sciences (SNS), Islamabad (Pakistan); Azreg-Ainou, Mustapha [Baskent University, Engineering Faculty, Ankara (Turkey); Faizal, Mir [University of Lethbridge, Department of Physics and Astronomy, Alberta (Canada); University of Waterloo, Department of Physics and Astronomy, Waterloo, ON (Canada)
2016-05-15
We investigate the Michel-type accretion onto a static spherically symmetric black hole. Using a Hamiltonian dynamical approach, we show that the standard method employed for tackling the accretion problem has masked some properties of the fluid flow. We determine new analytical solutions that are neither transonic nor supersonic as the fluid approaches the horizon(s); rather, they remain subsonic for all values of the radial coordinate. Moreover, the three-velocity vanishes and the pressure diverges on the horizon(s), resulting in a flow-out of the fluid under the effect of its own pressure. This is in favor of the earlier prediction that pressure-dominant regions form near the horizon. This result does not depend on the form of the metric and it applies to a neighborhood of any horizon where the time coordinate is timelike. For anti-de Sitter-like f(R) black holes we discuss the stability of the critical flow and determine separatrix heteroclinic orbits. For de Sitter-like f(R) black holes, we construct polytropic cyclic, non-homoclinic, physical flows connecting the two horizons. These flows become non-relativistic for Hamiltonian values higher than the critical value, allowing for a good estimate of the proper period of the flow. (orig.)
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.
Compact invariant sets of the static spherically symmetric Einstein-Yang-Mills equations
Energy Technology Data Exchange (ETDEWEB)
Starkov, Konstantin E., E-mail: konst@citedi.m [CITEDI-IPN, Av. del Parque 1310, Mesa de Otay, Tijuana, BC (Mexico)
2010-04-05
In this Letter we obtain results concerning compact invariant sets of the static spherically symmetric Einstein-Yang-Mills (EYM) equations with help of studies of its localization. Let a be a cosmological constant and s be another parameter entering into these equations which is used for considering the physical time as a temporal variable, with s=1, while s=-1 is used for considering the physical time as a spatial variable. We show that in case s=1; a<0 the location of any compact invariant set is described by some system of linear inequalities. Then we prove that in case s=1; a>0 the set of all compact invariant sets consists of two equilibrium points only. Further, we state that in cases s=-1; a<0 and s=-1; a>0 there are only two equilibrium points and there are no periodic orbits. In addition, we prove that in the last two cases there are neither homoclinic orbits nor heteroclinic orbits as well.
Single molecule diffusion and the solution of the spherically symmetric residence time equation.
Agmon, Noam
2011-06-16
The residence time of a single dye molecule diffusing within a laser spot is propotional to the total number of photons emitted by it. With this application in mind, we solve the spherically symmetric "residence time equation" (RTE) to obtain the solution for the Laplace transform of the mean residence time (MRT) within a d-dimensional ball, as a function of the initial location of the particle and the observation time. The solutions for initial conditions of potential experimental interest, starting in the center, on the surface or uniformly within the ball, are explicitly presented. Special cases for dimensions 1, 2, and 3 are obtained, which can be Laplace inverted analytically for d = 1 and 3. In addition, the analytic short- and long-time asymptotic behaviors of the MRT are derived and compared with the exact solutions for d = 1, 2, and 3. As a demonstration of the simplification afforded by the RTE, the Appendix obtains the residence time distribution by solving the Feynman-Kac equation, from which the MRT is obtained by differentiation. Single-molecule diffusion experiments could be devised to test the results for the MRT presented in this work. © 2011 American Chemical Society
Undergoing spherically symmetric steady-state accretion stability of white dwarfs
Energy Technology Data Exchange (ETDEWEB)
Sienkiewicz, R [Polska Akademia Nauk, Warsaw. N. Copernicus Astronomical Center
1980-01-01
Thermal and vibrational stabilities of accreting white dwarfs with steady-state nuclear burning were considered, assuming spherically symmetric accretion of the hydrogen-rich matter and using linear stability analysis. Almost all models with masses 0.2 M(sun) - 1.39 M(sun) were found to be unstable in some way. The type of instability expected to dominate is given as a function of the accretion rate. For most accretion rates it is the thermal instability. Oscillation periods are given for the models in which the vibrational instability is the most violent one. These periods are of the order of seconds or minutes. We expect that our stability analysis may suggest the cause of the variabilities of the hot components of some symbiotic stars, for a wide range of the accretion rates. In this case our models may serve as the initial conditions for evolutionary computations. The results predict that short-period oscillations should be observed in some hot nuclei of planetary nebulae.
Existence and stability of circular orbits in general static and spherically symmetric spacetimes
Jia, Junji; Liu, Jiawei; Liu, Xionghui; Mo, Zhongyou; Pang, Xiankai; Wang, Yaoguang; Yang, Nan
2018-02-01
The existence and stability of circular orbits (CO) in static and spherically symmetric (SSS) spacetime are important because of their practical and potential usefulness. In this paper, using the fixed point method, we first prove a necessary and sufficient condition on the metric function for the existence of timelike COs in SSS spacetimes. After analyzing the asymptotic behavior of the metric, we then show that asymptotic flat SSS spacetime that corresponds to a negative Newtonian potential at large r will always allow the existence of CO. The stability of the CO in a general SSS spacetime is then studied using the Lyapunov exponent method. Two sufficient conditions on the (in)stability of the COs are obtained. For null geodesics, a sufficient condition on the metric function for the (in)stability of null CO is also obtained. We then illustrate one powerful application of these results by showing that three SSS spacetimes whose metric function is not completely known will allow the existence of timelike and/or null COs. We also used our results to assert the existence and (in)stabilities of a number of known SSS metrics.
Numerical investigations of gravitational collapse
Energy Technology Data Exchange (ETDEWEB)
Csizmadia, Peter; Racz, Istvan, E-mail: iracz@rmki.kfki.h [RMKI, Budapest, Konkoly Thege Miklos ut 29-33, H-1121 (Hungary)
2010-03-01
Some properties of a new framework for simulating generic 4-dimensional spherically symmetric gravitating systems are discussed. The framework can be used to investigate spacetimes that undergo complete gravitational collapse. The analytic setup is chosen to ensure that our numerical method is capable to follow the time evolution everywhere, including the black hole region.
International Nuclear Information System (INIS)
Baxter, Mathew; Van Gorder, Robert A
2013-01-01
We obtain solutions to a transformation of the axially symmetric Ernst equation, which governs a class of exact solutions of Einstein's field equations. Physically, the equation serves as a model of axially symmetric stationary vacuum gravitational fields. By an application of the method of homotopy analysis, we are able to construct approximate analytic solutions to the relevant boundary value problem in the case where exact solutions are not possible. The results presented constitute a solution for a complicated nonlinear and singular initial value problem. Through appropriate selection of the auxiliary linear operator and convergence control parameter, we are able to obtain low order approximations which minimize residual error over the problem domain. The benefit to such approach is that we obtain very accurate approximations after computing very few terms, hence the computational efficiency is high. Finally, an exact solution is provided in a special case, and this corresponds to the analytical solutions obtained in the more general case. The approximate solutions agree qualitatively with the exact solutions. (paper)
Evaluation of gravitational curvatures of a tesseroid in spherical integral kernels
Deng, Xiao-Le; Shen, Wen-Bin
2018-04-01
Proper understanding of how the Earth's mass distributions and redistributions influence the Earth's gravity field-related functionals is crucial for numerous applications in geodesy, geophysics and related geosciences. Calculations of the gravitational curvatures (GC) have been proposed in geodesy in recent years. In view of future satellite missions, the sixth-order developments of the gradients are becoming requisite. In this paper, a set of 3D integral GC formulas of a tesseroid mass body have been provided by spherical integral kernels in the spatial domain. Based on the Taylor series expansion approach, the numerical expressions of the 3D GC formulas are provided up to sixth order. Moreover, numerical experiments demonstrate the correctness of the 3D Taylor series approach for the GC formulas with order as high as sixth order. Analogous to other gravitational effects (e.g., gravitational potential, gravity vector, gravity gradient tensor), numerically it is found that there exist the very-near-area problem and polar singularity problem in the GC east-east-radial, north-north-radial and radial-radial-radial components in spatial domain, and compared to the other gravitational effects, the relative approximation errors of the GC components are larger due to not only the influence of the geocentric distance but also the influence of the latitude. This study shows that the magnitude of each term for the nonzero GC functionals by a grid resolution 15^' } } × 15^' }} at GOCE satellite height can reach of about 10^{-16} m^{-1} s2 for zero order, 10^{-24 } or 10^{-23} m^{-1} s2 for second order, 10^{-29} m^{-1} s2 for fourth order and 10^{-35} or 10^{-34} m^{-1} s2 for sixth order, respectively.
Vector-tensor interaction of gravitation
Energy Technology Data Exchange (ETDEWEB)
Zhang Yuan-zhong; Guo han-ying
1982-11-01
In the paper, by using the equation of motion a particle, we show that the antigravity exist in the vector-tensor model of gravitation. Thus the motion of a particle deviates from the geodesic equation. In Newtonian approximation and weak gravitational field, acceleration of a particle in a spherically symmetric and astatic gravitation field is zero. The result is obviously not in agreement with gravitational phenomena.
Energy Technology Data Exchange (ETDEWEB)
Araújo, M.E. [Departamento de Física-Matemática, Instituto de Física, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, 21.945-970, Rio de Janeiro, R.J. (Brazil); Stoeger, W.R., E-mail: mearaujo@me.com, E-mail: wstoeger@as.arizona.edu [Vatican Observatory Research Group, Steward Observatory, University of Arizona, 933 N. Cherry Ave., Tucson, AZ 85721 (United States)
2011-07-01
One of the continuing challenges in cosmology has been to determine the large-scale space-time metric from observations with a minimum of assumptions — without, for instance, assuming that the universe is almost Friedmann-Lemaître-Robertson-Walker (FLRW). If we are lucky enough this would be a way of demonstrating that our universe is FLRW, instead of presupposing it or simply showing that the observations are consistent with FLRW. Showing how to do this within the more general spherically symmetric, inhomogeneous space-time framework takes us a long way towards fulfilling this goal. In recent work researchers have shown how this can be done both in the traditional Lemaître-Tolman-Bondi (LTB) 3 + 1 coordinate framework, and in the observational coordinate (OC) framework, in which the radial coordinate y is null (light-like) and measured down the past light cone of the observer. In this paper we investigate the stability of solutions, and the use of data in the OC field equations including their time evolution — i.e. our procedure is not restricted to our past light cone — and compare both approaches with respect to the singularity problem at the maximum of the angular-diameter distance, the stability of solutions, and the use of data in the field equations. We also compare the two approaches with regard to determining the cosmological constant Λ. This allows a more detailed account and assessment of the OC integration procedure, and enables a comparison of the relative advantages of the two equivalent solution frameworks. Both formulations and integration procedures should, in principle, lead to the same results. However, as we show in this paper, the OC procedure manifests certain advantages, particularly in the avoidance of coordinate singularities at the maximum of the angular-diameter distance, and in the stability of the solutions obtained. This particular feature is what allows us to do the best fitting of the data to smooth data functions and the
Wang, Tongjiang; Davila, Joseph M.
2014-01-01
Determining the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (spherically symmetric inversion, SSI) was developed in the 1950s and has been widely applied to interpret various observations. However, to date there is no study of the uncertainty estimation of this method. We here present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 solar radius as a model, which is reconstructed by a tomography method from STEREO/COR1 observations during the solar minimum in February 2008 (Carrington Rotation, CR 2066).We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally smaller than about a factor of two; the former has the lower peak but extends more in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50 deg. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt), as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with the reconstruction by tomography for a period of low solar activity (CR 2066). We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort.
On the Stability of Spherically Symmetric Self-Gravitating Classical and Quantum Systems
DEFF Research Database (Denmark)
Makedonski, Mathias
on to the description of the corresponding systems in the setting of general relativity, it is shown, that the Tolman-Oppenheimer-Volko equation can be obtained from a suitable variation of the total energy. We prove a previously unnoticed energetic instability of the model. Staying in the general relativistic setting....... As for the perfect fluid, we prove energetic instability and conclude our investigations by constructing a naive quantum version of the free massive scalar eld, that also suers energetic instability. ´...
The Thermal Response of a Pulsar Glitch : The Non-spherical Symmetric Case
Cheng, K. S.; Li, Y.; Suen, W. -M.
1999-01-01
We study the thermal evolution of a pulsar after a glitch in which the energy is released from a relative compact region. A set of relativistic thermal transport and energy balance equations is used to study the thermal evolution, without making the assumption of spherical symmetry. We use an exact cooling model to solve this set of differential equtions. Our results differ significantly from those obtained under the assumption of spherical symmetry. Even for young pulsars with a hot core lik...
International Nuclear Information System (INIS)
Linet, Bernard; Teyssandier, Pierre
2013-01-01
A new iterative method for calculating the travel time of a photon as a function of the spatial positions of the emitter and the receiver in the field of a static, spherically symmetric body is presented. The components of the metric are assumed to be expressible in power series in m/r, with m being half the Schwarzschild radius of the central body and r a radial coordinate. The procedure exclusively works for a light ray which may be described as a perturbation in powers of G of a Minkowskian null geodesic, with G being the Newtonian gravitational constant. It is shown that the expansion of the travel time of a photon along such a ray only involves elementary integrals whatever the order of approximation. An expansion of the impact parameter in power series of G is also obtained. The method is applied to explicitly calculate the perturbation expansions of the light travel time and the impact parameter up to the third order. The full expression yielding the terms of order G 3 is new. This expression confirms the existence of a third-order enhanced term when the emitter and the receiver are in conjunction relative to the central body. This term is shown to be necessary for determining the post-Newtonian parameter γ at a level of accuracy of 10 −8 with light rays grazing the Sun. (paper)
International Nuclear Information System (INIS)
Alexandre, Jean; Pasipoularides, Pavlos
2011-01-01
In this note we examine whether spherically symmetric solutions in covariant Horava-Lifshitz gravity can reproduce Newton's Law in the IR limit λ→1. We adopt the position that the auxiliary field A is independent of the space-time metric [J. Alexandre and P. Pasipoularides, Phys. Rev. D 83, 084030 (2011).][J. Greenwald, V. H. Satheeshkumar, and A. Wang, J. Cosmol. Astropart. Phys. 12 (2010) 007.], and we assume, as in [A. M. da Silva, Classical Quantum Gravity 28, 055011 (2011).], that λ is a running coupling constant. We show that under these assumptions, spherically symmetric solutions fail to restore the standard Newtonian physics in the IR limit λ→1, unless λ does not run, and has the fixed value λ=1. Finally, we comment on the Horava and Melby-Thompson approach [P. Horava and C. M. Melby-Thompson, Phys. Rev. D 82, 064027 (2010).] in which A is assumed as a part of the space-time metric in the IR.
Kong, Dali; Zhang, Keke; Schubert, Gerald; Anderson, John
2017-10-01
The structure/amplitude of the Jovian equatorially symmetric gravitational field is affected by both rotational distortion and the fast equatorially symmetric zonal flow. We construct a fully self-consistent, four-layer, non-spheroidal (i.e, the shape is irregular) model of Jupiter that comprises an inner core, a metallic region, an outer molecular envelope and a thin transition layer between the metallic and molecular regions. While the core is assumed to have a uniform density, three different equations of state are adopted for the metallic, molecular and transition regions. We solve the governing equations via a perturbation approach. The leading-order problem accounts for the full effect of rotational distortion, and determines the density, size and shape of the core, the location and thickness of the transition layer, and the shape of the 1-bar pressure level; it also produces the mass, the equatorial and polar radii of Jupiter, and the even zonal gravitational coefficients caused by the rotational distortion. The next-order problem determines the corrections caused by the zonal flow which is assumed to be confined within the molecular envelope and on cylinders parallel to the rotation axis. Our model provides the total even gravitational coefficients that can be compared with those acquired by the Juno spacecraft.
International Nuclear Information System (INIS)
Araujo, M. E.; Stoeger, W. R.
2009-01-01
A rigorous demonstration that given appropriate data on our past light cone leads to the determination of the metric functions and all their time derivatives on our past light cone is presented, thus showing how to evolve the solution we obtain from data on the light cone off it in a well-defined and straightforward way. It also automatically gives a procedure for constructing the solution for all spherically symmetric, inhomogeneous cosmological Lemaitre-Tolman-Bondi models in observational coordinates as a Taylor series in time of however many terms we need. Our procedure takes into account the essential data giving the maximum of the observer area (angular-diameter) distance, and the redshift z max at which that occurs. This enables the determination of the vacuum-energy density μ Λ , which would otherwise remain undetermined.
Haisch, B. M.
1976-01-01
A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.
Solutions of the linearized Bach-Einstein equation in the static spherically symmetric case
International Nuclear Information System (INIS)
Schmidt, H.J.
1985-01-01
The Bach-Einstein equation linearized around Minkowski space-time is completely solved. The set of solutions depends on three parameters; a two-parameter subset of it becomes asymptotically flat. In that region the gravitational potential is of the type phi = -m/r + epsilon exp (-r/l). Because of the different asymptotic behaviour of both terms, it became necessary to linearize also around the Schwarzschild solution phi = -m/r. The linearized equation resulting in this case is discussed using qualitative methods. The result is that for m = 2l phi = -m/r + epsilon r -2 exp (-r/l) u, where u is some bounded function; m is arbitrary and epsilon again small. Further, the relation between the solution of the linearized and the full equation is discussed. (author)
Propagation of a shock wave in a radiating spherically symmetric distribution of matter
International Nuclear Information System (INIS)
Herrera, L.; Nunez, L.; Universidad de Los Andes, Merida, Venezuela)
1987-01-01
A method used to study the evolution of radiating spheres reported by Herrera et al. (1980) is extended to the case in which the sphere is divided in two regions by a shock wave front. The equations of state at both sides of the shock are different, and the solutions are matched on it via the Rankine-Hugoniot conditions. The outer-region metric is matched with a Vaidya solution on the boundary surface of the sphere. As an example of the procedure, two known solutions for radiating systems are considered. The matter distribution is free of singularities everywhere within the sphere and a Gaussian-like pulse is assumed to carry out a fraction of the total mass. Exploding models are then obtained. Finally, the results are discussed in the light of recent work on gravitational collapse and supernovae. 29 references
Directory of Open Access Journals (Sweden)
Chifu E. N.
2009-07-01
Full Text Available Here, we present a profound and complete analytical solution to Einstein’s gravitational field equations exterior to astrophysically real or hypothetical time varying distribu- tions of mass or pressure within regions of spherical geometry. The single arbitrary function f in our proposed exterior metric tensor and constructed field equations makes our method unique, mathematically less combersome and astrophysically satisfactory. The obtained solution of Einstein’s gravitational field equations tends out to be a gen- eralization of Newton’s gravitational scalar potential exterior to the spherical mass or pressure distribution under consideration
International Nuclear Information System (INIS)
Hosokawa, Takashi; Omukai, Kazuyuki
2009-01-01
The final mass of a newborn star is set at the epoch when the mass accretion onto the star is terminated. We study the evolution of accreting protostars and the limits of accretion in low-metallicity environments under spherical symmetry. Accretion rates onto protostars are estimated via the temperature evolution of prestellar cores with different metallicities. The derived rates increase with decreasing metallicity, from M-dot≅10 -6 M odot yr -1 at Z = Z sun to 10 -3 M sun yr -1 at Z = 0. With the derived accretion rates, the protostellar evolution is numerically calculated. We find that, at lower metallicity, the protostar has a larger radius and reaches the zero-age main sequence (ZAMS) at higher stellar mass. Using this protostellar evolution, we evaluate the upper stellar mass limit where the mass accretion is hindered by radiative feedback. We consider the effects of radiation pressure exerted on the accreting envelope, and expansion of an H II region. The mass accretion is finally terminated by radiation pressure on dust grains in the envelope for Z ∼> 10 -3 Z sun and by the expanding H II region for lower metallicity. The mass limit from these effects increases with decreasing metallicity from M * ≅ 10 M sun at Z = Z sun to ≅300 M sun at Z = 10 -6 Z sun . The termination of accretion occurs after the central star arrives at the ZAMS at all metallicities, which allows us to neglect protostellar evolution effects in discussing the upper mass limit by stellar feedback. The fragmentation induced by line cooling in low-metallicity clouds yields prestellar cores with masses large enough that the final stellar mass is set by the feedback effects. Although relaxing the assumption of spherical symmetry will alter feedback effects, our results will be a benchmark for more realistic evolution to be explored in future studies.
Gravitational settling of a highly concentrated system of solid spherical particles
Arkhipov, V. A.; Usanina, A. S.
2017-09-01
In the present paper, we report on the results of an experimental study of the process of gravity sedimentation of a cloud of monodispersed solid spherical particles with initial volume concentration C > 0.03, which was performed in a wide range of Reynolds numbers. An analytical estimate of the settling regimes of spherical particle clouds is presented. A new method for creating a spherical particle cloud with a high concentration of particles is proposed. A qualitative picture of the settling process of a highly concentrated particle cloud under gravity is revealed. A criterial dependence for the drag coefficient of a sedimenting spherical particle cloud as an entity is obtained.
Addendum. Relation for the Light Absorption in the Presence of Gravitation Field
R.Vlokh; M.Kostyrko
2005-01-01
We argue for the validity of relation for electromagnetic wave electric field derived by us earlier. It includes an imaginary part responsible for the absorption induced by gravitation field of spherically symmetric mass.
On the application of a particular form of the gravitational potential
Directory of Open Access Journals (Sweden)
Ninković Slobodan D.
2003-01-01
Full Text Available A formula, already existing in the literature, describing the gravitational potential of a spherically symmetric stellar system is analyzed. Some interesting cases of comparison with empirical formulae are presented. A good agreement is found.
International Nuclear Information System (INIS)
Fiedler, B.; Schimming, R.
1983-01-01
The fourth order field equations proposed by TREDER with a linear combination of BACH's tensor and EINSTEIN's tensor on the left-hand side admit static centrally symmetric solutions which are analytical and non-flat in some neighborhood of the centre of symmetry. (author)
Sound wave generation by a spherically symmetric outburst and AGN feedback in galaxy clusters
Tang, Xiaping; Churazov, Eugene
2017-07-01
We consider the evolution of an outburst in a uniform medium under spherical symmetry, having in mind active galactic nucleus feedback in the intracluster medium. For a given density and pressure of the medium, the spatial structure and energy partition at a given time tage (since the onset of the outburst) are fully determined by the total injected energy Einj and the duration tb of the outburst. We are particularly interested in the late phase evolution when the strong shock transforms into a sound wave. We studied the energy partition during such transition with different combinations of Einj and tb. For an instantaneous outburst with tb → 0, which corresponds to the extension of classic Sedov-Taylor solution with counter-pressure, the fraction of energy that can be carried away by sound waves is ≲12 per cent of Einj. As tb increases, the solution approaches the 'slow piston' limit, with the fraction of energy in sound waves approaching zero. We then repeat the simulations using radial density and temperature profiles measured in Perseus and M87/Virgo clusters. We find that the results with a uniform medium broadly reproduce an outburst in more realistic conditions once proper scaling is applied. We also develop techniques to map intrinsic properties of an outburst (Einj, tb and tage) to the observables like the Mach number of the shock and radii of the shock and ejecta. For the Perseus cluster and M87, the estimated (Einj, tb and tage) agree with numerical simulations tailored for these objects with 20-30 per cent accuracy.
The gravitational potential of axially symmetric bodies from a regularized green kernel
Trova, A.; Huré, J.-M.; Hersant, F.
2011-12-01
The determination of the gravitational potential inside celestial bodies (rotating stars, discs, planets, asteroids) is a common challenge in numerical Astrophysics. Under axial symmetry, the potential is classically found from a two-dimensional integral over the body's meridional cross-section. Because it involves an improper integral, high accuracy is generally difficult to reach. We have discovered that, for homogeneous bodies, the singular Green kernel can be converted into a regular kernel by direct analytical integration. This new kernel, easily managed with standard techniques, opens interesting horizons, not only for numerical calculus but also to generate approximations, in particular for geometrically thin discs and rings.
International Nuclear Information System (INIS)
Chang Yiren; Hsu Long; Chi Sien
2006-01-01
Since their invention in 1986, optical tweezers have become a popular manipulation and force measurement tool in cellular and molecular biology. However, until recently there has not been a sophisticated model for optical tweezers on trapping cells in the ray-optics regime. We present a model for optical tweezers to calculate the optical force upon a spherically symmetric multilayer sphere representing a common biological cell. A numerical simulation of this model shows that not only is the magnitude of the optical force upon a Chinese hamster ovary cell significantly three times smaller than that upon a polystyrene bead of the same size, but the distribution of the optical force upon a cell is also much different from that upon a uniform particle, and there is a 30% difference in the optical trapping stiffness of these two cases. Furthermore, under a small variant condition for the refractive indices of any adjacent layers of the sphere, this model provides a simple approximation to calculate the optical force and the stiffness of an optical tweezers system
Tang, Xiaping; Churazov, Eugene
2018-04-01
We analyze the impact of thermal conduction on the appearance of a shock-heated gas shell which is produced when a spherically symmetric outburst of a supermassive black hole inflates bubbles of relativistic plasma at the center of a galaxy cluster. The presence of the hot and low-density shell can be used as an ancillary indicator for a high rate of energy release during the outburst, which is required to drive strong shocks into the gas. Here we show that conduction can effectively erase such shell, unless the diffusion of electrons is heavily suppressed. We conclude that a more robust proxy to the energy release rate is the ratio between the shock radius and bubble radius. We also revisited the issue of sound waves dissipation induced by thermal conduction in a scenario, where characteristic wavelength of the sound wave is set by the total energy of the outburst. For a fiducial short outburst model, the dissipation length does not exceed the cooling radius in a typical cluster, provided that the conduction is suppressed by a factor not larger than ˜100. For quasi-continuous energy injection neither the shock-heated shell nor the outgoing sound wave are important and the role of conduction is subdominant.
Anisotropic solutions by gravitational decoupling
Ovalle, J.; Casadio, R.; da Rocha, R.; Sotomayor, A.
2018-02-01
We investigate the extension of isotropic interior solutions for static self-gravitating systems to include the effects of anisotropic spherically symmetric gravitational sources by means of the gravitational decoupling realised via the minimal geometric deformation approach. In particular, the matching conditions at the surface of the star with the outer Schwarzschild space-time are studied in great detail, and we describe how to generate, from a single physically acceptable isotropic solution, new families of anisotropic solutions whose physical acceptability is also inherited from their isotropic parent.
Anisotropic solutions by gravitational decoupling
Energy Technology Data Exchange (ETDEWEB)
Ovalle, J. [Silesian University in Opava, Institute of Physics and Research Centre of Theoretical Physics and Astrophysics, Faculty of Philosophy and Science, Opava (Czech Republic); Universidad Simon Bolivar, Departamento de Fisica, Caracas (Venezuela, Bolivarian Republic of); Casadio, R. [Alma Mater Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); Istituto Nazionale di Fisica Nucleare, Bologna (Italy); Rocha, R. da [Universidade Federal do ABC (UFABC), Centro de Matematica, Computacao e Cognicao, Santo Andre, SP (Brazil); Sotomayor, A. [Universidad de Antofagasta, Departamento de Matematicas, Antofagasta (Chile)
2018-02-15
We investigate the extension of isotropic interior solutions for static self-gravitating systems to include the effects of anisotropic spherically symmetric gravitational sources by means of the gravitational decoupling realised via the minimal geometric deformation approach. In particular, the matching conditions at the surface of the star with the outer Schwarzschild space-time are studied in great detail, and we describe how to generate, from a single physically acceptable isotropic solution, new families of anisotropic solutions whose physical acceptability is also inherited from their isotropic parent. (orig.)
Iterative Spherical Downward Continuation Applied to Magnetic and Gravitational Data from Satellite
Czech Academy of Sciences Publication Activity Database
Sebera, J.; Šprlák, M.; Novák, P.; Bezděk, Aleš; Valko, M.
2014-01-01
Roč. 35, č. 4 (2014), s. 941-958 ISSN 0169-3298 R&D Projects: GA MŠk LH13071 Grant - others:ESA(XE) AO/1-6367/10/NL/AF Institutional support: RVO:67985815 Keywords : downward continuation * Earth's gravitational and magnetic field * poisson integral equation Subject RIV: DE - Earth Magnetism, Geodesy, Geography Impact factor: 3.447, year: 2014
Zhao, G.; Liu, J.; Chen, B.; Guo, R.; Chen, L.
2017-12-01
Forward modeling of gravitational fields at large-scale requires to consider the curvature of the Earth and to evaluate the Newton's volume integral in spherical coordinates. To acquire fast and accurate gravitational effects for subsurface structures, subsurface mass distribution is usually discretized into small spherical prisms (called tesseroids). The gravity fields of tesseroids are generally calculated numerically. One of the commonly used numerical methods is the 3D Gauss-Legendre quadrature (GLQ). However, the traditional GLQ integration suffers from low computational efficiency and relatively poor accuracy when the observation surface is close to the source region. We developed a fast and high accuracy 3D GLQ integration based on the equivalence of kernel matrix, adaptive discretization and parallelization using OpenMP. The equivalence of kernel matrix strategy increases efficiency and reduces memory consumption by calculating and storing the same matrix elements in each kernel matrix just one time. In this method, the adaptive discretization strategy is used to improve the accuracy. The numerical investigations show that the executing time of the proposed method is reduced by two orders of magnitude compared with the traditional method that without these optimized strategies. High accuracy results can also be guaranteed no matter how close the computation points to the source region. In addition, the algorithm dramatically reduces the memory requirement by N times compared with the traditional method, where N is the number of discretization of the source region in the longitudinal direction. It makes the large-scale gravity forward modeling and inversion with a fine discretization possible.
A new open-source code for spherically symmetric stellar collapse to neutron stars and black holes
International Nuclear Information System (INIS)
O'Connor, Evan; Ott, Christian D
2010-01-01
We present the new open-source spherically symmetric general-relativistic (GR) hydrodynamics code GR1D. It is based on the Eulerian formulation of GR hydrodynamics (GRHD) put forth by Romero-Ibanez-Gourgoulhon and employs radial-gauge, polar-slicing coordinates in which the 3+1 equations simplify substantially. We discretize the GRHD equations with a finite-volume scheme, employing piecewise-parabolic reconstruction and an approximate Riemann solver. GR1D is intended for the simulation of stellar collapse to neutron stars and black holes and will also serve as a testbed for modeling technology to be incorporated in multi-D GR codes. Its GRHD part is coupled to various finite-temperature microphysical equations of state in tabulated form that we make available with GR1D. An approximate deleptonization scheme for the collapse phase and a neutrino-leakage/heating scheme for the postbounce epoch are included and described. We also derive the equations for effective rotation in 1D and implement them in GR1D. We present an array of standard test calculations and also show how simple analytic equations of state in combination with presupernova models from stellar evolutionary calculations can be used to study qualitative aspects of black hole formation in failing rotating core-collapse supernovae. In addition, we present a simulation with microphysical equations of state and neutrino leakage/heating of a failing core-collapse supernova and black hole formation in a presupernova model of a 40 M o-dot zero-age main-sequence star. We find good agreement on the time of black hole formation (within 20%) and last stable protoneutron star mass (within 10%) with predictions from simulations with full Boltzmann neutrino radiation hydrodynamics.
A new open-source code for spherically symmetric stellar collapse to neutron stars and black holes
Energy Technology Data Exchange (ETDEWEB)
O' Connor, Evan; Ott, Christian D, E-mail: evanoc@tapir.caltech.ed, E-mail: cott@tapir.caltech.ed [TAPIR, Mail Code 350-17, California Institute of Technology, Pasadena, CA 91125 (United States)
2010-06-07
We present the new open-source spherically symmetric general-relativistic (GR) hydrodynamics code GR1D. It is based on the Eulerian formulation of GR hydrodynamics (GRHD) put forth by Romero-Ibanez-Gourgoulhon and employs radial-gauge, polar-slicing coordinates in which the 3+1 equations simplify substantially. We discretize the GRHD equations with a finite-volume scheme, employing piecewise-parabolic reconstruction and an approximate Riemann solver. GR1D is intended for the simulation of stellar collapse to neutron stars and black holes and will also serve as a testbed for modeling technology to be incorporated in multi-D GR codes. Its GRHD part is coupled to various finite-temperature microphysical equations of state in tabulated form that we make available with GR1D. An approximate deleptonization scheme for the collapse phase and a neutrino-leakage/heating scheme for the postbounce epoch are included and described. We also derive the equations for effective rotation in 1D and implement them in GR1D. We present an array of standard test calculations and also show how simple analytic equations of state in combination with presupernova models from stellar evolutionary calculations can be used to study qualitative aspects of black hole formation in failing rotating core-collapse supernovae. In addition, we present a simulation with microphysical equations of state and neutrino leakage/heating of a failing core-collapse supernova and black hole formation in a presupernova model of a 40 M{sub o-dot} zero-age main-sequence star. We find good agreement on the time of black hole formation (within 20%) and last stable protoneutron star mass (within 10%) with predictions from simulations with full Boltzmann neutrino radiation hydrodynamics.
International Nuclear Information System (INIS)
Zielinska, M.; Zawislawski, Z.; Strugalska-Gola, E.; Strugalski, Z.
1991-01-01
It is shown how it is possible to transform known data on radial distribution of the matter layer thickness to unknown radial distribution of the matter density inside spherically symmetric objects. Appropriate formulas and testing of them are presented. An application of the method for the radial distribution of the matter density inside a target nucleus is discussed as an example. 2 refs.; 2 figs
Self-similar spherical gravitational collapse and the cosmic censorship hypothesis
Energy Technology Data Exchange (ETDEWEB)
Ori, A.; Piran, T.
1988-01-01
The authors show that a self-similar general relativistic spherical collapse of a perfect fluid with an adiabatic equation of state p = (lambda -1)rho and low enough lambda values, results in a naked singularity. The singularity is tangent to an event horizon which surrounds a massive singularity and the redshift along a null geodesic from the singularity to an external observer is infinite. The authors believe that this is the most serious counter example to cosmic censorship obtained so far.
Nath, G.; Vishwakarma, J. P.
2016-11-01
Similarity solutions are obtained for the flow behind a spherical shock wave in a non-ideal gas under gravitational field with conductive and radiative heat fluxes, in the presence of a spatially decreasing azimuthal magnetic field. The shock wave is driven by a piston moving with time according to power law. The radiation is considered to be of the diffusion type for an optically thick grey gas model and the heat conduction is expressed in terms of Fourier's law for heat conduction. Similarity solutions exist only when the surrounding medium is of constant density. The gas is assumed to have infinite electrical conductivity and to obey a simplified van der Waals equation of state. It is shown that an increase of the gravitational parameter or the Alfven-Mach number or the parameter of the non-idealness of the gas decreases the compressibility of the gas in the flow-field behind the shock, and hence there is a decrease in the shock strength. The pressure and density vanish at the inner surface (piston) and hence a vacuum is formed at the center of symmetry. The shock waves in conducting non-ideal gas under gravitational field with conductive and radiative heat fluxes can be important for description of shocks in supernova explosions, in the study of a flare produced shock in the solar wind, central part of star burst galaxies, nuclear explosion etc. The solutions obtained can be used to interpret measurements carried out by space craft in the solar wind and in neighborhood of the Earth's magnetosphere.
Gravitational theory with the local quadratic Lagrangian
International Nuclear Information System (INIS)
Tentyukov, M.N.
1992-01-01
It is suggested that the vacuum gravitational equations should be derived from the local Lagrangian containing only first-order derivatives. As an example we demonstrate the properties of the derived equations by studying of the exact spherically-symmetric solutions. 23 refs
Gravitational effects in field gravitation theory
International Nuclear Information System (INIS)
Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.; Vlasov, A.A.
1979-01-01
The possibilities to describe various gravitation effects of field gravitation theory (FGT) are considered. Past-Newtonian approximation of the FGT has been constructed and on the basis of this approximation it has been shown that the field theory allows one to describe the whole set of experimental facts. The comparison of post-Newtonian parameters in FGT with those in the Einstein's theory makes it clear that these two; theories are undistinguishable from the viewpoint of any experiments, realized with post-Newtonian accuracy. Gravitational field of an island type source with spherically symmetrical distribution of matter and unstationary homogeneous model of Universe, which allows to describe the effect of cosmological red shift, are considered
Misner, Charles W; Wheeler, John Archibald
2017-01-01
First published in 1973, Gravitation is a landmark graduate-level textbook that presents Einstein’s general theory of relativity and offers a rigorous, full-year course on the physics of gravitation. Upon publication, Science called it “a pedagogic masterpiece,” and it has since become a classic, considered essential reading for every serious student and researcher in the field of relativity. This authoritative text has shaped the research of generations of physicists and astronomers, and the book continues to influence the way experts think about the subject. With an emphasis on geometric interpretation, this masterful and comprehensive book introduces the theory of relativity; describes physical applications, from stars to black holes and gravitational waves; and portrays the field’s frontiers. The book also offers a unique, alternating, two-track pathway through the subject. Material focusing on basic physical ideas is designated as Track 1 and formulates an appropriate one-semester graduate-level...
Cylindrical collapse and gravitational waves
Energy Technology Data Exchange (ETDEWEB)
Herrera, L [Escuela de FIsica, Faculdad de Ciencias, Universidad Central de Venezuela, Caracas, Venezuela (Venezuela); Santos, N O [Universite Pierre et Marie Curie, CNRS/FRE 2460 LERMA/ERGA, Tour 22-12, 4eme etage, BoIte 142, 4 place Jussieu, 75252 Paris Cedex 05 (France); Laboratorio Nacional de Computacao Cientifica, 25651-070 Petropolis RJ (Brazil); Centro Brasileiro de Pesquisas Fisicas, 22290-180 Rio de Janeiro RJ (Brazil)
2005-06-21
We study the matching conditions for a collapsing anisotropic cylindrical perfect fluid, and we show that its radial pressure is non-zero on the surface of the cylinder and proportional to the time-dependent part of the field produced by the collapsing fluid. This result resembles the one that arises for the radiation-though non-gravitational-in the spherically symmetric collapsing dissipative fluid, in the diffusion approximation.
International Nuclear Information System (INIS)
Higuchi, A.
1987-01-01
The symmetric tensor spherical harmonics (STSH's) on the N-sphere (S/sup N/), which are defined as the totally symmetric, traceless, and divergence-free tensor eigenfunctions of the Laplace--Beltrami (LB) operator on S/sup N/, are studied. Specifically, their construction is shown recursively starting from the lower-dimensional ones. The symmetric traceless tensors induced by STSH's are introduced. These play a crucial role in the recursive construction of STSH's. The normalization factors for STSH's are determined by using their transformation properties under SO(N+1). Then the symmetric, traceless, and divergence-free tensor eigenfunctions of the LB operator in the N-dimensional de Sitter space-time which are obtained by the analytic continuation of the STSH's on S/sup N/ are studied. Specifically, the allowed eigenvalues of the LB operator under the restriction of unitarity are determined. Our analysis gives a group-theoretical explanation of the forbidden mass range observed earlier for the spin-2 field theory in de Sitter space-time
International Nuclear Information System (INIS)
Mihalas, D.; Kunasz, P.B.; Hummer, D.G.
1976-01-01
A numerical method is presented of solving the radiative transfer equation in the comoving frame of a spherically symmetric expanding atmosphere in which both the line and the electron-scattering source function can depend on frequency (i.e., when there is partial frequency redistribution in the scattering process). This method is used to assess the adequacy of various assumptions regarding frequency redistribution in the comoving frame and to discuss the effects of electron scattering more accurately than previously possible. The methods developed here can be used in realistic model atmospheres to account for the (major) effects of electron scattering upon emergent flux profiles
International Nuclear Information System (INIS)
Fennelly, A.J.
1978-01-01
Investigations of several problems of gravitation are discussed. The question of the existence of black holes is considered. While black holes like those in Einstein's theory may not exist in other gravity theories, trapped surfaces implying such black holes certainly do. The theories include those of Brans-Dicke, Lightman-Lee, Rosen, and Yang. A similar two-tensor theory of Yilmaz is investigated and found inconsistent and nonviable. The Newman-Penrose formalism for Riemannian geometries is adapted to general gravity theories and used to implement a search for twisting solutions of the gravity theories for empty and nonempty spaces. The method can be used to find the gravitational fields for all viable gravity theories. The rotating solutions are of particular importance for strong field interpretation of the Stanford/Marshall gyroscope experiment. Inhomogeneous cosmologies are examined in Einstein's theory as generalizations of homogeneous ones by raising the dimension of the invariance groups by one more parameter. The nine Bianchi classifications are extended to Rosen's theory of gravity for homogeneous cosmological models
Variational formulation of two scalar-tetradic theories of gravitation
International Nuclear Information System (INIS)
Saez, D.
1983-01-01
In this paper we obtain two scalar-tetradic theories of gravitation (theories A and B) from a variational principle. In these theories the gravitational energy is localized and the principle of equivalence holds. They combine some aspects of Moller theory and the Brans-Dicke theory. The first-order approximations and an introduction to the study of both theories in the static spherically symmetric case are presented
Energy Technology Data Exchange (ETDEWEB)
El Ghazi, Haddou, E-mail: hadghazi@gmail.com [LPS, Faculty of Science, Dhar EL Mehrez, BP 1796 Fes-Atlas (Morocco); Special Mathematics, CPGE, 267 Quartier complémentaire Ennahda 1, Rabat (Morocco); Jorio, Anouar [LPS, Faculty of Science, Dhar EL Mehrez, BP 1796 Fes-Atlas (Morocco)
2014-01-01
Within the framework of effective-mass approximation and finite parabolic potential barrier, single particle and ground-state interband recombination energies in Core|well|shell based on GaN|(In,Ga)N|GaN spherical QDQW are investigated as a function of the inner and the outer radii. The temperature dependency of effective-mass, band-gap energy and potential barrier is taken into account. Particle eigenvalue and band-gap energy competing effects are speculated to explain our numerical results which show that the interband recombination energy increases when the temperature increases. The results we obtained are in quite good agreement with the findings.
International Nuclear Information System (INIS)
El Ghazi, Haddou; Jorio, Anouar
2014-01-01
Within the framework of effective-mass approximation and finite parabolic potential barrier, single particle and ground-state interband recombination energies in Core|well|shell based on GaN|(In,Ga)N|GaN spherical QDQW are investigated as a function of the inner and the outer radii. The temperature dependency of effective-mass, band-gap energy and potential barrier is taken into account. Particle eigenvalue and band-gap energy competing effects are speculated to explain our numerical results which show that the interband recombination energy increases when the temperature increases. The results we obtained are in quite good agreement with the findings
Schneider, M; Hirleman, E D
1994-04-20
A model based on geometric optics for predicting the response of interferometric (phase Doppler) instruments for size measurements of particles with radially symmetric but inhomogeneous internal refractive index profiles is developed. The model and results are important for applications in which heat or mass transfer from the particles or droplets is significant, for example, in liquid-fuel combustion. To quantify the magnitude of potential bias errors introduced by the classical assumption of uniform internal properties on phase Doppler measurements, we compute calibration curves for a sequence of times during the evaporation of a decane droplet immersed in an environment of T = 2000 K and p = 10 bars. The results reveal considerable effects on the relation between phase difference and droplet diameter caused by the refractive index gradients present. The model provides an important tool to assess sizing uncertainties that can be expected when applying conventional (based on uniform properties) phase Doppler calibration curves in spray combustion and similar processes.
International Nuclear Information System (INIS)
Mihalas, D.; Kunasz, P.B.; Hummer, D.G.
1976-01-01
We investigate the importance of the advection and aberration terms, which are of order V/c, in the comoving-frame transfer equation in spherical geometry. Characteristic trajectories are found which reduce the spatial derivatives to a perfect differential, and a generalization of the numerical procedure developed in the earlier papers of this series that permits the integration of the transfer equation on these characteristics is presented. For cases in which V/cvery-much-less-than1, a perturbation solution is developed which reduces the problem to that solved in the first paper in this series. For velocities of the form V (r) approx.r/subn/(n=0,1,2), it is shown that the magnitude of the effects arising from the advection and aberration terms is about 5V/c relative to the solution with these terms omitted. In stellar winds V/capproximately-less-than0.01; hence we conclude that aberration and advection terms may safely be ignored, and that consideration of the Doppler-shift term alone is adequate in the computation of spectra from such expanding atmospheres
International Nuclear Information System (INIS)
Blanchet, Luc; Faye, Guillaume; Iyer, Bala R; Sinha, Siddhartha
2008-01-01
The gravitational waveform (GWF) generated by inspiralling compact binaries moving in quasi-circular orbits is computed at the third post-Newtonian (3PN) approximation to general relativity. Our motivation is two-fold: (i) to provide accurate templates for the data analysis of gravitational wave inspiral signals in laser interferometric detectors; (ii) to provide the associated spin-weighted spherical harmonic decomposition to facilitate comparison and match of the high post-Newtonian prediction for the inspiral waveform to the numerically-generated waveforms for the merger and ringdown. This extension of the GWF by half a PN order (with respect to previous work at 2.5PN order) is based on the algorithm of the multipolar post-Minkowskian formalism, and mandates the computation of the relations between the radiative, canonical and source multipole moments for general sources at 3PN order. We also obtain the 3PN extension of the source multipole moments in the case of compact binaries, and compute the contributions of hereditary terms (tails, tails-of-tails and memory integrals) up to 3PN order. The end results are given for both the complete plus and cross polarizations and the separate spin-weighted spherical harmonic modes
International Nuclear Information System (INIS)
Shabbir, Ghulam; Khan, Suhail
2010-01-01
In this paper we classify cylindrically symmetric static space-times according to their teleparallel homothetic vector fields using direct integration technique. It turns out that the dimensions of the teleparallel homothetic vector fields are 4, 5, 7 or 11, which are the same in numbers as in general relativity. In case of 4, 5 or 7 proper teleparallel homothetic vector fields exist for the special choice to the space-times. In the case of 11 teleparallel homothetic vector fields the space-time becomes Minkowski with all the zero torsion components. Teleparallel homothetic vector fields in this case are exactly the same as in general relativity. It is important to note that this classification also covers the plane symmetric static space-times. (general)
Ortiz, Néstor; Sarbach, Olivier
2018-01-01
We analyze the stability of the Cauchy horizon associated with a globally naked, shell-focussing singularity arising from the complete gravitational collapse of a spherical dust cloud. In a previous work, we have studied the dynamics of spherical test scalar fields on such a background. In particular, we proved that such fields cannot develop any divergences which propagate along the Cauchy horizon. In the present work, we extend our analysis to the more general case of test fields without symmetries and to linearized gravitational perturbations with odd parity. To this purpose, we first consider test fields possessing a divergence-free stress-energy tensor satisfying the dominant energy condition, and we prove that a suitable energy norm is uniformly bounded in the domain of dependence of the initial slice. In particular, this result implies that free-falling observers co-moving with the dust particles measure a finite energy of the field, even as they cross the Cauchy horizon at points lying arbitrarily close to the central singularity. Next, for the case of Klein–Gordon fields, we derive point-wise bounds from our energy estimates which imply that the scalar field cannot diverge at the Cauchy horizon, except possibly at the central singular point. Finally, we analyze the behaviour of odd-parity, linear gravitational and dust perturbations of the collapsing spacetime. Similarly to the scalar field case, we prove that the relevant gauge-invariant combinations of the metric perturbations stay bounded away from the central singularity, implying that no divergences can propagate in the vacuum region. Our results are in accordance with previous numerical studies and analytic work in the self-similar case.
Topological geons with self-gravitating phantom scalar field
Kratovitch, P. V.; Potashov, I. M.; Tchemarina, Ju V.; Tsirulev, A. N.
2017-12-01
A topological geon is the quotient manifold M/Z 2 where M is a static spherically symmetric wormhole having the reflection symmetry with respect to its throat. We distinguish such asymptotically at solutions of the Einstein equations according to the form of the time-time metric function by using the quadrature formulas of the so-called inverse problem for self-gravitating spherically symmetric scalar fields. We distinguish three types of geon spacetimes and illustrate them by simple examples. We also study possible observational effects associated with bounded geodesic motion near topological geons.
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'.
Hirt, Christian; Kuhn, Michael
2017-08-01
Theoretically, spherical harmonic (SH) series expansions of the external gravitational potential are guaranteed to converge outside the Brillouin sphere enclosing all field-generating masses. Inside that sphere, the series may be convergent or may be divergent. The series convergence behavior is a highly unstable quantity that is little studied for high-resolution mass distributions. Here we shed light on the behavior of SH series expansions of the gravitational potential of the Moon. We present a set of systematic numerical experiments where the gravity field generated by the topographic masses is forward-modeled in spherical harmonics and with numerical integration techniques at various heights and different levels of resolution, increasing from harmonic degree 90 to 2160 ( 61 to 2.5 km scales). The numerical integration is free from any divergence issues and therefore suitable to reliably assess convergence versus divergence of the SH series. Our experiments provide unprecedented detailed insights into the divergence issue. We show that the SH gravity field of degree-180 topography is convergent anywhere in free space. When the resolution of the topographic mass model is increased to degree 360, divergence starts to affect very high degree gravity signals over regions deep inside the Brillouin sphere. For degree 2160 topography/gravity models, severe divergence (with several 1000 mGal amplitudes) prohibits accurate gravity modeling over most of the topography. As a key result, we formulate a new hypothesis to predict divergence: if the potential degree variances show a minimum, then the SH series expansions diverge somewhere inside the Brillouin sphere and modeling of the internal potential becomes relevant.
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
A study of the neutrino-gravitation interaction
International Nuclear Information System (INIS)
Soares, I.D.
1976-01-01
A study of the neutrino-gravitation interaction is made in the framework of Einstein-Dirac coupled equations. Two classes of solutions are obtained, corresponding to two specific physical situations. One cosmological model with expansion is obtained, having neutrinos as the only curvature source; their properties and the parameters which can to characterize the solution as a cosmological model are studied. The second class of solutions corresponds to a naive complete model of a spherically symmetric star emitting neutrinos: the inner region is suposed to be built up of a spherically symmetric distribution of a perfect fluid, bounded in space and which emitts neutrinos; the star matter is considered transparent for neutrinos; the outer region contains only neutrinos and gravitational field. The problem of neutrino compatibility with spherically symmetric gravitational fields is examined. The local conservation laws and the function conditions of the inner and outer solutions in the fluid surface are studied and permit to characterize two kinds of solutions. In one case, the solution describes the neutrino emission phase, with consequent configuration contraction, immediately before the fluid to be completely contained in the interior of the schwarzchild radius, when the neutrino emission and the star contraction stop. The other possibility can correspond to a quasi-stationary configuration, with neutrino emission, where the relativistic equation of radiative equilibrium permits to define the equivalent of 'Radiation pressure' for neutrinos, which acts in the same sense of the gravitational pressure. (L.C.) [pt
Spherically symmetric scalar field collapse
Indian Academy of Sciences (India)
2013-03-01
Mar 1, 2013 ... The very recent interest in scalar field collapse stems from a cosmological ... The objective of the present investigation is to explore the collapsing modes of a simple ..... The authors thank the BRNS (DAE) for financial support.
Olafsson, Gestur; Helgason, Sigurdur
1996-01-01
This book is intended to introduce researchers and graduate students to the concepts of causal symmetric spaces. To date, results of recent studies considered standard by specialists have not been widely published. This book seeks to bring this information to students and researchers in geometry and analysis on causal symmetric spaces.Includes the newest results in harmonic analysis including Spherical functions on ordered symmetric space and the holmorphic discrete series and Hardy spaces on compactly casual symmetric spacesDeals with the infinitesimal situation, coverings of symmetric spaces, classification of causal symmetric pairs and invariant cone fieldsPresents basic geometric properties of semi-simple symmetric spacesIncludes appendices on Lie algebras and Lie groups, Bounded symmetric domains (Cayley transforms), Antiholomorphic Involutions on Bounded Domains and Para-Hermitian Symmetric Spaces
On geometrized gravitation theories
International Nuclear Information System (INIS)
Logunov, A.A.; Folomeshkin, V.N.
1977-01-01
General properties of the geometrized gravitation theories have been considered. Geometrization of the theory is realized only to the extent that by necessity follows from an experiment (geometrization of the density of the matter Lagrangian only). Aor a general case the gravitation field equations and the equations of motion for matter are formulated in the different Riemann spaces. A covariant formulation of the energy-momentum conservation laws is given in an arbitrary geometrized theory. The noncovariant notion of ''pseudotensor'' is not required in formulating the conservation laws. It is shown that in the general case (i.e., when there is an explicit dependence of the matter Lagrangian density on the covariant derivatives) a symmetric energy-momentum tensor of the matter is explicitly dependent on the curvature tensor. There are enlisted different geometrized theories that describe a known set of the experimental facts. The properties of one of the versions of the quasilinear geometrized theory that describes the experimental facts are considered. In such a theory the fundamental static spherically symmetrical solution has a singularity only in the coordinate origin. The theory permits to create a satisfactory model of the homogeneous nonstationary Universe
A new geometrical gravitational theory
International Nuclear Information System (INIS)
Obata, T.; Chiba, J.; Oshima, H.
1981-01-01
A geometrical gravitational theory is developed. The field equations are uniquely determined apart from one unknown dimensionless parameter ω 2 . It is based on an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metric gsub(μν) and two gauge scalars phi and psi. The theory satisfies the weak equivalence principle, but breaks the strong one generally. u(phi, psi) = phi is found out on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus there is the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power -4 algebraically made of psi and u(phi, psi), so it is dynamical, too. Finally spherically symmetric exact solutions are given. The permissible range of the unknown parameter ω 2 is experimentally determined by applying the solutions to the solar system. (author)
International Nuclear Information System (INIS)
Wu Ning; Zhang Dahua
2007-01-01
A systematic method is developed to study the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton's second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.
Gravitational 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.
International Nuclear Information System (INIS)
Wei Shaowen; Liu Yuxiao; Guo Heng
2011-01-01
In this paper, we obtain a relation between the high-energy absorption cross section and the strong gravitational lensing for a static and spherically symmetric black hole. It provides us a possible way to measure the high-energy absorption cross section for a black hole from strong gravitational lensing through astronomical observation. More importantly, it allows us to compute the total energy emission rate for high-energy particles emitted from the black hole acting as a gravitational lens. It could tell us the range of the frequency, among which the black hole emits the most of its energy and the gravitational waves are most likely to be observed. We also apply it to the Janis-Newman-Winicour solution. The results suggest that we can test the cosmic censorship hypothesis through the observation of gravitational lensing by the weakly naked singularities acting as gravitational lenses.
Energy Technology Data Exchange (ETDEWEB)
Clarisse, J.M
2007-07-01
A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)
Gravitational lensing in plasmic medium
Energy Technology Data Exchange (ETDEWEB)
Bisnovatyi-Kogan, G. S., E-mail: gkogan@iki.rssi.ru; Tsupko, O. Yu., E-mail: tsupko@iki.rssi.ru [Russian Academy of Sciences, Space Research Institute (Russian Federation)
2015-07-15
The influence of plasma on different effects of gravitational lensing is reviewed. Using the Hamiltonian approach for geometrical optics in a medium in the presence of gravity, an exact formula for the photon deflection angle by a black hole (or another body with a Schwarzschild metric) embedded in plasma with a spherically symmetric density distribution is derived. The deflection angle in this case is determined by the mutual combination of different factors: gravity, dispersion, and refraction. While the effects of deflection by the gravity in vacuum and the refractive deflection in a nonhomogeneous medium are well known, the new effect is that, in the case of a homogeneous plasma, in the absence of refractive deflection, the gravitational deflection differs from the vacuum deflection and depends on the photon frequency. In the presence of a plasma nonhomogeneity, the chromatic refractive deflection also occurs, so the presence of plasma always makes gravitational lensing chromatic. In particular, the presence of plasma leads to different angular positions of the same image if it is observed at different wavelengths. It is discussed in detail how to apply the presented formulas for the calculation of the deflection angle in different situations. Gravitational lensing in plasma beyond the weak deflection approximation is also considered.
Gravitational bags and solitary cosmological evolution
International Nuclear Information System (INIS)
Davidson, A.; Guendelman, E.I.
1989-01-01
The role played by the sophisticated scalar potential, dictated by spontaneous compactification, is analyzed. A fine-tuning is mandatory for achieving asymptotic flatness. Two main aspects are studied. 1. The three-fold spherically symmetric case exhibits localized four-dimensional objects, to be referred to as ''gravitational bags''. These are cores of scalar fields confined by means of a cosmic domain wall, whose size only slightly exceeds equal-mass black holes. 2. The cosmological case introduces a novel scenario of ''solitary evolution''. Triggered by the collapse of the extra dimensions, the universe undergoes an inflationary stage before settling in an oscillating fashion, in its ground state. (orig.)
Gravitational mass in an expanding universe
International Nuclear Information System (INIS)
Sannan, S.
1986-01-01
A test for the Hawking definition of mass is given in a Tolman--Bondi model that asymptotically approaches the open Friedmann universe. An expanding universe filled with dustlike matter of zero pressure is considered. The matter distribution is spherically symmetric but nonhomogeneous. With appropriate boundary conditions, the calculation yields a finite and nonzero value for the Hawking mass, measured as a deviation from a ''renormalized'' zero mass in the unperturbed Friedmann model. These boundary conditions are more restrictive than those found for a model with gravitational radiation
Horizon thermodynamics and gravitational field equations in Horava-Lifshitz gravity
International Nuclear Information System (INIS)
Cai Ronggen; Ohta, Nobuyoshi
2010-01-01
We explore the relationship between the first law of thermodynamics and gravitational field equation at a static, spherically symmetric black hole horizon in Horava-Lifshitz theory with/without detailed balance. It turns out that as in the cases of Einstein gravity and Lovelock gravity, the gravitational field equation can be cast to a form of the first law of thermodynamics at the black hole horizon. This way we obtain the expressions for entropy and mass in terms of black hole horizon, consistent with those from other approaches. We also define a generalized Misner-Sharp energy for static, spherically symmetric spacetimes in Horava-Lifshitz theory. The generalized Misner-Sharp energy is conserved in the case without matter field, and its variation gives the first law of black hole thermodynamics at the black hole horizon.
Self-gravitating black hole scalar wigs
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.
Entropy of self-gravitating radiation
International Nuclear Information System (INIS)
Sorkin, R.D.; Wald, R.M.; Jiu, Z.Z.
1981-01-01
The entropy of self-gravitating radiation confined to a spherical box of radius R is examined in the context of general relativity. It is expected that configurations (i.e., initial data) which extremize total entropy will be spherically symmetric, time symmetric distributions of radiation in local thermodynamic equilibrium. Assuming this is the case, it is proved that extrema of S coincide precisely with static equilibrium configurations of the radiation fluid. Furthermore, dynamically stable equilibrium configurations are shown to coincide with local maxima of S. The equilibrium configurations and their entropies are calculated and their properties are discussed. However, it is shown that entropies higher than these local extrema can be achieved and, indeed, arbitrarily high entropies can be attained by configurations inside of or outside but arbitrarily near their own Schwarzschild radius. However, consideration is limited to configurations which are outside their own Schwarzschild radius by at least one radiation wavelength, then the entropy is bounded and it is found Ssub(max) < is approximately equal to MR, where M is the total mass. This supports the validity for self-gravitating systems of the Bekenstein upper limit on the entropy to energy ratio of material bodies. (author)
International Nuclear Information System (INIS)
Moffat, J.W.; Svoboda, T.
1991-01-01
The stress-energy tensor for a a general spherically symmetric matter distribution in the nonsymmetric gravitational theory (NGT) is determined using a heuristic argument. Using this tensor and the NGT field equations, it is shown that a wormhole threaded with matter must necessarily have a radial tension greater than the mass-energy density in the throat region. Hence, as in general relativity, a traversible wormhole in NGT must contain matter with a negative stress energy
Interaction of gravitational waves with magnetic and electric fields
International Nuclear Information System (INIS)
Barrabes, C.; Hogan, P. A.
2010-01-01
The existence of large-scale magnetic fields in the universe has led to the observation that if gravitational waves propagating in a cosmological environment encounter even a small magnetic field then electromagnetic radiation is produced. To study this phenomenon in more detail we take it out of the cosmological context and at the same time simplify the gravitational radiation to impulsive waves. Specifically, to illustrate our findings, we describe the following three physical situations: (1) a cylindrical impulsive gravitational wave propagating into a universe with a magnetic field, (2) an axially symmetric impulsive gravitational wave propagating into a universe with an electric field and (3) a 'spherical' impulsive gravitational wave propagating into a universe with a small magnetic field. In cases (1) and (3) electromagnetic radiation is produced behind the gravitational wave. In case (2) no electromagnetic radiation appears after the wave unless a current is established behind the wave breaking the Maxwell vacuum. In all three cases the presence of the magnetic or electric fields results in a modification of the amplitude of the incoming gravitational wave which is explicitly calculated using the Einstein-Maxwell vacuum field equations.
Tensor spherical harmonics and tensor multipoles. II. Minkowski space
International Nuclear Information System (INIS)
Daumens, M.; Minnaert, P.
1976-01-01
The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4-vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation
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
General proof of the entropy principle for self-gravitating fluid in f(R) gravity
Energy Technology Data Exchange (ETDEWEB)
Fang, Xiongjun [Department of Physics and Key Laboratory of Low Dimensional Quantum Structures andQuantum Control of Ministry of Education, Hunan Normal University,Changsha, Hunan 410081 (China); Guo, Minyong [Department of Physics, Beijing Normal University,Beijing 100875 (China); Jing, Jiliang [Department of Physics and Key Laboratory of Low Dimensional Quantum Structures andQuantum Control of Ministry of Education, Hunan Normal University,Changsha, Hunan 410081 (China)
2016-08-29
The discussions on the connection between gravity and thermodynamics attract much attention recently. We consider a static self-gravitating perfect fluid system in f(R) gravity, which is an important theory could explain the accelerated expansion of the universe. We first show that the Tolman-Oppenheimer-Volkoff equation of f(R) theories can be obtained by thermodynamical method in spherical symmetric spacetime. Then we prove that the maximum entropy principle is also valid for f(R) gravity in general static spacetimes beyond spherical symmetry. The result shows that if the constraint equation is satisfied and the temperature of fluid obeys Tolmans law, the extrema of total entropy implies other components of gravitational equations. Conversely, if f(R) gravitational equation hold, the total entropy of the fluid should be extremum. Our work suggests a general and solid connection between f(R) gravity and thermodynamics.
Gravitational wave generation by stellar core collapse
International Nuclear Information System (INIS)
Moore, T.A.
1981-01-01
Stars which have masses greater than 5 to 8 solar masses are thought to undergo a stage of catastrophic core collapse and subsequent supernova explosion at the end of their lives. If the core is not spherically symmetric, the bounce which halts its collapse at transnuclear densities will generate a pulse of gravitational waves. This thesis presents a fully relativistic model of core collapse which treats deviations from spherical symmetry as small perturbations on a spherical background. This model may be used to predict qualitative and quantitative features of the gravitational radiation emitted by stellar cores with odd-parity, axisymmetric fluid perturbations, and represents a first step in the application of perturbative methods to more general asymmetries. The first chapter reviews the present consensus on the physics of core collapse and outlines the important features, assumptions, and limitations of the model. A series of model runs are presented and discussed. Finally, several proposals for future research are presented. Subsequent chapters explore in detail the mathematical features of the present model and its realization on the computer
Bach, Rudolf; Weyl, Hermann
2012-03-01
This is the English translation of the third of a series of 3 papers by Hermann Weyl (the third one jointly with Rudolf Bach), first published in 1917-1922, in which the authors derived and discussed the now-famous Weyl two-body static axially symmetric vacuum solution of Einstein's equations. The English translations of the other two papers are published alongside this one. The papers have been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Gernot Neugebauer, David Petroff and Bahram Mashhoon, and by a brief biography of R. Bach, written by H. Goenner.
Chameleon scalar fields in relativistic gravitational backgrounds
International Nuclear Information System (INIS)
Tsujikawa, Shinji; Tamaki, Takashi; Tavakol, Reza
2009-01-01
We study the field profile of a scalar field φ that couples to a matter fluid (dubbed a chameleon field) in the relativistic gravitational background of a spherically symmetric spacetime. Employing a linear expansion in terms of the gravitational potential Φ c at the surface of a compact object with a constant density, we derive the thin-shell field profile both inside and outside the object, as well as the resulting effective coupling with matter, analytically. We also carry out numerical simulations for the class of inverse power-law potentials V(φ) = M 4+n φ −n by employing the information provided by our analytical solutions to set the boundary conditions around the centre of the object and show that thin-shell solutions in fact exist if the gravitational potential Φ c is smaller than 0.3, which marginally covers the case of neutron stars. Thus the chameleon mechanism is present in the relativistic gravitational backgrounds, capable of reducing the effective coupling. Since thin-shell solutions are sensitive to the choice of boundary conditions, our analytic field profile is very helpful to provide appropriate boundary conditions for Φ c ∼< O(0.1)
Chameleon scalar fields in relativistic gravitational backgrounds
Energy Technology Data Exchange (ETDEWEB)
Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Tamaki, Takashi [Department of Physics, Waseda University, Okubo 3-4-1, Tokyo 169-8555 (Japan); Tavakol, Reza, E-mail: shinji@rs.kagu.tus.ac.jp, E-mail: tamaki@gravity.phys.waseda.ac.jp, E-mail: r.tavakol@qmul.ac.uk [Astronomy Unit, School of Mathematical Sciences, Queen Mary University of London, London E1 4NS (United Kingdom)
2009-05-15
We study the field profile of a scalar field {phi} that couples to a matter fluid (dubbed a chameleon field) in the relativistic gravitational background of a spherically symmetric spacetime. Employing a linear expansion in terms of the gravitational potential {Phi}{sub c} at the surface of a compact object with a constant density, we derive the thin-shell field profile both inside and outside the object, as well as the resulting effective coupling with matter, analytically. We also carry out numerical simulations for the class of inverse power-law potentials V({phi}) = M{sup 4+n}{phi}{sup -n} by employing the information provided by our analytical solutions to set the boundary conditions around the centre of the object and show that thin-shell solutions in fact exist if the gravitational potential {Phi}{sub c} is smaller than 0.3, which marginally covers the case of neutron stars. Thus the chameleon mechanism is present in the relativistic gravitational backgrounds, capable of reducing the effective coupling. Since thin-shell solutions are sensitive to the choice of boundary conditions, our analytic field profile is very helpful to provide appropriate boundary conditions for {Phi}{sub c}{approx}
A benign property of the ghost mode in massive theory of gravitation
Chugreev, Yu. V.
2018-01-01
It was shown in the frameworks of massive gravitational theories having in linear approximation mass term {m^2}( {φ ^{α β }}{φ_{α β }} - 1/2{φ ^2}} ) in the lagrangian, that created some time ago spherically-symmetric static sources should possess inside their light cone not only Yukawa potential, but also nonstationary component. It leads to the long ( 1/ m) period of gravitational evaporation of such sources with the mass loss Ṁ m 2 M 2 The magnitude of the flux is c 4/ v 4 times ( c—speed of light, v—velocity of the source particles) bigger then negative gravitational radiation flux corresponding to the ghost scalar mode in the spectrum of such gravitational field, with stabilizing the source.
Analysis of Weyl-affine theories of gravity in terms of the gravitational frequency shift effect
International Nuclear Information System (INIS)
Coley, A.A.; Sarmiento, G.A.
1986-01-01
A subclass of nonmetric theories of gravity, called Weyl-affine theories of gravity (WATGs), is analyzed by calculating their predictions for the gravitational frequency shift undergone by a wave signal in a planned solar probe. The analysis is carried out using a formalism in a spherically symmetric and static gravitational field. One of the advantages of the formalism is that any possible ''nonmetricity'' is contained in an arbitrary function, λ, of the Newtonian gravitational potential, U. The numerical results are calculated for a situation modeling a future experiment in the solar system. In the calculations, the metric components and the function, λ, are expanded up to third order in U. Within the limits of the gravitational redshift experiments performed to date, it is found that WATGs must coincide with their metric counterparts (i.e., λ is unity). It is hoped that the planned solar probe will test the nature of the theories under investigation to a higher degree of accuracy
Finite energy for a gravitational potential falling slower than 1/r
International Nuclear Information System (INIS)
Comelli, Denis; Crisostomi, Marco; Pilo, Luigi; Nesti, Fabrizio
2011-01-01
The total energy of any acceptable self-gravitating physical system has to be finite. In GR, the static gravitational potential of a self-gravitating body goes as 1/r at large distances and any slower decrease leads to infinite energy. In this work we show that in modified gravity theories the situation can be much different. We show that there exist spherically symmetric solutions with finite total energy, featuring an asymptotic behavior slower than 1/r and generically of the form r γ . This suggests that configurations with nonstandard asymptotics may well turn out to be physical. The effect is due to an extra field coupled only gravitationally, which allows for modifications of the static potential generated by matter, while counterbalancing the apparently infinite energy budget.
Quantum fluctuations of some gravitational waves
Enginer, Y.; Hortacsu, M.; Kaya, R.; Ozdemir, N.; Ulker, K.; Yapiskan, B.
1998-01-01
We review our previous work on the the calculation of the stress-energy tensor for a scalar particle in the background metric of different types of spherical impulsive, spherical shock and plane impulsive gravitational waves.
Relativity in Combinatorial Gravitational Fields
Directory of Open Access Journals (Sweden)
Mao Linfan
2010-04-01
Full Text Available A combinatorial spacetime $(mathscr{C}_G| uboverline{t}$ is a smoothly combinatorial manifold $mathscr{C}$ underlying a graph $G$ evolving on a time vector $overline{t}$. As we known, Einstein's general relativity is suitable for use only in one spacetime. What is its disguise in a combinatorial spacetime? Applying combinatorial Riemannian geometry enables us to present a combinatorial spacetime model for the Universe and suggest a generalized Einstein gravitational equation in such model. Forfinding its solutions, a generalized relativity principle, called projective principle is proposed, i.e., a physics law ina combinatorial spacetime is invariant under a projection on its a subspace and then a spherically symmetric multi-solutions ofgeneralized Einstein gravitational equations in vacuum or charged body are found. We also consider the geometrical structure in such solutions with physical formations, and conclude that an ultimate theory for the Universe maybe established if all such spacetimes in ${f R}^3$. Otherwise, our theory is only an approximate theory and endless forever.
Directory of Open Access Journals (Sweden)
Stavroulakis N.
2008-04-01
Full Text Available The equations of gravitation together with the equations of electromagnetism in terms of the General Theory of Relativity allow to conceive an interdependence between the gravitational field and the electromagnetic field. However the technical difficulties of the relevant problems have precluded from expressing clearly this interdependence. Even the simple problem related to the field generated by a charged spherical mass is not correctly solved. In the present paper we reexamine from the outset this problem and propose a new solution.
Energy Technology Data Exchange (ETDEWEB)
Zakharov, Aleksandr F [Russian Federation State Scientific Center ' A.I. Alikhanov Institute for Theoretical and Experimental Physics' , Moscow (Russian Federation); Sazhin, Mikhail V [P.K. Shternberg State Astronomical Institute at the M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
1998-10-31
The foundations of standard microlensing theory are discussed as applied to stars in the Galactic bulge, Magellanic Clouds or other nearby galaxies and gravitational microlenses assumed to lie in-between these stars and the terrestrial observer. In contrast to the review article by Gurevich et al. [48], microlensing by compact objects is mainly considered. Criteria for the identification of microlensing events are discussed as also are microlensing events not satisfying these criteria, such as non-symmetrical light curves and chromatic and polarization effects. The Large Magellanic Cloud (LMC) and Galactic bulge microlensing data of the MACHO group are discussed in detail and also the LMC data of EROS and the Galactic bulge data of OGLE are presented. A detailed comparison of theoretical predictions and observations is given. (reviews of topical problems)
International Nuclear Information System (INIS)
Zakharov, Aleksandr F; Sazhin, Mikhail V
1998-01-01
The foundations of standard microlensing theory are discussed as applied to stars in the Galactic bulge, Magellanic Clouds or other nearby galaxies and gravitational microlenses assumed to lie in-between these stars and the terrestrial observer. In contrast to the review article by Gurevich et al. [48], microlensing by compact objects is mainly considered. Criteria for the identification of microlensing events are discussed as also are microlensing events not satisfying these criteria, such as non-symmetrical light curves and chromatic and polarization effects. The Large Magellanic Cloud (LMC) and Galactic bulge microlensing data of the MACHO group are discussed in detail and also the LMC data of EROS and the Galactic bulge data of OGLE are presented. A detailed comparison of theoretical predictions and observations is given. (reviews of topical problems)
Fundamentals of spherical array processing
Rafaely, Boaz
2015-01-01
This book provides a comprehensive introduction to the theory and practice of spherical microphone arrays. It is written for graduate students, researchers and engineers who work with spherical microphone arrays in a wide range of applications. The first two chapters provide the reader with the necessary mathematical and physical background, including an introduction to the spherical Fourier transform and the formulation of plane-wave sound fields in the spherical harmonic domain. The third chapter covers the theory of spatial sampling, employed when selecting the positions of microphones to sample sound pressure functions in space. Subsequent chapters present various spherical array configurations, including the popular rigid-sphere-based configuration. Beamforming (spatial filtering) in the spherical harmonics domain, including axis-symmetric beamforming, and the performance measures of directivity index and white noise gain are introduced, and a range of optimal beamformers for spherical arrays, includi...
Metric elasticity in a collapsing star: Gravitational radiation coupled to torsional motion
International Nuclear Information System (INIS)
Gerlach, U.H.; Scott, J.F.
1986-01-01
Torsional oscillatory matter motion as well as differential rotation couple via the linearized Einstein field equations to the gravitational degrees of freedom. For an arbitrary spherically symmetric background, such as that of a wildly pulsating or a catastrophically collapsing star, we exhibit (a) the strain tensor and (b) the corresponding stress-energy tensor. It is found that in the star there are two elasticity tensors. One expresses the familiar elasticity of matter, the other expresses the elasticity of the geometry. This metric elasticity is responsible for coupling the gravitational and matter degrees of freedom. The two coupled scalar wave equations for these degrees of freedom are exhibited. Also exhibited are their characteristics as well as the junction conditions for their solutions across any spherical surface of discontinuity
Note on self-gravitating radiation in AdS spacetime
International Nuclear Information System (INIS)
Li Zhonghua; Hu Bin; Cai Ronggen
2008-01-01
Recently Vaganov and Hammersley investigated independently the equilibrium self-gravitating radiation in higher (d≥4)-dimensional, spherically symmetric anti-de Sitter space. It was found that in 4≤d≤10, there exist locally stable radiation configurations all the way up to a maximum red-shifted temperature, above which there are no solutions; there is also a maximum mass and maximum entropy configuration occurring at a higher central density than the maximal temperature configuration. Beyond their peaks the temperature, mass, and entropy undergo an infinite series of damped oscillations, which indicates the configurations in this range are unstable. In d≥11, the temperature, mass, and entropy of the self-gravitating configuration are monotonic functions of the central energy density, asymptoting to their maxima as the central density goes to infinity. In this paper we investigate the equilibrium self-gravitating radiation in higher-dimensional, plane-symmetric anti-de Sitter space. We find that there exist essential differences from the spherically symmetric case: In each dimension (d≥4), there are maximal mass (density), maximal entropy (density), and maximal temperature configurations; they do not appear at the same central energy density; the oscillation behavior appearing in the spherically symmetric case does not happen in this case; and the mass (density), as a function of the central energy density, increases first and reaches its maximum at a certain central energy density and then decreases monotonically in 4≤d≤7, while in d≥8, besides the maximum, the mass (density) of the equilibrium configuration has a minimum: the mass (density) first increases and reaches its maximum, then decreases to its minimum, and then increases to its asymptotic value monotonically. The reason causing the difference is discussed
General exact solution for homogeneous time-dependent self-gravitating perfect fluids
International Nuclear Information System (INIS)
Gaete, P.; Hojman, R.
1988-01-01
A procedure to obtain the general exact solution of Einstein equations for a self-gravitating spherically-symmetric static perfect fluid obeying an arbitrary equation of state, is applied to time-dependent Kantowsky-Sachs line elements (with spherical, planar and hyperbolic symmetry). As in the static case, the solution is generated by an arbitrary function of the independent variable and its first derivative. To illustrate the results, the whole family of (plane-symmetric) solutions with a ''gamma-law'' equation of state is explicity obtained in terms of simple known functions. It is also shown that, while in the static plane-symmtric line elements, every metric is in one to one correspondence with a ''partner-metric'' (both originated from the same generatrix function), in this case every generatrix function univocally determines one metric. (author) [pt
Gravitational lensing beyond the weak-field approximation
Perlick, Volker
2014-01-01
Gravitational lensing is considered in the full spacetime formalism of general relativity, assuming that the light rays are lightlike geodesics in a Lorentzian manifold. The review consists of three parts. The first part is devoted to spherically symmetric and static spacetimes. In particular, an exact lens map for this situation is discussed. The second part is on axisymmetric and stationary spacetimes. It concentrates on the investigation of the photon region, i.e., the region filled by spherical lightlike geodesics, in the Kerr spacetime. The photon region is of crucial relevance for the formation of a shadow. Finally, the third part briefly addresses two topics that apply to spacetimes without symmetry, namely Fermat's principle and the exact lens map of Frittelli and Newman.
Gravitational lensing beyond the weak-field approximation
Energy Technology Data Exchange (ETDEWEB)
Perlick, Volker, E-mail: perlick@zarm.uni-bremen.de [ZARM, University of Bremen, 28359 Bremen (Germany)
2014-01-14
Gravitational lensing is considered in the full spacetime formalism of general relativity, assuming that the light rays are lightlike geodesics in a Lorentzian manifold. The review consists of three parts. The first part is devoted to spherically symmetric and static spacetimes. In particular, an exact lens map for this situation is discussed. The second part is on axisymmetric and stationary spacetimes. It concentrates on the investigation of the photon region, i.e., the region filled by spherical lightlike geodesics, in the Kerr spacetime. The photon region is of crucial relevance for the formation of a shadow. Finally, the third part briefly addresses two topics that apply to spacetimes without symmetry, namely Fermat’s principle and the exact lens map of Frittelli and Newman.
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)
Spherical dust collapse in higher dimensions
International Nuclear Information System (INIS)
Goswami, Rituparno; Joshi, Pankaj S.
2004-01-01
We consider here whether it is possible to recover cosmic censorship when a transition is made to higher-dimensional spacetimes, by studying the spherically symmetric dust collapse in an arbitrary higher spacetime dimension. It is pointed out that if only black holes are to result as the end state of a continual gravitational collapse, several conditions must be imposed on the collapsing configuration, some of which may appear to be restrictive, and we need to study carefully if these can be suitably motivated physically in a realistic collapse scenario. It would appear, that, in a generic higher-dimensional dust collapse, both black holes and naked singularities would develop as end states as indicated by the results here. The mathematical approach developed here generalizes and unifies the earlier available results on higher-dimensional dust collapse as we point out. Further, the dependence of black hole or naked singularity end states as collapse outcomes on the nature of the initial data from which the collapse develops is brought out explicitly and in a transparent manner as we show here. Our method also allows us to consider here in some detail the genericity and stability aspects related to the occurrence of naked singularities in gravitational collapse
On the stability of a radiating fluid in a porous spherical shell
International Nuclear Information System (INIS)
Bestman, A.R.
1987-09-01
The onset of thermal instability in a fluid filled porous spherical shell is investigated when the temperatures of the walls are large enough for thermal radiation to be significant. Assuming that the gravitational field is radially symmetric and the porous medium consists of fluid which is optically thin, non-grey and near equilibrium, the problem is reduced to the determination of the eigenvalues for a set of linear homogeneous equations with variable coefficients. The effect of porosity and radiation on the stability parameter is discussed quantitatively. (author). 6 refs, 1 tab
International Nuclear Information System (INIS)
Ramond, P.
1993-01-01
The Wolfenstein parametrization is extended to the quark masses in the deep ultraviolet, and an algorithm to derive symmetric textures which are compatible with existing data is developed. It is found that there are only five such textures
Test-particle motion in the nonsymmetric gravitation theory
Moffat, J. W.
1987-06-01
A derivation of the motion of test particles in the nonsymmetric gravitational theory (NGT) is given using the field equations in the presence of matter. The motion of the particle is governed by the Christoffel symbols, which are formed from the symmetric part of the fundamental tensor gμν, as well as by a tensorial piece determined by the skew part of the contracted curvature tensor Rμν. Given the energy-momentum tensor for a perfect fluid and the definition of a test particle in the NGT, the equations of motion follow from the conservation laws. The tensorial piece in the equations of motion describes a new force in nature that acts on the conserved charge in a body. Particles that carry this new charge do not follow geodesic world lines in the NGT, whereas photons do satisfy geodesic equations of motion and the equivalence principle of general relativity. Astronomical predictions, based on the exact static, spherically symmetric solution of the field equations in a vacuum and the test-particle equations of motion, are derived in detail. The maximally extended coordinates that remove the event-horizon singularities in the static, spherically symmetric solution are presented. It is shown how an inward radially falling test particle can be prevented from forming an event horizon for a value greater than a specified critical value of the source charge. If a test particle does fall through an event horizon, then it must continue to fall until it reaches the singularity at r=0.
Gravitational wave reception by a sphere
International Nuclear Information System (INIS)
Ashby, N.; Dreitlein, J.
1975-01-01
The reception of gravitational waves by an elastic self-gravitating spherical detector is studied in detail. The equations of motion of a detector driven by a gravitational wave are presented in the intuitively convenient coordinate system of Fermi. An exact analytic solution is given for the homogeneous isotropic sphere. Nonlinear effects of a massive self-gravitating system are computed for a body of mass equal to that of the earth, and are shown to be numerically important
Spherical collapse and cluster counts in modified gravity models
International Nuclear Information System (INIS)
Martino, Matthew C.; Stabenau, Hans F.; Sheth, Ravi K.
2009-01-01
Modifications to the gravitational potential affect the nonlinear gravitational evolution of large scale structures in the Universe. To illustrate some generic features of such changes, we study the evolution of spherically symmetric perturbations when the modification is of Yukawa type; this is nontrivial, because we should not and do not assume that Birkhoff's theorem applies. We then show how to estimate the abundance of virialized objects in such models. Comparison with numerical simulations shows reasonable agreement: When normalized to have the same fluctuations at early times, weaker large scale gravity produces fewer massive halos. However, the opposite can be true for models that are normalized to have the same linear theory power spectrum today, so the abundance of rich clusters potentially places interesting constraints on such models. Our analysis also indicates that the formation histories and abundances of sufficiently low mass objects are unchanged from standard gravity. This explains why simulations have found that the nonlinear power spectrum at large k is unaffected by such modifications to the gravitational potential. In addition, the most massive objects in models with normalized cosmic microwave background and weaker gravity are expected to be similar to the high-redshift progenitors of the most massive objects in models with stronger gravity. Thus, the difference between the cluster and field galaxy populations is expected to be larger in models with stronger large scale gravity.
Regular reduction of relativistic theories of gravitation with a quadratic Lagrangian
International Nuclear Information System (INIS)
Bel, L.; Zia, H.S.
1985-01-01
We consider those relativistic theories of gravitation which generalize Einstein's theory in the sense that their field equations derive from a scalar Lagrangian which, besides the matter term, contains a linear combination of the Ricci scalar, its square, and the square of the Ricci tensor. Using a generalization of a technique which has been used to deal with some dynamical systems, we regularly and covariantly reduce the corresponding fourth-order differential equations to second-order ones. We examine, in particular, at a low order of approximation, these reduced equations in cosmology, and for static and spherically symmetric interior solutions with constant density
Scale-covariant theory of gravitation and astrophysical applications
International Nuclear Information System (INIS)
Canuto, V.; Adams, P.J.; Hsieh, S.; Tsiang, E.
1977-01-01
By associating the mathematical operation of scale transformation with the physics of using different dynamical systems to measure space-time distances, we formulate a scale-covariant theory of gravitation. Corresponding to each dynamical system of units is a gauge condition which determines the otherwise arbitrary gauge function. For gravitational units, the gauge condition is chosen so that the standard Einstein equations are recovered. Assuming the atomic units, derivable from atomic dynamics, to be distinct from the gravitational units, a different gauge condition must be imposed. It is suggested that Dirac's large-number hypothesis be used for the determination of this condition so that gravitational phenomena can be described in atomic units. The result allows a natural interpretation of the possible variation of the gravitational constant without compromising the validity of general relativity. A geometrical interpretation of the scale-covariant theory is possible if the covariant tensors in Riemannian space are replaced by cocovariant cotensors in an integrable Weyl space. A scale-invariant action principle is constructed from the metrical potentials of the integrable Weyl space. Application of the dynamical equations in atomic units to cosmology yields a family of homogeneous solutions characterized by R approx. t for large cosmological times. Equations of motion in atomic units are solved for spherically symmetric gravitational fields. Expressions for perihelion shift and light deflection are derived. They do not differ from the predictions of general relativity except for secular variations, having the age of the universe as a time scale. Similar variations of periods and radii for planetary orbits are also derived
Trapped surfaces in spherical stars
International Nuclear Information System (INIS)
Bizon, P.; Malec, E.; O'Murchadha, N.
1988-01-01
We give necessary and sufficient conditions for the existence of trapped surfaces in spherically symmetric spacetimes. These conditions show that the formation of trapped surfaces depends on both the degree of concentration and the average flow of the matter. The result can be considered as a partial validation of the cosmic-censorship hypothesis
Gravitationally confined relativistic neutrinos
Vayenas, C. G.; Fokas, A. S.; Grigoriou, D.
2017-09-01
Combining special relativity, the equivalence principle, and Newton’s universal gravitational law with gravitational rather than rest masses, one finds that gravitational interactions between relativistic neutrinos with kinetic energies above 50 MeV are very strong and can lead to the formation of gravitationally confined composite structures with the mass and other properties of hadrons. One may model such structures by considering three neutrinos moving symmetrically on a circular orbit under the influence of their gravitational attraction, and by assuming quantization of their angular momentum, as in the Bohr model of the H atom. The model contains no adjustable parameters and its solution, using a neutrino rest mass of 0.05 eV/c2, leads to composite state radii close to 1 fm and composite state masses close to 1 GeV/c2. Similar models of relativistic rotating electron - neutrino pairs give a mass of 81 GeV/c2, close to that of W bosons. This novel mechanism of generating mass suggests that the Higgs mass generation mechanism can be modeled as a latent gravitational field which gets activated by relativistic neutrinos.
Proca stars: Gravitating Bose–Einstein condensates of massive spin 1 particles
Directory of Open Access Journals (Sweden)
Richard Brito
2016-01-01
Full Text Available We establish that massive complex Abelian vector fields (mass μ can form gravitating solitons, when minimally coupled to Einstein's gravity. Such Proca stars (PSs have a stationary, everywhere regular and asymptotically flat geometry. The Proca field, however, possesses a harmonic time dependence (frequency w, realizing Wheeler's concept of geons for an Abelian spin 1 field. We obtain PSs with both a spherically symmetric (static and an axially symmetric (stationary line element. The latter form a countable number of families labelled by an integer m∈Z+. PSs, like (scalar boson stars, carry a conserved Noether charge, and are akin to the latter in many ways. In particular, both types of stars exist for a limited range of frequencies and there is a maximal ADM mass, Mmax, attained for an intermediate frequency. For spherically symmetric PSs (rotating PSs with m=1,2,3, Mmax≃1.058MPl2/μ (Mmax≃1.568,2.337,3.247MPl2/μ, slightly larger values than those for (mini-boson stars. We establish perturbative stability for a subset of solutions in the spherical case and anticipate a similar conclusion for fundamental modes in the rotating case. The discovery of PSs opens many avenues of research, reconsidering five decades of work on (scalar boson stars, in particular as possible dark matter candidates.
Gravitation compensation using a spherical magnetic spring
2016-01-01
A magnetic positioning device is provided that includes a first cup-shape permanent magnet having at least one permanent magnet segment conforming to the first cup-shape, where the first cup-shape permanent magnet has a first polarity, a second cup-shape permanent magnet that includes at least one
Quantum Fluctuations for Gravitational Impulsive Waves
Enginer, Y.; Hortacsu, M.; Ozdemir, N.
1998-01-01
Quantum fluctuations for a massless scalar field in the background metric of spherical impulsive gravitational waves through Minkowski and de Sitter spaces are investigated. It is shown that there exist finite fluctuations for de Sitter space.
Freeden, Willi; Schreiner, Michael
2018-01-01
This book presents, in a consistent and unified overview, results and developments in the field of today´s spherical sampling, particularly arising in mathematical geosciences. Although the book often refers to original contributions, the authors made them accessible to (graduate) students and scientists not only from mathematics but also from geosciences and geoengineering. Building a library of topics in spherical sampling theory it shows how advances in this theory lead to new discoveries in mathematical, geodetic, geophysical as well as other scientific branches like neuro-medicine. A must-to-read for everybody working in the area of spherical sampling.
Observing a Gravitational Wave Background With Lisa
National Research Council Canada - National Science Library
Tinto, M; Armstrong, J; Estabrook, F
2000-01-01
.... Comparison of the conventional Michelson interferometer observable with the fully-symmetric Sagnac data-type allows unambiguous discrimination between a gravitational wave background and instrumental noise. The method presented here can be used to detect a confusion-limited gravitational wave background.
Cohen, Taco S.; Geiger, Mario; Koehler, Jonas; Welling, Max
2018-01-01
Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naive application of convolutional networks to a planar projection of the spherical signal is destined t...
Energy Technology Data Exchange (ETDEWEB)
Miller, Jonah Maxwell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-10-18
This report has slides on Gravitational Waves; Pound and Rebka: A Shocking Fact; Light is a Ruler; Gravity is the Curvature of Spacetime; Gravitational Waves Made Simple; How a Gravitational Wave Affects Stuff Here; LIGO; This Detection: Neutron Stars; What the Gravitational Wave Looks Like; The Sound of Merging Neutron Stars; Neutron Star Mergers: More than GWs; The Radioactive Cloud; The Kilonova; and finally Summary, Multimessenger Astronomy.
Painleve-Gullstrand synchronizations in spherical symmetry
International Nuclear Information System (INIS)
Herrero, Alicia; Morales-Lladosa, Juan Antonio
2010-01-01
A Painleve-Gullstrand synchronization is a slicing of the spacetime by a family of flat space-like 3-surfaces. For spherically symmetric spacetimes, we show that a Painleve-Gullstrand synchronization only exists in the region where (dr) 2 ≤ 1, r being the curvature radius of the isometry group orbits (2-spheres). This condition states that the Misner-Sharp gravitational energy of these 2-spheres is not negative and has an intrinsic meaning in terms of the norm of the mean extrinsic curvature vector. It also provides an algebraic inequality involving the Weyl curvature scalar and the Ricci eigenvalues. We prove that the energy and momentum densities associated with the Weinberg complex of a Painleve-Gullstrand slice vanish in these curvature coordinates, and we give a new interpretation of these slices by using semi-metric Newtonian connections. It is also outlined that, by solving the vacuum Einstein's equations in a coordinate system adapted to a Painleve-Gullstrand synchronization, the Schwarzschild solution is directly obtained in a whole coordinate domain that includes the horizon and both its interior and exterior regions.
Scalar, electromagnetic, and gravitational fields interaction: Particlelike solutions
International Nuclear Information System (INIS)
Bronnikov, K.A.; Melnikov, V.N.; Shikin, G.N.; Staniukovich, K.P.
1979-01-01
Particlelike static spherically symmetric solutions to massless scalar and electromagnetic field equations combined with gravitational field equations are considered. Two criteria for particlelike solutions are formulated: the strong one (solutions are required to be singularity free) and the weak one (singularities are admitted but the total energy and material field energy should be finite). Exact solutions for the following physical systems are considered with their own gravitational field: (i) linear scalar (minimally coupled or conformal) plus electromagnetic field; (ii) the same fields with a bare mass source in the form of charged incoherent matter distributions; (iii) nonlinear electromagnetic field with an abritrary dependence on the invariant F/sub alphabeta/F/sup alphabeta/; and (iv) directly interacting scalar and electromagnetic fields. Case (i) solutions are not particlelike (except those with horizons, in which static regions formally satisfy the weak criterion). For systems (ii), examples of nonsingular models are constructed, in particular, a model for a particle--antiparticle pair of a Wheeler-handle type, without scalar field and explict electric charges. Besides, a number of limitations upon nonsingular model parameters is indicated. Systems (iii) are proved to violate the strong criterion for any type of nonlinearity but can satisfy the weak criterion (e.g., the Born--Infeld nonlinearity). For systems (iv) some particlelike solutions by the weak criterion are constructed and a regularizing role of gravitation is demonstrated. Finally, an example of a field system satisfying the strong criterion is given
Gravitational Metric Tensor Exterior to Rotating Homogeneous ...
African Journals Online (AJOL)
The covariant and contravariant metric tensors exterior to a homogeneous spherical body rotating uniformly about a common φ axis with constant angular velocity ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is ...
Newtonian cosmology with a time-varying constant of gravitation
International Nuclear Information System (INIS)
McVittie, G.C.
1978-01-01
Newtonian cosmology is based on the Eulerian equations of fluid mechanics combined with Poisson's equation modified by the introduction of a time-varying G. Spherically symmetric model universes are worked out with instantaneously uniform densities. They are indeterminate unless instantaneous uniformity of the pressure is imposed. When G varies as an inverse power of the time, the models can in some cases be shown to depend on the solution of a second-order differential equation which also occurs in the Friedmann models of general relativity. In Section 3, a method for 'passing through' a singularity of this equation is proposed which entails making four arbitrary mathematical assumptions. When G varies as (time) -1 , models with initially cycloidal motion are possible, each cycle becoming longer as time progresses. Finally, gravitation becomes so weak that the model expands to infinity. Kinetic and potential energies for the whole model are derived from the basic equations; their sum is not constant. (author)
Gravitational collapse and evolution of holographic black holes
Energy Technology Data Exchange (ETDEWEB)
Casadio, R [Dipartimento di Fisica, Universita di Bologna and I.N.F.N., Sezione di Bologna, via Irnerio 46, 40126 Bologna (Italy); Germani, C [D.A.M.T.P., Centre for Mathematical Sciences, University of Cambridge, Wilberforce road, Cambridge CB3 0WA (United Kingdom)
2006-03-01
Gravitational collapse is analyzed in the Brane-World by arguing that regularity of five-dimensional geodesics require that stars on the brane have an atmosphere. For the simple case of a spherically symmetric cloud of non-dissipating dust, conditions are found for which the collapsing star evaporates and approaches the Hawking behavior as the (apparent) horizon is being formed. The effective energy of the star vanishes at a finite radius and the star afterwards re-expands and 'anti-evaporates'. Israel junction conditions across the brane (holographically related to the matter trace anomaly) and the projection of the Weyl tensor on the brane (holographically interpreted as the quantum back-reaction on the brane metric) contribute to the total energy as, respectively, an 'anti-evaporation' and an 'evaporation' term.
Entanglement of heavy quark impurities and generalized gravitational entropy
Kumar, S. Prem; Silvani, Dorian
2018-01-01
We calculate the contribution from non-conformal heavy quark sources to the entanglement entropy (EE) of a spherical region in N=4 SUSY Yang-Mills theory. We apply the generalized gravitational entropy method to non-conformal probe D-brane embeddings in AdS5×S5, dual to pointlike impurities exhibiting flows between quarks in large-rank tensor representations and the fundamental representation. For the D5-brane embedding which describes the screening of fundamental quarks in the UV to the antisymmetric tensor representation in the IR, the EE excess decreases non-monotonically towards its IR asymptotic value, tracking the qualitative behaviour of the one-point function of static fields sourced by the impurity. We also examine two classes of D3-brane embeddings, one which connects a symmetric representation source in the UV to fundamental quarks in the IR, and a second category which yields the symmetric representation source on the Coulomb branch. The EE excess for the former increases from the UV to the IR, whilst decreasing and becoming negative for the latter. In all cases, the probe free energy on hyperbolic space with β = 2 π increases monotonically towards the IR, supporting its interpretation as a relative entropy. We identify universal corrections, depending logarithmically on the VEV, for the symmetric representation on the Coulomb branch.
Determining Symmetry Properties of Gravitational Fields of Terrestrial Group Planets
Directory of Open Access Journals (Sweden)
R.A. Kascheev
2016-09-01
Full Text Available Numerous models of gravity fields of the Solar system bodies have been constructed recently owing to successful space missions. These models are sets of harmonic coefficients of gravity potential expansion in series of spherical functions, which is Laplace series. The sets of coefficients are different in quantity of numerical parameters, sources and composition of the initial observational data, methods to obtain and process them, and, consequently, in a variety of properties and accuracy characteristics. For this reason, the task of comparison of different models of celestial bodies considered in the paper is of interest and relevant. The main purpose of this study is comparison of the models of gravitational potential of the Earth, Moon, Mars, and Venus with the quantitative criteria of different types of symmetries developed by us. It is assumed that some particular symmetry of the density distribution function of the planetary body causes similar symmetry of its gravitational potential. The symmetry of gravitational potential, in its turn, imposes additional conditions (restrictions, which must be satisfied by the harmonic coefficients. The paper deals with seven main types of symmetries: central, axial, two symmetries specular relative to the equatorial planes and prime meridian, as well as three rotational symmetries (at π angle around the coordinate system axes. According to the results of calculations carried out for the Earth, Moon, Mars, and Venus, the values of the criteria vary considerably for different types of symmetries and for different planets. It means that the specific value of each criterion corresponding to a particular celestial body is indicative of the properties and internal structure characteristics of the latter and, therefore, it can be used as a tool for comparative planetology. On the basis of the performed calculations, it is possible to distinguish two groups of celestial bodies having similar properties of
Doblas, Ana; Dutta, Ananya; Saavedra, Genaro; Preza, Chrysanthe
2018-02-01
Previously, a wavefront encoded (WFE) imaging system implemented using a squared cubic (SQUBIC) phase mask has been verified to reduce the sensitivity of the imaging system to spherical aberration (SA). The strength of the SQUBIC phase mask and, as consequence, the performance of the WFE system are controlled by a design parameter, A. Although the higher the A-value, the more tolerant the WFE system is to SA, this is accomplished at the expense of the effective imaging resolution. In this contribution, we investigate this tradeoff in order to find an optimal A-value to balance the effect of SA and loss of resolution.
CERN. Geneva
2005-01-01
We will present a brief introduction to the physics of gravitational waves and their properties. We will review potential astrophysical sources of gravitational waves, and the physics and astrophysics that can be learned from their study. We will survey the techniques and technologies for detecting gravitational waves for the first time, including bar detectors and broadband interferometers, and give a brief status report on the international search effort, with special emphasis on the LIGO detectors and search results.
Test-particle motion in the nonsymmetric gravitation theory
International Nuclear Information System (INIS)
Moffat, J.W.
1987-01-01
A derivation of the motion of test particles in the nonsymmetric gravitational theory (NGT) is given using the field equations in the presence of matter. The motion of the particle is governed by the Christoffel symbols, which are formed from the symmetric part of the fundamental tensor g/sub μ//sub ν/, as well as by a tensorial piece determined by the skew part of the contracted curvature tensor R/sub μ//sub ν/. Given the energy-momentum tensor for a perfect fluid and the definition of a test particle in the NGT, the equations of motion follow from the conservation laws. The tensorial piece in the equations of motion describes a new force in nature that acts on the conserved charge in a body. Particles that carry this new charge do not follow geodesic world lines in the NGT, whereas photons do satisfy geodesic equations of motion and the equivalence principle of general relativity. Astronomical predictions, based on the exact static, spherically symmetric solution of the field equations in a vacuum and the test-particle equations of motion, are derived in detail. The maximally extended coordinates that remove the event-horizon singularities in the static, spherically symmetric solution are presented. It is shown how an inward radially falling test particle can be prevented from forming an event horizon for a value greater than a specified critical value of the source charge. If a test particle does fall through an event horizon, then it must continue to fall until it reaches the singularity at r = 0
On the spherical harmonic expansion of the neutron angular distribution function
Energy Technology Data Exchange (ETDEWEB)
Depken, Sven
1959-03-15
The neutron (one-velocity) angular distribution function is expanded in terms of spherical harmonic tensors. The solution to the equations of the moments is given explicitly and the result is applied to the plane, spherical and cylinder symmetrical cases.
On the spherical harmonic expansion of the neutron angular distribution function
International Nuclear Information System (INIS)
Depken, Sven
1959-03-01
The neutron (one-velocity) angular distribution function is expanded in terms of spherical harmonic tensors. The solution to the equations of the moments is given explicitly and the result is applied to the plane, spherical and cylinder symmetrical cases
Cuspidal discrete series for semisimple symmetric spaces
DEFF Research Database (Denmark)
Andersen, Nils Byrial; Flensted-Jensen, Mogens; Schlichtkrull, Henrik
2012-01-01
We propose a notion of cusp forms on semisimple symmetric spaces. We then study the real hyperbolic spaces in detail, and show that there exists both cuspidal and non-cuspidal discrete series. In particular, we show that all the spherical discrete series are non-cuspidal. (C) 2012 Elsevier Inc. All...
Normalization of Gravitational Acceleration Models
Eckman, Randy A.; Brown, Aaron J.; Adamo, Daniel R.
2011-01-01
Unlike the uniform density spherical shell approximations of Newton, the con- sequence of spaceflight in the real universe is that gravitational fields are sensitive to the nonsphericity of their generating central bodies. The gravitational potential of a nonspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities which must be removed in order to generalize the method and solve for any possible orbit, including polar orbits. Three unique algorithms have been developed to eliminate these singularities by Samuel Pines [1], Bill Lear [2], and Robert Gottlieb [3]. This paper documents the methodical normalization of two1 of the three known formulations for singularity-free gravitational acceleration (namely, the Lear [2] and Gottlieb [3] algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre Polynomials and ALFs for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms.
International Nuclear Information System (INIS)
Bleyer, U.; Muecket, J.P.
1980-01-01
In general the Birkhoff theorem is violated in non-Einsteinian theories of gravitation. We show for theories in which the dynamical equations do not follow from the field equations that time-dependent vacuum solutions are needed in order to join nonstatic spherically symmetric incoherent matter distributions. It is shown for Treder's tetrad theories that such vacuum solutions exist and a continuous and unique junction is possible. In generalization of these results we consider the problem in what theories of gravitation the dynamical equations do not follow from the field equations. This consideration leads to non-Einsteinian theories like bimetric theories or Treder's tetrad theories containing supplementary geometrical quantities which are not dynamical variables of the theory. (author)
Electron Optics for Biologists: Physical Origins of Spherical Aberrations
Geissler, Peter; Zadunaisky, Jose
1974-01-01
Reports on the physical origins of spherical aberrations in axially symmetric electrostatic lenses to convey the essentials of electon optics to those who must think critically about the resolution of the electron microscope. (GS)
Energy Technology Data Exchange (ETDEWEB)
Ferraioli, F; Virgopia, N [Rome Univ. (Italy). Ist. di Matematica; Ruggeri, T [Bologna Univ. (Italy)
1978-07-01
The gravitational collapse of a spherically symmetric interstellar gas cloud has been investigated following the non-linear discontinuity waves propagation theory. It has been pointed out that macroscopic phenomena, such as the process of fragmentation, can arise (shock wave formation) - even in the case of spherical symmetry - at times smaller than the free-fall time tsub(ff), provided the initial data of the Cauchy problem be discontinuous within a sphere of radius R(mean) < Rsub(cloud) (caustic cases). It has also been proved that strong discontinuities outside the mentioned sphere may generate critical times tsub(cr) < tsub(ff) (depending on the typical non-linear structure of the differential system). The cooling-heating function plays an important role in contrasting the formation of shock waves.
International Nuclear Information System (INIS)
Bondi, H.
1979-01-01
In spite of the strength of gravitational focres between celestial bodies, gravitational capture is not a simple concept. The principles of conservation of linear momentum and of conservation of angular momentum, always impose severe constraints, while conservation of energy and the vital distinction between dissipative and non-dissipative systems allows one to rule out capture in a wide variety of cases. In complex systems especially those without dissipation, long dwell time is a more significant concept than permanent capture. (author)
An experimental test of Newton's law of gravitation for small accelerations
International Nuclear Information System (INIS)
Schubert, Sven
2011-10-01
The experiment presented in this thesis has been designed to test Newton's law of gravitation in the limit of small accelerations caused by weak gravitational forces. It is located at DESY, Hamburg, and is a modification of an experiment that was carried out in Wuppertal, Germany, until 2002 in order to measure the gravitational constant G. The idea of testing Newton's law in the case of small accelerations emerged from the question whether the flat rotation curves of spiral galaxies can be traced back to Dark Matter or to a law of gravitation that deviates from Newton on cosmic scales like e.g. MOND (Modified Newtonian Dynamics). The core of this experiment is a microwave resonator which is formed by two spherical concave mirrors that are suspended as pendulums. Masses between 1 and 9 kg symmetrically change their distance to the mirrors from far to near positions. Due to the increased gravitational force the mirrors are pulled apart and the length of the resonator increases. This causes a shift of the resonance frequency which can be translated into a shift of the mirror distance. The small masses are sources of weak gravitational forces and cause accelerations on the mirrors of about 10 -10 m/s 2 . These forces are comparable to those between stars on cosmic scales and the accelerations are in the vicinity of the characteristic acceleration of MOND a 0 ∼ 1.2.10 -10 m/s 2 , where deviations from Newton's law are expected. Thus Newton's law could be directly checked for correctness under these conditions. First measurements show that due to the sensitivity of this experiment many systematic influences have to be accounted for in order to get consistent results. Newton's law has been confirmed with an accuracy of 3%. MOND has also been checked. In order to be able to distinguish Newton from MOND with other interpolation functions the accuracy of the experiment has to be improved. (orig.)
Nonlinear effects in Pulsations of Compact Stars and Gravitational Waves
International Nuclear Information System (INIS)
Passamonti, A
2007-01-01
Nonlinear stellar oscillations can be studied by using a multiparameter perturbative approach, which is appropriate for investigating the low and mild nonlinear dynamical regimes. We present the main properties of our perturbative framework for describing, in the time domain, the nonlinear coupling between the radial and nonradial perturbations of spherically symmetric and perfect fluid compact stars. This particular coupling can be described by gauge invariant quantities that obeys a system of partial differential equations with source terms, which are made up of product of first order radial and nonradial perturbations. We report the results of numerical simulations for both the axial and polar coupling perturbations, that exhibit in the stellar dynamics and in the associated gravitational wave signal some interesting nonlinear effects, such as combination harmonics and resonances. In particular, we concentrate on the axial case, where the linear axial perturbations describe a harmonic component of a differentially rotating neutron star. The gravitational wave signal of this stellar configuration mirrors at second perturbative order the spectral features of the linear radial normal modes. In addition, a signal amplification appears when one of the radial frequencies is close to the axial w-mode frequencies of the star
Entropy of gravitating systems: scaling laws versus radial profiles
International Nuclear Information System (INIS)
Pesci, Alessandro
2007-01-01
Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which it is no longer an extensive quantity (it does not scale with the system's size). To accomplish this, the methods introduced by Oppenheim (2003 Phys. Rev.E 68 016108) to characterize non-extensivity are used, suitably generalized to the case of gravitating systems subject to an external pressure. In particular when, far from the system's Schwarzschild limit, both area scaling for conventional entropy and inverse radius law for the temperature set in (i.e. the same properties of the corresponding black hole thermodynamical quantities), the entropy profile is found to behave like 1/r, with r the area radius inside the system. In such circumstances entropy heavily resides in internal layers, in opposition to what happens when area scaling is gained while approaching the Schwarzschild mass, in which case conventional entropy lies at the surface of the system. The information content of these systems, even if it globally scales like the area, is then stored in the whole volume, instead of packed on the boundary
Gravitational lensing as a mechanism for effective cloaking
International Nuclear Information System (INIS)
Tippett, Benjamin K.
2011-01-01
In light of the surge in popularity of electromagnetic cloaking devices, we consider whether it is possible to use general relativity to cloak a volume of spacetime through gravitational lensing. We explore the cloaking properties of a spacetime through a ray-tracing procedure, wherein we plot the spatial trajectories of a congruence of initially parallel null geodesics as they cross the geometry. In this context, a cloaking device would cause all of the null geodesics in an initially parallel congruence incident upon the cloaking geometry to circumnavigate an internal region, and as the geodesics emerge from the geometry, they regain their original configuration. Thus, if gravitational lensing were used as a mechanism for cloaking, the internal region would be causally isolated from the external spacetime. For this reason, we propose an effective cloaking geometry wherein (only) most of ingoing null geodesics will splay away from a central region, and then regain their initial configuration as they exit the geometry. Thus, a compact object sitting within the effective cloaking geometry will impede a smaller cross section of the null congruence, and therefore appear optically smaller from all sides. We build our effective cloaking geometry by connecting a Minkowski spacetime exterior to a spherically symmetric, curved spacetime along a timelike hypersurface of constant radius using the Israel junction conditions. The junction conditions require a shell of matter of infinitesimal width confined to the junction surface. The matter required to build such a spacetime must violate the null energy condition.
Conformally symmetric traversable wormholes
International Nuclear Information System (INIS)
Boehmer, Christian G.; Harko, Tiberiu; Lobo, Francisco S. N.
2007-01-01
Exact solutions of traversable wormholes are found under the assumption of spherical symmetry and the existence of a nonstatic conformal symmetry, which presents a more systematic approach in searching for exact wormhole solutions. In this work, a wide variety of solutions are deduced by considering choices for the form function, a specific linear equation of state relating the energy density and the pressure anisotropy, and various phantom wormhole geometries are explored. A large class of solutions impose that the spatial distribution of the exotic matter is restricted to the throat neighborhood, with a cutoff of the stress-energy tensor at a finite junction interface, although asymptotically flat exact solutions are also found. Using the 'volume integral quantifier', it is found that the conformally symmetric phantom wormhole geometries may, in principle, be constructed by infinitesimally small amounts of averaged null energy condition violating matter. Considering the tidal acceleration traversability conditions for the phantom wormhole geometry, specific wormhole dimensions and the traversal velocity are also deduced
Telles, J. E.; de Souza, R. E.; Penereiro, J. C.
1990-11-01
RESUMEN. Presentamos fotometria fotografica de 8 objetos y espectrosco- pla para 3 galaxias, las cuales son buenos candidatos para galaxias esfericas. Los resultados fotometricos se presentan en la forma de iso- fotas y de perfiles radiales promedlo, de los cuales se derivan para- metros estructurales. Estas observaciones combinadas con parametros di- namicos obtenidos de observaciones espectrosc6picas, son consistentes con el plano fundamental derivado por Djorgovski y Davis (1987). ABSTRACT. We present photographic surface photometry for 8 objects and spectroscopy for 3 galaxies which are good candidates for spherical galaxies. Photometric results are presented in the form of isophotes and mean radial profiles from which we derived structural parameters. These observations combined with dynamical parameters obtained from spectroscopic observations are consistent with the fundamental plane derived by Djorgovski and Davis (1987). Keq wo : CALAXIES-ELLIPTICAL
Effect of the spherical Earth on a simple pendulum
Burko, Lior M.
2003-01-01
We consider the period of a simple pendulum in the gravitational field of the spherical Earth. Effectively, gravity is enhanced compared with the often used flat Earth approximation, such that the period of the pendulum is shortened. We discuss the flat Earth approximation, and show when the corrections due to the spherical Earth may be of interest.
Gravitational waves from gravitational collapse
Energy Technology Data Exchange (ETDEWEB)
Fryer, Christopher L [Los Alamos National Laboratory; New, Kimberly C [Los Alamos National Laboratory
2008-01-01
Gravitational wave emission from stellar collapse has been studied for nearly four decades. Current state-of-the-art numerical investigations of collapse include those that use progenitors with more realistic angular momentum profiles, properly treat microphysics issues, account for general relativity, and examine non-axisymmetric effects in three dimensions. Such simulations predict that gravitational waves from various phenomena associated with gravitational collapse could be detectable with ground-based and space-based interferometric observatories. This review covers the entire range of stellar collapse sources of gravitational waves: from the accretion induced collapse of a white dwarf through the collapse down to neutron stars or black holes of massive stars to the collapse of supermassive stars.
Gravitational Waves from Gravitational Collapse
Directory of Open Access Journals (Sweden)
Chris L. Fryer
2011-01-01
Full Text Available Gravitational-wave emission from stellar collapse has been studied for nearly four decades. Current state-of-the-art numerical investigations of collapse include those that use progenitors with more realistic angular momentum profiles, properly treat microphysics issues, account for general relativity, and examine non-axisymmetric effects in three dimensions. Such simulations predict that gravitational waves from various phenomena associated with gravitational collapse could be detectable with ground-based and space-based interferometric observatories. This review covers the entire range of stellar collapse sources of gravitational waves: from the accretion-induced collapse of a white dwarf through the collapse down to neutron stars or black holes of massive stars to the collapse of supermassive stars.
Gravitational Waves from Gravitational Collapse.
Fryer, Chris L; New, Kimberly C B
2011-01-01
Gravitational-wave emission from stellar collapse has been studied for nearly four decades. Current state-of-the-art numerical investigations of collapse include those that use progenitors with more realistic angular momentum profiles, properly treat microphysics issues, account for general relativity, and examine non-axisymmetric effects in three dimensions. Such simulations predict that gravitational waves from various phenomena associated with gravitational collapse could be detectable with ground-based and space-based interferometric observatories. This review covers the entire range of stellar collapse sources of gravitational waves: from the accretion-induced collapse of a white dwarf through the collapse down to neutron stars or black holes of massive stars to the collapse of supermassive stars. Supplementary material is available for this article at 10.12942/lrr-2011-1.
Nondissipative gravitational turbulence
International Nuclear Information System (INIS)
Gurevich, A.V.; Zybin, K.P.
1988-01-01
The nonlinear stage of development of the Jeans instability in a cold nondissipative gravitating gas is considered. It is shown that for a time exceeding the Jeans time a nondissipative gravitational singularity (NGS) is formed in the vicinity of a local density maximum. The NGS is a stationary dynamic structure, the basis of which is the singularity. The density of the gas at the center of the NGS (for r → 0) tends to infinity, and the field potential and the mean velocity of the trapped gas, possess a power singularity. The turbulent state arises as the result of development of the instability in the case of an irregular initial density distribution. It is an hierarchic structure consisting of nested moving NGS of various sizes, the NGS of smaller dimensions being trapped in the field of a NGS of larger dimensions. The scaling relations for each given NGS in this case hold for both the gas density and density of smaller size trapped NGS. A brief comparison with the observational data shows that the real hierarchic structure of the Universe ranging from scales pertaining to spherical stellar clusters up to those of rich galaxy clusters is apparently a developed gravitational turbulence
Energy Technology Data Exchange (ETDEWEB)
Troxel, M.A.; Peel, Austin; Ishak, Mustapha, E-mail: troxel@utdallas.edu, E-mail: austin.peel@utdallas.edu, E-mail: mishak@utdallas.edu [Department of Physics, The University of Texas at Dallas, Richardson, TX, 75083 (United States)
2013-12-01
We study the effects and implications of anisotropies at the scale of galaxy clusters by building an exact general relativistic model of a cluster using the inhomogeneous and anisotropic Szekeres metric. The model is built from a modified Navarro-Frenk-White (NFW) density profile. We compare this to a corresponding spherically symmetric structure in the Lemaȋtre-Tolman (LT) model and quantify the impact of introducing varying levels of anisotropy. We examine two physical measures of gravitational infall — the growth rate of density and the velocity of the source dust in the model. We introduce a generalization of the LT dust velocity profile for the Szekeres metric and demonstrate its consistency with the growth rate of density. We find that the growth rate of density in one substructure increases by 0.5%, 1.5%, and 3.75% for 5%, 10%, and 15% levels of introduced anisotropy, which is measured as the fractional displaced mass relative to the spherically symmetric case. The infall velocity of the dust is found to increase by 2.5, 10, and 20 km s{sup −1} (0.5%, 2%, and 4.5%), respectively, for the same three levels of anisotropy. This response to the anisotropy in a structure is found to be strongly nonlinear with respect to the strength of anisotropy. These relative velocities correspond to an equivalent increase in the total mass of the spherically symmetric structure of 1%, 3.8%, and 8.4%, indicating that not accounting for the presence of anisotropic mass distributions in cluster models can strongly bias the determination of physical properties like the total mass.
Dodelson, Scott
2017-01-01
Gravitational lensing is a consequence of general relativity, where the gravitational force due to a massive object bends the paths of light originating from distant objects lying behind it. Using very little general relativity and no higher level mathematics, this text presents the basics of gravitational lensing, focusing on the equations needed to understand the phenomena. It then applies them to a diverse set of topics, including multiply imaged objects, time delays, extrasolar planets, microlensing, cluster masses, galaxy shape measurements, cosmic shear, and lensing of the cosmic microwave background. This approach allows undergraduate students and others to get quickly up to speed on the basics and the important issues. The text will be especially relevant as large surveys such as LSST and Euclid begin to dominate the astronomical landscape. Designed for a one semester course, it is accessible to anyone with two years of undergraduate physics background.
Schäfer, G.; Schutz, B.
1996-01-01
Gravity is truly universal. It is the force that pulls us to the Earth, that keeps the planets and moons in their orbits, and that causes the tides on the Earth to ebb and flow. It even keeps the Sun shining. Yet on a laboratory scale gravity is extremely weak. The Coulomb force between two protons is 1039 times stronger than the gravitational force between them. Moreover, Newton's gravitational constant is the least accurately known of the fundamental constants: it has been measured to 1 par...
Theory of gravitation with an alternative to black holes
International Nuclear Information System (INIS)
Chang, D.B.; Johnson, H.H.
1980-01-01
A gauge theory of gravitation is proposed in which the Lagrangian is constructed from vierbein-based invariants rather than local affine connections. The vierbein invariants are more basic than the connection-based invariants: involving coefficients of lower-order differential forms, providing a reasonable field energy-momentum tensor, and not requiring arbitrary introduction of quantities into the gauge-theory formalism in the special case of scalar wave functions. Covariance of the equations notwithstanding, the speed of light measured with atomic clocks and rigid rulers is hypothesized to be independent of direction in a gravitational field. This hypothesis constrains the Lagrangian for variations which give the field equations in the operationally significant class of coordinate systems whose time and spatial intervals are directly measurable with these same clocks and rulers. Out of the general family of quadratic Lagrangians permitted by this constraint, only two possible Lagrangians are selected by the standard weak-field observational tests (perihelion precession, light deflection, etc.) of the general theory of relativity. Although both of these Lagrangians give solutions which agree with the standard weak-field observational tests of the general theory of relativity, they do give different predictions in other situations: For a static spherically symmetric field, one Lagrangian gives the standard isotropic Schwarzschild metric of the Einstein general theory of relativity, while the second yields a metric of exponential form. Thus, the second predicts that a very massive body does not create a black hole, but a ''dark red hole''. The source terms for gravitational radiation differ for the two Lagrangians. A cosmology is predicted in which the expanding universe has zero curvature and involves the continuous creation of matter following a big bang
On the Field of a Stationary Charged Spherical Source
Directory of Open Access Journals (Sweden)
Stavroulakis N.
2009-04-01
Full Text Available The equations of gravitation related to the field of a spherical charged source imply the existence of an interdependence between gravitation and electricity [5]. The present paper deals with the joint action of gravitation and electricity in the case of a stationary charged spherical source. Let m and " be respectively the mass and the charge of the source, and let k be the gravitational constant. Then the equations of gravitation need specific discussion according as j " j m p k (source strongly charged. In any case the curvature radius of the sphere bounding the matter possesses a strictly positive greatest lower hound, so that the source is necessarily an extended object. Pointwise sources do not exist. In particular, charged black holes do not exist.
Jiang, Haiyong
2016-04-11
We present an automatic algorithm for symmetrizing facade layouts. Our method symmetrizes a given facade layout while minimally modifying the original layout. Based on the principles of symmetry in urban design, we formulate the problem of facade layout symmetrization as an optimization problem. Our system further enhances the regularity of the final layout by redistributing and aligning boxes in the layout. We demonstrate that the proposed solution can generate symmetric facade layouts efficiently. © 2015 IEEE.
Symmetrization of Facade Layouts
Jiang, Haiyong; Yan, Dong-Ming; Dong, Weiming; Wu, Fuzhang; Nan, Liangliang; Zhang, Xiaopeng
2016-01-01
We present an automatic approach for symmetrizing urban facade layouts. Our method can generate a symmetric layout through minimally modifying the original input layout. Based on the principles of symmetry in urban design, we formulate facade layout symmetrization as an optimization problem. Our method further enhances the regularity of the final layout by redistributing and aligning elements in the layout. We demonstrate that the proposed solution can effectively generate symmetric facade layouts.
Jiang, Haiyong; Dong, Weiming; Yan, Dongming; Zhang, Xiaopeng
2016-01-01
We present an automatic algorithm for symmetrizing facade layouts. Our method symmetrizes a given facade layout while minimally modifying the original layout. Based on the principles of symmetry in urban design, we formulate the problem of facade layout symmetrization as an optimization problem. Our system further enhances the regularity of the final layout by redistributing and aligning boxes in the layout. We demonstrate that the proposed solution can generate symmetric facade layouts efficiently. © 2015 IEEE.
Symmetrization of Facade Layouts
Jiang, Haiyong
2016-02-26
We present an automatic approach for symmetrizing urban facade layouts. Our method can generate a symmetric layout through minimally modifying the original input layout. Based on the principles of symmetry in urban design, we formulate facade layout symmetrization as an optimization problem. Our method further enhances the regularity of the final layout by redistributing and aligning elements in the layout. We demonstrate that the proposed solution can effectively generate symmetric facade layouts.
Non-Euclidean Geometry and Gravitation
Directory of Open Access Journals (Sweden)
Stavroulakis N.
2006-04-01
Full Text Available A great deal of misunderstandings and mathematical errors are involved in the currently accepted theory of the gravitational field generated by an isotropic spherical mass. The purpose of the present paper is to provide a short account of the rigorous mathematical theory and exhibit a new formulation of the problem. The solution of the corresponding equations of gravitation points out several new and unusual features of the stationary gravitational field which are related to the non-Euclidean structure of the space. Moreover it precludes the black hole from being a mathematical and physical notion.
International Nuclear Information System (INIS)
Bassi, Angelo; Großardt, André; Ulbricht, Hendrik
2017-01-01
We discuss effects of loss of coherence in low energy quantum systems caused by or related to gravitation, referred to as gravitational decoherence. These effects, resulting from random metric fluctuations, for instance, promise to be accessible by relatively inexpensive table-top experiments, way before the scales where true quantum gravity effects become important. Therefore, they can provide a first experimental view on gravity in the quantum regime. We will survey models of decoherence induced both by classical and quantum gravitational fluctuations; it will be manifest that a clear understanding of gravitational decoherence is still lacking. Next we will review models where quantum theory is modified, under the assumption that gravity causes the collapse of the wave functions, when systems are large enough. These models challenge the quantum-gravity interplay, and can be tested experimentally. In the last part we have a look at the state of the art of experimental research. We will review efforts aiming at more and more accurate measurements of gravity ( G and g ) and ideas for measuring conventional and unconventional gravity effects on nonrelativistic quantum systems. (topical review)
Rahvar, Sohrab
2018-05-01
In this work, we study the interaction of the electromagnetic wave (EW) from a distant quasar with the gravitational wave (GW) sourced by the binary stars. While in the regime of geometric optics, the light bending due to this interaction is negligible, we show that the phase shifting on the wavefront of an EW can produce the diffraction pattern on the observer plane. The diffraction of the light (with the wavelength of λe) by the gravitational wave playing the role of gravitational grating (with the wavelength of λg) has the diffraction angle of Δβ ˜ λe/λg. The relative motion of the observer, the source of gravitational wave and the quasar results in a relative motion of the observer through the interference pattern on the observer plane. The consequence of this fringe crossing is the modulation in the light curve of a quasar with the period of few hours in the microwave wavelength. The optical depth for the observation of this phenomenon for a Quasar with the multiple images strongly lensed by a galaxy where the light trajectory of some of the images crosses the lensing galaxy is τ ≃ 0.2. By shifting the time-delay of the light curves of the multiple images in a strong lensed quasar and removing the intrinsic variations of a quasar, our desired signals, as a new method for detection of GWs can be detected.
Pre-Big-Bang bubbles from the gravitational instability of generic string vacua
International Nuclear Information System (INIS)
Buonanno, A.; Damour, T.; Veneziano, G.
1999-01-01
We formulate the basic postulate of pre-Big-Bang cosmology as one of 'asymptotic past triviality', by which we mean that the initial state is a generic perturbative solution of the tree-level low-energy effective action. Such a past-trivial 'string vacuum' is made of an arbitrary ensemble of incoming gravitational and dilatonic waves, and is generically prone to gravitational instability, leading to the possible formation of many black holes hiding singular space-like hypersurfaces. Each such singular space-like hypersurface of gravitational collapse becomes, in the string-frame metric, the usual Big-Bang t = 0 hypersurface, i.e. the place of birth of a baby Friedmann universe after a period of dilaton-driven inflation. Specializing to the spherically symmetric case, we review and reinterpret previous work on the subject, and propose a simple, scale-invariant criterion for collapse/inflation in terms of asymptotic data at past null infinity. Those data should determine whether, when, and where collapse/inflation occurs, and, when it does, fix its characteristics, including anisotropies on the Big-Bang hypersurface whose imprint could have survived till now. Using Bayesian probability concepts, we finally attempt to answer some fine-tuning objections recently moved to the pre-Big-Bang scenario
Pre-Big-Bang bubbles from the gravitational instability of generic string vacua
Energy Technology Data Exchange (ETDEWEB)
Buonanno, A.; Damour, T.; Veneziano, G
1999-03-22
We formulate the basic postulate of pre-Big-Bang cosmology as one of 'asymptotic past triviality', by which we mean that the initial state is a generic perturbative solution of the tree-level low-energy effective action. Such a past-trivial 'string vacuum' is made of an arbitrary ensemble of incoming gravitational and dilatonic waves, and is generically prone to gravitational instability, leading to the possible formation of many black holes hiding singular space-like hypersurfaces. Each such singular space-like hypersurface of gravitational collapse becomes, in the string-frame metric, the usual Big-Bang t = 0 hypersurface, i.e. the place of birth of a baby Friedmann universe after a period of dilaton-driven inflation. Specializing to the spherically symmetric case, we review and reinterpret previous work on the subject, and propose a simple, scale-invariant criterion for collapse/inflation in terms of asymptotic data at past null infinity. Those data should determine whether, when, and where collapse/inflation occurs, and, when it does, fix its characteristics, including anisotropies on the Big-Bang hypersurface whose imprint could have survived till now. Using Bayesian probability concepts, we finally attempt to answer some fine-tuning objections recently moved to the pre-Big-Bang scenario.
Pre-big bang bubbles from the gravitational instability of generic string vacua
Buonanno, A; Veneziano, Gabriele
1999-01-01
We formulate the basic postulate of pre-big bang cosmology as one of ``asymptotic past triviality'', by which we mean that the initial state is a generic perturbative solution of the tree-level low-energy effective action. Such a past-trivial ``string vacuum'' is made of an arbitrary ensemble of incoming gravitational and dilatonic waves, and is generically prone to gravitational instability, leading to the possible formation of many black holes hiding singular space-like hypersurfaces. Each such singular space-like hypersurface of gravitational collapse becomes, in the string-frame metric, the usual big-bang t=0 hypersurface, i.e. the place of birth of a baby Friedmann universe after a period of dilaton-driven inflation. Specializing to the spherically-symmetric case, we review and reinterpret previous work on the subject, and propose a simple, scale-invariant criterion for collapse/inflation in terms of asymptotic data at past null infinity. Those data should determine whether, when, and where collapse/infl...
Comment on 'Late-time tails of a self-gravitating massless scalar field revisited'
International Nuclear Information System (INIS)
Szpak, Nikodem
2009-01-01
Bizon et al (2009 Class. Quantum Grav. 26 175006) discuss the power-law tail in the long-time evolution of a spherically symmetric self-gravitating massless scalar field in odd spatial dimensions. They derive explicit expressions for the leading-order asymptotics for solutions with small initial data by using formal series expansions. Unfortunately, this approach misses an interesting observation that the actual decay rate is a product of asymptotic cancellations occurring due to a special structure of the nonlinear terms. Here, we show that one can calculate the leading asymptotics more directly by recognizing the special structure and cancellations already on the level of the wave equation. (comments and replies)
The status of the Brazilian spherical detector
International Nuclear Information System (INIS)
Aguiar, O D; Andrade, L A; Filho, L Camargo; Costa, C A; Araujo, J C N de; Neto, E C de Rey; Souza, S T de; Fauth, A C; Frajuca, C; Frossati, G; Furtado, S R; Furtado, V G S; Magalhaes, N S; Jr, R M Marinho; Matos, E S; Meliani, M T; Melo, J L; Miranda, O D; Jr, N F Oliveira; Ribeiro, K L; Salles, K B M; Stellati, C; Jr, W F Velloso
2002-01-01
The first phase of the Brazilian Graviton Project is the construction and operation of the gravitational wave detector Mario Schenberg at the Physics Institute of the University of Sao Paulo. This gravitational wave spherical antenna is planned to feature a sensitivity better than h = 10 -21 Hz -1/2 at the 3.0-3.4 kHz bandwidth, and to work not only as a detector, but also as a testbed for the development of new technologies. Here we present the status of this detector
International Nuclear Information System (INIS)
Balakrishna, Jayashree; Bondarescu, Ruxandra; Daues, Gregory; Bondarescu, Mihai
2008-01-01
Excited state soliton stars are studied numerically for the first time. The stability of spherically symmetric S-branch excited state oscillatons under radial perturbations is investigated using a 1D code. We find that these stars are inherently unstable either migrating to the ground state or collapsing to black holes. Higher excited state configurations are observed to cascade through intermediate excited states during their migration to the ground state. This is similar to excited state boson stars [J. Balakrishna, E. Seidel, and W.-M. Suen, Phys. Rev. D 58, 104004 (1998).]. Ground state oscillatons are then studied in full 3D numerical relativity. Finding the appropriate gauge condition for the dynamic oscillatons is much more challenging than in the case of boson stars. Different slicing conditions are explored, and a customized gauge condition that approximates polar slicing in spherical symmetry is implemented. Comparisons with 1D results and convergence tests are performed. The behavior of these stars under small axisymmetric perturbations is studied and gravitational waveforms are extracted. We find that the gravitational waves damp out on a short time scale, enabling us to obtain the complete waveform. This work is a starting point for the evolution of real scalar field systems with arbitrary symmetries
Effective pair potentials for spherical nanoparticles
International Nuclear Information System (INIS)
Van Zon, Ramses
2009-01-01
An effective description for rigid spherical nanoparticles in a fluid of point particles is presented. The points inside the nanoparticles and the point particles are assumed to interact via spherically symmetric additive pair potentials, while the distribution of points inside the nanoparticles is taken to be spherically symmetric and smooth. The resulting effective pair interactions between a nanoparticle and a point particle, as well as between two nanoparticles, are then given by spherically symmetric potentials. If overlap between particles is allowed, as can occur for some forms of the pair potentials, the effective potential generally has non-analytic points. It is shown that for each effective potential the expressions for different overlapping cases can be written in terms of one analytic auxiliary potential. Even when only non-overlapping situations are possible, the auxiliary potentials facilitate the formulation of the effective potentials. Effective potentials for hollow nanoparticles (appropriate e.g. for buckyballs) are also considered and shown to be related to those for solid nanoparticles. For hollow nanoparticles overlap is more physical, since this covers the case of a smaller particle embedded in a larger, hollow nanoparticle. Finally, explicit expressions are given for the effective potentials derived from basic pair potentials of power law and exponential form, as well as from the commonly used London–van der Waals, Morse, Buckingham, and Lennard-Jones potentials. The applicability of the latter is demonstrated by comparison with an atomic description of nanoparticles with an internal face centered cubic structure
Energy Technology Data Exchange (ETDEWEB)
Dowker, J S, E-mail: dowker@man.ac.uk [Theory Group, School of Physics and Astronomy, University of Manchester, Manchester (United Kingdom)
2011-08-07
A piston is introduced into a spherical lune Casimir cavity turning it into two adjacent lunes separated by the (hemispherical) piston. On the basis of zeta-function regularization, the vacuum energy of the arrangement is finite for conformal propagation in spacetime. For even spheres this energy is independent of the angle of the lune. For odd dimensions it is shown that for all Neumann, or all Dirichlet, boundary conditions the piston is repelled or attracted by the nearest wall if d = 3, 7, ... or if d = 1, 5, ... , respectively. For hybrid N-D conditions these requirements are switched. If a mass is added, divergences arise which render the model suspect. The analysis, however, is relatively straightforward and involves the Barnes zeta function. The extension to finite temperatures is made and it is shown that for the 3, 7, ... series of odd spheres, the repulsion by the walls continues but that, above a certain temperature, the free energy acquires two minima symmetrically placed about the midpoint.
International Nuclear Information System (INIS)
Dowker, J S
2011-01-01
A piston is introduced into a spherical lune Casimir cavity turning it into two adjacent lunes separated by the (hemispherical) piston. On the basis of zeta-function regularization, the vacuum energy of the arrangement is finite for conformal propagation in spacetime. For even spheres this energy is independent of the angle of the lune. For odd dimensions it is shown that for all Neumann, or all Dirichlet, boundary conditions the piston is repelled or attracted by the nearest wall if d = 3, 7, ... or if d = 1, 5, ... , respectively. For hybrid N-D conditions these requirements are switched. If a mass is added, divergences arise which render the model suspect. The analysis, however, is relatively straightforward and involves the Barnes zeta function. The extension to finite temperatures is made and it is shown that for the 3, 7, ... series of odd spheres, the repulsion by the walls continues but that, above a certain temperature, the free energy acquires two minima symmetrically placed about the midpoint.
Ciufolini, I; Moschella, U; Fre, P
2001-01-01
Gravitational waves (GWs) are a hot topic and promise to play a central role in astrophysics, cosmology, and theoretical physics. Technological developments have led us to the brink of their direct observation, which could become a reality in the coming years. The direct observation of GWs will open an entirely new field: GW astronomy. This is expected to bring a revolution in our knowledge of the universe by allowing the observation of previously unseen phenomena, such as the coalescence of compact objects (neutron stars and black holes), the fall of stars into supermassive black holes, stellar core collapses, big-bang relics, and the new and unexpected.With a wide range of contributions by leading scientists in the field, Gravitational Waves covers topics such as the basics of GWs, various advanced topics, GW detectors, astrophysics of GW sources, numerical applications, and several recent theoretical developments. The material is written at a level suitable for postgraduate students entering the field.
Hakim, Rémi
1994-01-01
Il existe à l'heure actuelle un certain nombre de théories relativistes de la gravitation compatibles avec l'expérience et l'observation. Toutefois, la relativité générale d'Einstein fut historiquement la première à fournir des résultats théoriques corrects en accord précis avec les faits.
He, Ping
2012-01-01
The long-standing puzzle surrounding the statistical mechanics of self-gravitating systems has not yet been solved successfully. We formulate a systematic theoretical framework of entropy-based statistical mechanics for spherically symmetric collisionless self-gravitating systems. We use an approach that is very different from that of the conventional statistical mechanics of short-range interaction systems. We demonstrate that the equilibrium states of self-gravitating systems consist of both mechanical and statistical equilibria, with the former characterized by a series of velocity-moment equations and the latter by statistical equilibrium equations, which should be derived from the entropy principle. The velocity-moment equations of all orders are derived from the steady-state collisionless Boltzmann equation. We point out that the ergodicity is invalid for the whole self-gravitating system, but it can be re-established locally. Based on the local ergodicity, using Fermi-Dirac-like statistics, with the non-degenerate condition and the spatial independence of the local microstates, we rederive the Boltzmann-Gibbs entropy. This is consistent with the validity of the collisionless Boltzmann equation, and should be the correct entropy form for collisionless self-gravitating systems. Apart from the usual constraints of mass and energy conservation, we demonstrate that the series of moment or virialization equations must be included as additional constraints on the entropy functional when performing the variational calculus; this is an extension to the original prescription by White & Narayan. Any possible velocity distribution can be produced by the statistical-mechanical approach that we have developed with the extended Boltzmann-Gibbs/White-Narayan statistics. Finally, we discuss the questions of negative specific heat and ensemble inequivalence for self-gravitating systems.
UCN gravitational spectrometer
International Nuclear Information System (INIS)
Kawabata, Yuji
1988-01-01
Concept design is carried out of two types of ultra cold neutron scallering equipment using the fall-focusing principle. One of the systems comprises a vertical gravitational spectrometer and the other includes a horizontal gravitation analyzer. A study is made of their performance and the following results are obtained. Fall-focusing type ultra cold neutron scattering equipment can achieve a high accuracy for measurement of energy and momentum. Compared with conventional neutron scattering systems, this type of equipment can use neutron very efficiently because scattered neutrons within a larger solid angle can be used. The maximum solid angle is nearly 4π and 2π for the vertical and horizontal type, respectively. Another feature is that the size of equipment can be reduced. In the present concept design, the equipment is spherical with a diameter of about 1 m, as compared with NESSIE which is 6.7 m in length and 4.85 m in height with about the same accuracy. Two horizontal analyzers and a vertical spectroscope are proposed. They are suitable for angle-dependent non-elastic scattering in the neutron velocity range of 6∼15 m/s, pure elastic scattering in the range of 4∼7 m/s, or angle-integration non-elastic scattering in the range of 4∼15 m/s. (N.K.)
Spherically symmetric inhomogeneous bianisotropic media: Wave propagation and light scattering
DEFF Research Database (Denmark)
Novitsky, Andrey; Shalin, Alexander S.; Lavrinenko, Andrei
2017-01-01
We develop a technique for finding closed-form expressions for electromagnetic fields in radially inhomogeneous bianisotropic media, both the solutions of the Maxwell equations and material tensors being defined by the set of auxiliary two-dimensional matrices. The approach is applied to determine...
Spherically symmetric random walks. II. Dimensionally dependent critical behavior
International Nuclear Information System (INIS)
Bender, C.M.; Boettcher, S.; Meisinger, P.N.
1996-01-01
A recently developed model of random walks on a D-dimensional hyperspherical lattice, where D is not restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state distributions of random walkers are obtained for all dimensions D approx-gt 0 by solving a discrete eigenvalue problem. These distributions exhibit dimensionally dependent critical behavior as a function of the birth rate. This remarkably simple model exhibits a second-order phase transition with a universal, nontrivial critical exponent for all dimensions D approx-gt 0. copyright 1996 The American Physical Society
A new model for spherically symmetric anisotropic compact star
Energy Technology Data Exchange (ETDEWEB)
Maurya, S.K.; Dayanandan, Baiju [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Gupta, Y.K. [Raj Kumar Goel Institute of Technology, Department of Mathematics, Ghaziabad, UP (India); Ray, Saibal [Government College of Engineering and Ceramic Technology, Department of Physics, Kolkata, West Bengal (India)
2016-05-15
In this article we obtain a new anisotropic solution for Einstein's field equations of embedding class one metric. The solution represents realistic objects such as Her X-1 and RXJ 1856-37. We perform a detailed investigation of both objects by solving numerically the Einstein field equations with anisotropic pressure. The physical features of the parameters depend on the anisotropic factor i.e. if the anisotropy is zero everywhere inside the star then the density and pressures will become zero and the metric turns out to be flat. We report our results and compare with the above mentioned two compact objects as regards a number of key aspects: the central density, the surface density onset and the critical scaling behaviour, the effective mass and radius ratio, the anisotropization with isotropic initial conditions, adiabatic index and red shift. Along with this we have also made a comparison between the classical limit and theoretical model treatment of the compact objects. Finally we discuss the implications of our findings for the stability condition in a relativistic compact star. (orig.)
Boundary stress tensors for spherically-symmetric conformal Rindler observers
Energy Technology Data Exchange (ETDEWEB)
Culetu, Hristu [Ovidius University, Constanta (Romania)
2010-06-15
The boundary energy-momentum tensors for a static observer in the conformally flat Rindler geometry are considered. We find that the surface energy density is positive far from the Planck world, but that the transversal pressures are negative. The kinematical parameters associated with the nongeodesic congruence of static observers are computed. The entropy S corresponding to the degrees of freedom on the 2-surface of constant {rho} and t equals the horizon entropy of a black hole with a time-dependent mass, and the Padmanabhan expression E = 2ST is obeyed. The 2-surface shear tensor is vanishing, and the coefficient of the bulk viscosity {zeta} is 1/16 {pi}, so the negative pressure due to it acts as a surface tension.
International Nuclear Information System (INIS)
Rockstroh, J.M.
1977-01-01
Cosmic-ray electrons generate the observed radio-frequency background. Previous attempts in the literature to reconcile quantitatively the measured radio-frequency intensity with the intensity deduced from the electron spectrum measured at earth have culminated in the problem that to get the respective emissivities to agree, an unacceptably high interstellar B field must be chosen. In the light of new experimental data on the emissivity as deduced from H II region studies and on the functional dependence of the diffusion coefficient with solar radius and particle rigidity, the assumptions under which the electron emissivity comparison has been made have been reexamined closely. The paradox between predicted and measured emissivity was resolved by ascribing to the magnetic fields of the galaxy a distribution of magnetic field strengths. From modified synchrotron formulas, the interstellar electron spectrum has been constructed from the radio frequency emission data with greatly improved precision. The interstellar electron spectrum has been determined independently of the solar modulation and provides, therefore, an estimate of the absolute depth of the electron modulation. Then the measured electron, proton, and helium-nuclei fluxes were systematically compared to the predictions of the spherically symmetric Fokker-Planck equation using the electron modulation as a base. A previously unnoticed non-tracking of the modulation parameters was observed during the recent recovery that did not occur during the 1965 to 1969 period. Although the argument could be presented just as well by attributing the anomaly to the nuclei, the discussion here arbitrarily tailored it to the electrons, and this new phenomenon was named, the modulation reluctance of the cosmic-ray electrons
Golden, Ryan; Cho, Ilwoo
2015-01-01
In this paper, we study structure theorems of algebras of symmetric functions. Based on a certain relation on elementary symmetric polynomials generating such algebras, we consider perturbation in the algebras. In particular, we understand generators of the algebras as perturbations. From such perturbations, define injective maps on generators, which induce algebra-monomorphisms (or embeddings) on the algebras. They provide inductive structure theorems on algebras of symmetric polynomials. As...
Gravitational Zero Point Energy induces Physical Observables
Garattini, Remo
2010-01-01
We consider the contribution of Zero Point Energy on the induced Cosmological Constant and on the induced Electric/Magnetic charge in absence of matter fields. The method is applicable to every spherically symmetric background. Extensions to a generic $f(R) $ theory are also allowed. Only the graviton appears to be fundamental to the determination of Zero Point Energy.
Light rays in gravitating, refractive media
International Nuclear Information System (INIS)
Noonan, T.W.
1982-01-01
The field-to-particle method of H. P. Robertson is applied to the general-relativistic Maxwell equations in order to obtain the general-relativistic equation of motion for a photon in a refractive medium. For the special case of an uncharged, refractive, spherically symmetric mass, the exact first-order differential equation for the light-ray path is given
Gravitational Wave Experiments - Proceedings of the First Edoardo Amaldi Conference
Coccia, E.; Pizzella, G.; Ronga, F.
1995-07-01
Production of Gravitational Radiation by Particle Accelerators and by High Power Lasers * NESTOR: An Underwater Cerenkov Detector for Neutrino Astronomy * A Cosmic-Ray Veto System for the Gravitational Wave Detector NAUTLUS * Interferometers * Development of a 20m Prototype Laser Interferometric Gravitational Wave Detector at NAO * Production of Higher-Order Light Modes by High Quality Optical Components * Vibration Isolation and Suspension Systems for Laser Interferometer Gravitational Wave Detectors * Quality Factors of Stainless Steel Pendulum Wires * Reduction of Suspension Thermal Noises in Laser Free Masses Gravitational Antenna by Correlation of the Output with Additional Optical Signal * Resonant Detectors * Regeneration Effects in a Resonant Gravitational Wave Detector * A Cryogenic Sapphire Transducer with Double Frequency Pumping for Resonant Mass GW Detectors * Effect of Parametric Instability of Gravitational Wave Antenna with Microwave Cavity Transducer * Resonators of Novel Geometry for Large Mass Resonant Transducers * Measurements on the Gravitational Wave Antenna ALTAIR Equipped with a BAE Transducer * The Rome BAE Transducer: Perspectives of its Application to Ultracryogenic Gravitational Wave Antennas * Behavior of a de SQUID Tightly Coupled to a High-Q Resonant Transducer * High Q-Factor LC Resonators for Optimal Coupling * Comparison Between Different Data Analysis Procedures for Gravitational Wave Pulse Detection * Supernova 1987A Rome Maryland Gravitational Radiation Antenna Observations * Analysis of the Data Recorded by the Maryland and Rome Gravitational-Wave Detectors and the Seismic Data from Moscow and Obninsk Station during SN1987A * Multitransducer Resonant Gravitational Antennas * Local Array of High Frequency Antennas * Interaction Cross-Sections for Spherical Resonant GW Antennae * Signal-To-Noise Analysis for a Spherical Gravitational Wave Antenna Instrumented with Multiple Transducers * On the Design of Ultralow Temperature Spherical
Energy Technology Data Exchange (ETDEWEB)
Leutwyler, H; Mallik, S
1986-12-01
The effective action for fermions moving in external gravitational and gauge fields is analyzed in terms of the corresponding external field propagator. The central object in our approach is the covariant energy-momentum tensor which is extracted from the regular part of the propagator at short distances. It is shown that the Lorentz anomaly, the conformal anomaly and the gauge anomaly can be expressed in terms of the local polynomials which determine the singular part of the propagator. (There are no coordinate anomalies). Except for the conformal anomaly, for which we give explicit representations only in dless than or equal to4, we consider an arbitrary number of dimensions.
Directory of Open Access Journals (Sweden)
Metin SALTIK
1996-03-01
Full Text Available According to classical electromagnetic theory, an accelerated charge or system of charges radiates electromagnetic waves. In a radio transmitter antenna charges are accelerated along the antenna and release electromagnetic waves, which is radiated at the velocity of light in the surrounding medium. All of the radio transmitters work on this principle today. In this study an analogy is established between the principles by which accelerated charge systems markes radiation and the accelerated mass system, and the systems cousing gravitational radiation are investigated.
International Nuclear Information System (INIS)
Turner, E.L.
1989-01-01
The author discusses how gravitational lens studies is becoming a major focus of extragalactic astronomy and cosmology. This review is organized into five parts: an overview of the observational situation, a look at the state of theoretical work on lenses, a detailed look at three recently discovered types of lensing phenomena (luminous arcs, radio rings, quasar-galaxy associations), a review of progress on two old problems in lens studies (deriving unique lens mass distribution models, measurements of differential time delays), and an attempt to look into the future of lens studies
International Nuclear Information System (INIS)
Sahni, D.C.; Sharma, A.
2000-01-01
The integral form of one-speed, spherically symmetric neutron transport equation with isotropic scattering is considered. Two standard problems are solved using normal mode expansion technique. The expansion coefficients are obtained by solving their singular integral equations. It is shown that these expansion coefficients provide a representation of all spherical harmonics moments of the angular flux as a superposition of Bessel functions. It is seen that large errors occur in the computation of higher moments unless we take certain precautions. The reasons for this phenomenon are explained. They throw some light on the failure of spherical harmonics method in treating spherical geometry problems as observed by Aronsson
Topological quantization of gravitational fields
International Nuclear Information System (INIS)
Patino, Leonardo; Quevedo, Hernando
2005-01-01
We introduce the method of topological quantization for gravitational fields in a systematic manner. First we show that any vacuum solution of Einstein's equations can be represented in a principal fiber bundle with a connection that takes values in the Lie algebra of the Lorentz group. This result is generalized to include the case of gauge matter fields in multiple principal fiber bundles. We present several examples of gravitational configurations that include a gravitomagnetic monopole in linearized gravity, the C-energy of cylindrically symmetric fields, the Reissner-Nordstroem and the Kerr-Newman black holes. As a result of the application of the topological quantization procedure, in all the analyzed examples we obtain conditions implying that the parameters entering the metric in each case satisfy certain discretization relationships
Gravitational waves and dragging effects
Bičák, Jiří; Katz, Joseph; Lynden-Bell, Donald
2008-08-01
Linear and rotational dragging effects of gravitational waves on local inertial frames are studied in purely vacuum spacetimes. First, the linear dragging caused by a simple cylindrical pulse is investigated. Surprisingly strong transverse effects of the pulse are exhibited. The angular momentum in cylindrically symmetric spacetimes is then defined and confronted with some results in the literature. In the main part, a general procedure is developed for studying weak gravitational waves with translational but not axial symmetry which can carry angular momentum. After a suitable averaging the rotation of local inertial frames due to such rotating waves can be calculated explicitly and illustrated graphically. This is done in detail in the accompanying paper. Finally, the rotational dragging is given for strong cylindrical waves interacting with a rotating cosmic string with a small angular momentum.
Gravitational Waves from Oscillons after Inflation.
Antusch, Stefan; Cefalà, Francesco; Orani, Stefano
2017-01-06
We investigate the production of gravitational waves during preheating after inflation in the common case of field potentials that are asymmetric around the minimum. In particular, we study the impact of oscillons, comparatively long lived and spatially localized regions where a scalar field (e.g., the inflaton) oscillates with large amplitude. Contrary to a previous study, which considered a symmetric potential, we find that oscillons in asymmetric potentials associated with a phase transition can generate a pronounced peak in the spectrum of gravitational waves that largely exceeds the linear preheating spectrum. We discuss the possible implications of this enhanced amplitude of gravitational waves. For instance, for low scale inflation models, the contribution from the oscillons can strongly enhance the observation prospects at current and future gravitational wave detectors.
Gravitational Waves from a Dark Phase Transition.
Schwaller, Pedro
2015-10-30
In this work, we show that a large class of models with a composite dark sector undergo a strong first order phase transition in the early Universe, which could lead to a detectable gravitational wave signal. We summarize the basic conditions for a strong first order phase transition for SU(N) dark sectors with n_{f} flavors, calculate the gravitational wave spectrum and show that, depending on the dark confinement scale, it can be detected at eLISA or in pulsar timing array experiments. The gravitational wave signal provides a unique test of the gravitational interactions of a dark sector, and we discuss the complementarity with conventional searches for new dark sectors. The discussion includes the twin Higgs and strongly interacting massive particle models as well as symmetric and asymmetric composite dark matter scenarios.
Symmetric cryptographic protocols
Ramkumar, Mahalingam
2014-01-01
This book focuses on protocols and constructions that make good use of symmetric pseudo random functions (PRF) like block ciphers and hash functions - the building blocks for symmetric cryptography. Readers will benefit from detailed discussion of several strategies for utilizing symmetric PRFs. Coverage includes various key distribution strategies for unicast, broadcast and multicast security, and strategies for constructing efficient digests of dynamic databases using binary hash trees. • Provides detailed coverage of symmetric key protocols • Describes various applications of symmetric building blocks • Includes strategies for constructing compact and efficient digests of dynamic databases
Rotationally symmetric breather-like solutions to the sine-Gordon equation
International Nuclear Information System (INIS)
Olsen, O.H.; Samuelsen, M.R.
1980-01-01
Breather-like solutions to the spherically symmetric sine-Gordon equation are examined numerically. Depending on the initial conditions they either exhibit a return effect or expand towards infinity. (orig.)
Spherical collapse in chameleon models
International Nuclear Information System (INIS)
Brax, Ph.; Rosenfeld, R.; Steer, D.A.
2010-01-01
We study the gravitational collapse of an overdensity of nonrelativistic matter under the action of gravity and a chameleon scalar field. We show that the spherical collapse model is modified by the presence of a chameleon field. In particular, we find that even though the chameleon effects can be potentially large at small scales, for a large enough initial size of the inhomogeneity the collapsing region possesses a thin shell that shields the modification of gravity induced by the chameleon field, recovering the standard gravity results. We analyse the behaviour of a collapsing shell in a cosmological setting in the presence of a thin shell and find that, in contrast to the usual case, the critical density for collapse in principle depends on the initial comoving size of the inhomogeneity
Spherical collapse in chameleon models
Energy Technology Data Exchange (ETDEWEB)
Brax, Ph. [Institut de Physique Théorique, CEA, IPhT, CNRS, URA 2306, F-91191Gif/Yvette Cedex (France); Rosenfeld, R. [Instituto de Física Teórica, Universidade Estadual Paulista, Rua Dr. Bento T. Ferraz, 271, 01140-070, São Paulo (Brazil); Steer, D.A., E-mail: brax@spht.saclay.cea.fr, E-mail: rosenfel@ift.unesp.br, E-mail: daniele.steer@apc.univ-paris7.fr [APC, UMR 7164, CNRS, Université Paris 7, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13 (France)
2010-08-01
We study the gravitational collapse of an overdensity of nonrelativistic matter under the action of gravity and a chameleon scalar field. We show that the spherical collapse model is modified by the presence of a chameleon field. In particular, we find that even though the chameleon effects can be potentially large at small scales, for a large enough initial size of the inhomogeneity the collapsing region possesses a thin shell that shields the modification of gravity induced by the chameleon field, recovering the standard gravity results. We analyse the behaviour of a collapsing shell in a cosmological setting in the presence of a thin shell and find that, in contrast to the usual case, the critical density for collapse in principle depends on the initial comoving size of the inhomogeneity.
Spherical Collapse in Chameleon Models
Brax, Ph; Steer, D A
2010-01-01
We study the gravitational collapse of an overdensity of nonrelativistic matter under the action of gravity and a chameleon scalar field. We show that the spherical collapse model is modified by the presence of a chameleon field. In particular, we find that even though the chameleon effects can be potentially large at small scales, for a large enough initial size of the inhomogeneity the collapsing region possesses a thin shell that shields the modification of gravity induced by the chameleon field, recovering the standard gravity results. We analyse the behaviour of a collapsing shell in a cosmological setting in the presence of a thin shell and find that, in contrast to the usual case, the critical density for collapse depends on the initial comoving size of the inhomogeneity.
Spherical cows in dark matter indirect detection
Energy Technology Data Exchange (ETDEWEB)
Bernal, Nicolás [Centro de Investigaciones, Universidad Antonio Nariño, Cra 3 Este # 47A-15, Bogotá (Colombia); Necib, Lina; Slatyer, Tracy R., E-mail: nicolas.bernal@uan.edu.co, E-mail: lnecib@mit.edu, E-mail: tslatyer@mit.edu [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)
2016-12-01
Dark matter (DM) halos have long been known to be triaxial, but in studies of possible annihilation and decay signals they are often treated as approximately spherical. In this work, we examine the asymmetry of potential indirect detection signals of DM annihilation and decay, exploiting the large statistics of the hydrodynamic simulation Illustris. We carefully investigate the effects of the baryons on the sphericity of annihilation and decay signals for both the case where the observer is at 8.5 kpc from the center of the halo (exemplified in the case of Milky Way-like halos), and for an observer situated well outside the halo. In the case of Galactic signals, we find that both annihilation and decay signals are expected to be quite symmetric, with axis ratios very different from 1 occurring rarely. In the case of extragalactic signals, while decay signals are still preferentially spherical, the axis ratio for annihilation signals has a much flatter distribution, with elongated profiles appearing frequently. Many of these elongated profiles are due to large subhalos and/or recent mergers. Comparing to gamma-ray emission from the Milky Way and X-ray maps of clusters, we find that the gamma-ray background appears less spherical/more elongated than the expected DM signal from the large majority of halos, and the Galactic gamma ray excess appears very spherical, while the X-ray data would be difficult to distinguish from a DM signal by elongation/sphericity measurements alone.
Quasilocal energy and conserved charges derived from the gravitational action
International Nuclear Information System (INIS)
Brown, J.D.; York, J.W. Jr.
1993-01-01
The quasilocal energy of gravitational and matter fields in a spatially bounded region is obtained by employing a Hamilton-Jacobi analysis of the action functional. First, a surface stress-energy-momentum tensor is defined by the functional derivative of the action with respect to the three-metric on 3 B, the history of the system's boundary. Energy surface density, momentum surface density, and spatial stress are defined by projecting the surface stress tensor normally and tangentially to a family of spacelike two-surfaces that foliate 3 B. The integral of the energy surface density over such a two-surface B is the quasilocal energy associated with a spacelike three-surface Σ whose orthogonal intersection with 3 B is the boundary B. The resulting expression for quasilocal energy is given in terms of the total mean curvature of the spatial boundary B as a surface embedded in Σ. The quasilocal energy is also the value of the Hamiltonian that generates unit magnitude proper-time translations on 3 B in the timelike direction orthogonal to B. Conserved charges such as angular momentum are defined using the surface stress tensor and Killing vector fields on 3 B. For spacetimes that are asymptotically flat in spacelike directions, the quasilocal energy and angular momentum defined here agree with the results of Arnowitt, Deser, and Misner in the limit that the boundary tends to spatial infinity. For spherically symmetric spacetimes, it is shown that the quasilocal energy has the correct Newtonian limit, and includes a negative contribution due to gravitational binding
Quantum self-gravitating collapsing matter in a quantum geometry
International Nuclear Information System (INIS)
Campiglia, Miguel; Gambini, Rodolfo; Olmedo, Javier; Pullin, Jorge
2016-01-01
The problem of how space–time responds to gravitating quantum matter in full quantum gravity has been one of the main questions that any program of quantization of gravity should address. Here we analyze this issue by considering the quantization of a collapsing null shell coupled to spherically symmetric loop quantum gravity. We show that the constraint algebra of canonical gravity is Abelian both classically and when quantized using loop quantum gravity techniques. The Hamiltonian constraint is well defined and suitable Dirac observables characterizing the problem were identified at the quantum level. We can write the metric as a parameterized Dirac observable at the quantum level and study the physics of the collapsing shell and black hole formation. We show how the singularity inside the black hole is eliminated by loop quantum gravity and how the shell can traverse it. The construction is compatible with a scenario in which the shell tunnels into a baby universe inside the black hole or one in which it could emerge through a white hole. (letter)
Strong gravitational lensing by a charged Kiselev black hole
Energy Technology Data Exchange (ETDEWEB)
Azreg-Ainou, Mustapha [Baskent University, Engineering Faculty, Ankara (Turkey); Bahamonde, Sebastian [University College London, Department of Mathematics, London (United Kingdom); Jamil, Mubasher [National University of Sciences and Technology (NUST), Department of Mathematics, School of Natural Sciences (SNS), Islamabad (Pakistan)
2017-06-15
We study the gravitational lensing scenario where the lens is a spherically symmetric charged black hole (BH) surrounded by quintessence matter. The null geodesic equations in the curved background of the black hole are derived. The resulting trajectory equation is solved analytically via perturbation and series methods for a special choice of parameters, and the distance of the closest approach to black hole is calculated. We also derive the lens equation giving the bending angle of light in the curved background. In the strong field approximation, the solution of the lens equation is also obtained for all values of the quintessence parameter w{sub q}. For all w{sub q}, we show that there are no stable closed null orbits and that corrections to the deflection angle for the Reissner-Nordstroem black hole when the observer and the source are at large, but finite, distances from the lens do not depend on the charge up to the inverse of the distances squared. A part of the present work, analyzed, however, with a different approach, is the extension of Younas et al. (Phys Rev D 92:084042, 2015) where the uncharged case has been treated. (orig.)
Static solutions with spherical symmetry in f(T) theories
International Nuclear Information System (INIS)
Wang Tower
2011-01-01
The spherically symmetric static solutions are searched for in some f(T) models of gravity theory with a Maxwell term. To do this, we demonstrate that reconstructing the Lagrangian of f(T) theories is sensitive to the choice of frame, and then we introduce a particular frame based on the conformally Cartesian coordinates. In this particular frame, the existence conditions of various solutions are presented. Our results imply that only a limited class of f(T) models can be solved in this frame. For more general models, the search for spherically symmetric static solutions is still an open and challenging problem, hopefully solvable in other frames.
Rotationally symmetric numerical solutions to the sine-Gordon equation
DEFF Research Database (Denmark)
Olsen, O. H.; Samuelsen, Mogens Rugholm
1981-01-01
We examine numerically the properties of solutions to the spherically symmetric sine-Gordon equation given an initial profile which coincides with the one-dimensional breather solution and refer to such solutions as ring waves. Expanding ring waves either exhibit a return effect or expand towards...
The 5D Fully-Covariant Theory of Gravitation and Its Astrophysical Applications
Directory of Open Access Journals (Sweden)
Tianxi Zhang
2014-12-01
Full Text Available In this paper, we comprehensively review the five-dimensional (5D fully-covariant theory of gravitation developed by Zhang two decades ago and its recent applications in astrophysics and cosmology. This 5D gravity describes not only the fields, but also the matter and its motion in a 5D spacetime. The greatest advantage of this theory is that there does not exist any unknown parameter, so that we can apply it to explain astrophysical and cosmological issues by quantitatively comparing the results obtained from it with observations and to predict new effects that could not be derived from any other gravitational theories. First, the 5D covariant description of matter and its motion enabled Zhang to analytically derive the fifteenth component of the 5D energy-momentum tensor of matter ( T - 44 , which significantly distinguishes this 5D gravity from other 5D gravitational theories that usually assumed a T - 44 with an unknown parameter, called the scalar charge s, and, thus, to split the 5D covariant field equation into (4 + 1 splitting form as the gravitational, electromagnetic, and scalar field equations. The gravitational field equation turns into the 4D Einstein’s field equation of general relativity if the scalar field is equal to unity. Then, Zhang solved the field equations and obtained an exact static spherically-symmetric external solution of the gravitational, electromagnetic and scalar fields, in which all integral constants were completely determined with a perfect set of simple numbers and parameters that only depend on the mass and electric charge of the matter, by comparing with the obtained weak internal solution of the fields at a large radial distance. In the Einstein frame, the exact field solution obtained from the 5D fully-covariant theory of gravitation reduces to the Schwarzschild solution when the matter is electrically neutral and the fields are weak in strength. This guarantees that the four fundamental tests (light
Centrioles in Symmetric Spaces
Quast, Peter
2011-01-01
We describe all centrioles in irreducible simply connected pointed symmetric spaces of compact type in terms of the root system of the ambient space, and we study some geometric properties of centrioles.
BOOK REVIEW: Gravitational Waves, Volume 1: Theory and Experiments
Poisson, Eric
2008-10-01
discussion is helpful, as it clarifies some of the puzzling aspects of general covariance. Next the treatment becomes more sophisticated: the waves are allowed to propagate in an arbitrary background spacetime, and the energy momentum carried by the wave is identified by the second-order perturbation of the Einstein tensor. In chapter 2 the waves are given a field-theoretic foundation that is less familiar (but refreshing) to a relativist, but would appeal to a practitioner of effective field theories. In an interesting section of chapter 2, the author gives a mass to the (classical) graviton and explores the physical consequences of this proposal. In chapter 3 the author returns to the standard linearized theory and develops the multipolar expansion of the gravitational-wave field in the context of slowly-moving sources; at leading order he obtains the famous quadrupole formula. His treatment is very detailed, and it includes a complete account of symmetric-tracefree tensors and tensorial spherical harmonics. It is, however, necessarily limited to sources with negligible internal gravity. Unfortunately (and this is a familiar complaint of relativists) the author omits to warn the reader of this important limitation. In fact, the chapter opens with a statement of the virial theorem of Newtonian gravity, which may well mislead the reader to believe that the linearized theory can be applied to a system bound by gravitational forces. This misconception is confirmed when, in chapter 4, the author applies the quadrupole formula to gravitationally-bound systems such as an inspiraling compact binary, a rigidly rotating body, and a mass falling toward a black hole. This said, the presentation of these main sources of gravitational waves is otherwise irreproachable, and a wealth of useful information is presented in a clear and lucid manner. For example, the discussion of inspiraling compact binaries includes a derivation of the orbital evolution of circular and eccentric orbits
A symmetrical rail accelerator
International Nuclear Information System (INIS)
Igenbergs, E.
1991-01-01
This paper reports on the symmetrical rail accelerator that has four rails, which are arranged symmetrically around the bore. The opposite rails have the same polarity and the adjacent rails the opposite polarity. In this configuration the radial force acting upon the individual rails is significantly smaller than in a conventional 2-rail configuration and a plasma armature is focussed towards the axis of the barrel. Experimental results indicate a higher efficiency compared to a conventional rail accelerator
International Nuclear Information System (INIS)
Matsuki, Takayuki
1976-01-01
Symmetric eikonal expansion for the scattering amplitude is formulated for nonrelativistic and relativistic potential scatterings and also for the quantum field theory. The first approximations coincide with those of Levy and Sucher. The obtained scattering amplitudes are time reversal invariant for all cases and are crossing symmetric for the quantum field theory in each order of approximation. The improved eikonal phase introduced by Levy and Sucher is also derived from the different approximation scheme from the above. (auth.)
Astronomical observations with a network of detectors of gravitational waves: Pt. 1
International Nuclear Information System (INIS)
Dhurandhar, S.V.; Tinto, Massimo
1988-01-01
Two different representations for the antenna pattern of Earth-based gravitational wave detectors (laser interferometers and bars) observing arbitrarily polarized waves are investigated in the long wavelength limit. We show that the response of a gravitational wave detector can be written either as a contraction between two symmetric trace-free (STF) tensors, one associated with the wave and the other with the detector, or as a linear combination of generalized spherical functions. We then apply this formalism to solve the simplest form of the 'inverse problem' for bursts: determining the direction of an incoming wave, the orientation of its polarization ellipse and the wave's two independent amplitudes, using only the response amplitudes of five wide-band detectors located in the same place. We give a simple linear expression for the components of the STF tensor that characterize the wave as a function of the detector responses. We then show how to solve for the wave's direction, polarization and amplitude from its STF tensor. (author)
Shearfree cylindrical gravitational collapse
International Nuclear Information System (INIS)
Di Prisco, A.; Herrera, L.; MacCallum, M. A. H.; Santos, N. O.
2009-01-01
We consider diagonal cylindrically symmetric metrics, with an interior representing a general nonrotating fluid with anisotropic pressures. An exterior vacuum Einstein-Rosen spacetime is matched to this using Darmois matching conditions. We show that the matching conditions can be explicitly solved for the boundary values of metric components and their derivatives, either for the interior or exterior. Specializing to shearfree interiors, a static exterior can only be matched to a static interior, and the evolution in the nonstatic case is found to be given in general by an elliptic function of time. For a collapsing shearfree isotropic fluid, only a Robertson-Walker dust interior is possible, and we show that all such cases were included in Cocke's discussion. For these metrics, Nolan and Nolan have shown that the matching breaks down before collapse is complete, and Tod and Mena have shown that the spacetime is not asymptotically flat in the sense of Berger, Chrusciel, and Moncrief. The issues about energy that then arise are revisited, and it is shown that the exterior is not in an intrinsic gravitational or superenergy radiative state at the boundary.
Comparison of advanced gravitational-wave detectors
International Nuclear Information System (INIS)
Harry, Gregory M.; Houser, Janet L.; Strain, Kenneth A.
2002-01-01
We compare two advanced designs for gravitational-wave antennas in terms of their ability to detect two possible gravitational wave sources. Spherical, resonant mass antennas and interferometers incorporating resonant sideband extraction (RSE) were modeled using experimentally measurable parameters. The signal-to-noise ratio of each detector for a binary neutron star system and a rapidly rotating stellar core were calculated. For a range of plausible parameters we found that the advanced LIGO interferometer incorporating RSE gave higher signal-to-noise ratios than a spherical detector resonant at the same frequency for both sources. Spheres were found to be sensitive to these sources at distances beyond our galaxy. Interferometers were sensitive to these sources at far enough distances that several events per year would be expected
An experimental test of Newton's law of gravitation for small accelerations
Energy Technology Data Exchange (ETDEWEB)
Schubert, Sven
2011-10-15
The experiment presented in this thesis has been designed to test Newton's law of gravitation in the limit of small accelerations caused by weak gravitational forces. It is located at DESY, Hamburg, and is a modification of an experiment that was carried out in Wuppertal, Germany, until 2002 in order to measure the gravitational constant G. The idea of testing Newton's law in the case of small accelerations emerged from the question whether the flat rotation curves of spiral galaxies can be traced back to Dark Matter or to a law of gravitation that deviates from Newton on cosmic scales like e.g. MOND (Modified Newtonian Dynamics). The core of this experiment is a microwave resonator which is formed by two spherical concave mirrors that are suspended as pendulums. Masses between 1 and 9 kg symmetrically change their distance to the mirrors from far to near positions. Due to the increased gravitational force the mirrors are pulled apart and the length of the resonator increases. This causes a shift of the resonance frequency which can be translated into a shift of the mirror distance. The small masses are sources of weak gravitational forces and cause accelerations on the mirrors of about 10{sup -10} m/s{sup 2}. These forces are comparable to those between stars on cosmic scales and the accelerations are in the vicinity of the characteristic acceleration of MOND a{sub 0} {approx} 1.2.10{sup -10} m/s{sup 2}, where deviations from Newton's law are expected. Thus Newton's law could be directly checked for correctness under these conditions. First measurements show that due to the sensitivity of this experiment many systematic influences have to be accounted for in order to get consistent results. Newton's law has been confirmed with an accuracy of 3%. MOND has also been checked. In order to be able to distinguish Newton from MOND with other interpolation functions the accuracy of the experiment has to be improved. (orig.)
Problem of energy-momentum and theory of gravitation
International Nuclear Information System (INIS)
Logunov, A.A.; Folomeshkin, V.N.
1977-01-01
General properties of geometrised theories of gravitation are considered. Covariant formulation of conservation laws in arbitrary riemannian space-time is given. In the Einstein theory the symmetric as well as canonical energy-momentum tensor of the system ''matter plus gravitational field'' and in particular, the energy-momentum of free gravitational waves, turns out to be equal to zero. To understand the origin of the problems and difficulties concerning the energy-momentum in the Einstein theory, the gravitational filed is considered in the usual framework of the Lorentz invariant field theory, just like any other physical field. Combination of the approach proposed with the Einstein's idea of geometrization makes it possible to formulate the geometrised gravitation theory, in which there are no inner contradictions, the energy-momentum of gravitational field is defined precisely and all the known experimental facts are described successfully. For strong gravitational fields the predictions of the quasilinear geometrised theory under consideration are different from those of the gravitational theory in the Einstein formulation. Black holes are absent in the theory. Evaluation of the energy-flux of gravitational waves leads to unambiguous results and shows that the gravitational waves transfer the positive-definite energy
Multiparty symmetric sum types
DEFF Research Database (Denmark)
Nielsen, Lasse; Yoshida, Nobuko; Honda, Kohei
2010-01-01
This paper introduces a new theory of multiparty session types based on symmetric sum types, by which we can type non-deterministic orchestration choice behaviours. While the original branching type in session types can represent a choice made by a single participant and accepted by others...... determining how the session proceeds, the symmetric sum type represents a choice made by agreement among all the participants of a session. Such behaviour can be found in many practical systems, including collaborative workflow in healthcare systems for clinical practice guidelines (CPGs). Processes...... with the symmetric sums can be embedded into the original branching types using conductor processes. We show that this type-driven embedding preserves typability, satisfies semantic soundness and completeness, and meets the encodability criteria adapted to the typed setting. The theory leads to an efficient...
Counting with symmetric functions
Mendes, Anthony
2015-01-01
This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya’s enu...
Symmetric Tensor Decomposition
DEFF Research Database (Denmark)
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....
Quantum gravitational optics in the field of a gravitomagnetic monopole
Energy Technology Data Exchange (ETDEWEB)
Ahmadi, N [Department of Physics, North Karegar Avenue, University of Tehran, P O Box 14395-547, Tehran (Iran, Islamic Republic of); Khoeini-Moghaddam, S [Department of Physics, Sharif University of Technology, P O Box 19365-9161, Tehran (Iran, Islamic Republic of); Nouri-Zonoz, M [Department of Physics, North Karegar Avenue, University of Tehran, P O Box 14395-547, Tehran (Iran, Islamic Republic of)
2007-05-15
Vacuum polarization in QED in a background gravitational field induces interactions which effectively modify the classical picture of light rays as the null geodesies of spacetime. After a short introduction on the main aspects of the quantum gravitational optics, as a nontrivial example, we study this effect in the background of NUT space characterizing the spacetime of a spherical mass endowed with a gravitomagnetic monopole charge, the so called NUT factor.
Are Nanoparticles Spherical or Quasi-Spherical?
Sokolov, Stanislav V; Batchelor-McAuley, Christopher; Tschulik, Kristina; Fletcher, Stephen; Compton, Richard G
2015-07-20
The geometry of quasi-spherical nanoparticles is investigated. The combination of SEM imaging and electrochemical nano-impact experiments is demonstrated to allow sizing and characterization of the geometry of single silver nanoparticles. © 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim.
Charged Tori in Spherical Gravitational and Dipolar Magnetic Fields
Czech Academy of Sciences Publication Activity Database
Slaný, P.; Kovář, J.; Stuchlík, Z.; Karas, Vladimír
2013-01-01
Roč. 205, č. 1 (2013), 3/1-3/16 ISSN 0067-0049 R&D Projects: GA ČR(CZ) GC13-00070J Institutional support: RVO:67985815 Keywords : accretion * accretion disks * magnetic fields Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 14.137, year: 2013
Interiors of Vaidya's radiating metric: Gravitational collapse
International Nuclear Information System (INIS)
Fayos, F.; Jaen, X.; Llanta, E.; Senovilla, J.M.M.
1992-01-01
Using the Darmois junction conditions, we give the necessary and sufficient conditions for the matching of a general spherically symmetric metric to a Vaidya radiating solution. We present also these conditions in terms of the physical quantities of the corresponding energy-momentum tensors. The physical interpretation of the results and their possible applications are studied, and we also perform a detailed analysis of previous work on the subject by other authors
Distributed Searchable Symmetric Encryption
Bösch, C.T.; Peter, Andreas; Leenders, Bram; Lim, Hoon Wei; Tang, Qiang; Wang, Huaxiong; Hartel, Pieter H.; Jonker, Willem
Searchable Symmetric Encryption (SSE) allows a client to store encrypted data on a storage provider in such a way, that the client is able to search and retrieve the data selectively without the storage provider learning the contents of the data or the words being searched for. Practical SSE schemes
Leung, Ka-Ngo
2006-11-21
A spherical neutron generator is formed with a small spherical target and a spherical shell RF-driven plasma ion source surrounding the target. A deuterium (or deuterium and tritium) ion plasma is produced by RF excitation in the plasma ion source using an RF antenna. The plasma generation region is a spherical shell between an outer chamber and an inner extraction electrode. A spherical neutron generating target is at the center of the chamber and is biased negatively with respect to the extraction electrode which contains many holes. Ions passing through the holes in the extraction electrode are focused onto the target which produces neutrons by D-D or D-T reactions.
Spherical conformal models for compact stars
Energy Technology Data Exchange (ETDEWEB)
Takisa, P.M.; Maharaj, S.D.; Manjonjo, A.M.; Moopanar, S. [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)
2017-10-15
We consider spherical exact models for compact stars with anisotropic pressures and a conformal symmetry. The conformal symmetry condition generates an integral relationship between the gravitational potentials. We solve this condition to find a new anisotropic solution to the Einstein field equations. We demonstrate that the exact solution produces a relativistic model of a compact star. The model generates stellar radii and masses consistent with PSR J1614-2230, Vela X1, PSR J1903+327 and Cen X-3. A detailed physical examination shows that the model is regular, well behaved and stable. The mass-radius limit and the surface red shift are consistent with observational constraints. (orig.)
Prevention of gravitational collapse
International Nuclear Information System (INIS)
Moffat, J.W.; Taylor, J.G.
1981-01-01
We apply a new theory of gravitation to the question of gravitational collapse to show that collapse is prevented in this theory under very reasonable conditions. This result also extends to prevent ultimate collapse of the Universe. (orig.)
Underdevelopment’s gravitation
Directory of Open Access Journals (Sweden)
Marin Dinu
2013-09-01
Full Text Available The energy necessary to escape the gravitational pull of underdevelopment and to enter an evolutional trajectory dependent on the gravitational pull of development is unintelligible in economic terms.
Gravitational collapse of charged dust shell and maximal slicing condition
International Nuclear Information System (INIS)
Maeda, Keiichi
1980-01-01
The maximal slicing condition is a good time coordinate condition qualitatively when pursuing the gravitational collapse by the numerical calculation. The analytic solution of the gravitational collapse under the maximal slicing condition is given in the case of a spherical charged dust shell and the behavior of time slices with this coordinate condition is investigated. It is concluded that under the maximal slicing condition we can pursue the gravitational collapse until the radius of the shell decreases to about 0.7 x (the radius of the event horizon). (author)
The gravitational lens effect and its optical equivalents
International Nuclear Information System (INIS)
Freitas, L.R. de.
1987-01-01
This work presents the evolution of the use of the so called gravitational lens effect from a simple observational teste of the General Relativity theory to an instrument to measure cosmological parameters. A detailed analysis of how a gravitational ''lens'' deflects light without forming images is shown for the case of the deflector with spherical symmetry. In addition, the exact optical equivalent of a cylindrical gravitational lens, which forms true images, is proposed. Finally the problem of the formation of multiple images and the related astronomical observations is discussed. (author) [pt
Ridgely, Charles T.
2011-01-01
When two gravitating bodies reside in a material medium, Newton's law of universal gravitation must be modified to account for the presence of the medium. A modified expression of Newton's law is known in the literature, but lacks a clear connection with existing gravitational theory. Newton's law in the presence of a homogeneous material medium…
Detection of gravitational radiation
Energy Technology Data Exchange (ETDEWEB)
Holten, J.W. van [ed.
1994-12-31
In this report the main contributions presented at the named symposium are collected. These concern astrophysical sources of gravitational radiation, ultracryogenic gravitational wave experiments, read out and data analysis of gravitational wave antennas, cryogenic aspects of large mass cooling to mK temperatures, and metallurgical and engineering aspects of large Cu structure manufacturing. (HSI).
Detection of gravitational radiation
International Nuclear Information System (INIS)
Holten, J.W. van
1994-01-01
In this report the main contributions presented at the named symposium are collected. These concern astrophysical sources of gravitational radiation, ultracryogenic gravitational wave experiments, read out and data analysis of gravitational wave antennas, cryogenic aspects of large mass cooling to mK temperatures, and metallurgical and engineering aspects of large Cu structure manufacturing. (HSI)
Relativity theory and gravitation
International Nuclear Information System (INIS)
Bondi, H.
1986-01-01
The paper on relativity theory and gravitation is presented as a preface to the first of the articles submitted to the Journal on general relativity. Newtonian gravitation and and observation, relativity, and the sources of the gravitational field, are all discussed. (UK)
Chiral pion dynamics for spherical nucleon bags
International Nuclear Information System (INIS)
Vento, V.; Rho, M.; Nyman, E.M.; Jun, J.H.; Brown, G.E.; CEA Centre d'Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette
1980-01-01
A chirally symmetric quark-bag model for the nucleon is obtained by introducing an explicit, classical, pion field exterior to the bag. The coupling at the bag surface is determined by the requirement of a conserved axial-vector current. The pion field satisfies equations of motion corresponding to the non-linear sigma-model. We study on this paper the simplified case where the bag and the pion field are spherically symmetric. Corrections due to gluon exchange between the quarks are ignored along with other interactions which split the N- and Δ-masses. The equations of motion for the pion field are solved and we find a substantial pion pressure at the bag surface, along with an attractive contribution to the nucleon self-energy. The total energy of the system, bag plus meson cloud, turns out to be approximately Msub(n)c 2 for a wide range of bag radii, from 1.5 fm down to about 0.5 fm. Introduction of a form factor for the pion would extend the range of possible radii to even smaller values. We propose that the bag with the smallest allowed radius be identified with the 'little bag' discussed before. One surprising result of the paper is that as long as one restricts to spherically symmetric bags, restoring chiral symmetry to the bag model makes the axial-vector current coupling constant gsub(A) to be always too large compared with the experimental value for any bag radius, suggesting a deviation from spherical symmetry for the intrinsic bag wave functions of the 'ground-state' hadrons. (orig.)
General projective relativity and the vector-tensor gravitational field
International Nuclear Information System (INIS)
Arcidiacono, G.
1986-01-01
In the general projective relativity, the induced 4-dimensional metric is symmetric in three cases, and we obtain the vector-tensor, the scalar-tensor, and the scalar-vector-tensor theories of gravitation. In this work we examine the vector-tensor theory, similar to the Veblen's theory, but with a different physical interpretation
Trapped surfaces due to concentration of gravitational radiation
International Nuclear Information System (INIS)
Beig, R.; O Murchadha, N.
1991-01-01
Sequences of global, asympotically flat solutions to the time-symmetric initial value constraints of general relativity in vacuo are constructed which develop outer trapped surfaces for large values of the argument. Thus all such configurations must gravitationally collapse. A new proof of the positivity of mass in the strong-field regime is also found. (Authors) 22 refs
Relativistic equations for axisymmetric gravitational collapse with escaping neutrinos
International Nuclear Information System (INIS)
Patel, M.D.
1979-01-01
Einstein's field equations for the dynamics of a self-gravitating axially symmetric source of a perfect fluid, presented by Chandrasekhar and Friedman (1964), are modified to allow emission of neutrinos. The boundary conditions at the outer surface of the radiating axisymmetric source are obtained by matching to an exterior solution of an axisymmetric rotating, radiating core. (auth.)
Chen, Yan; Feng, Huijuan; Ma, Jiayao; Peng, Rui; You, Zhong
2016-06-01
The traditional waterbomb origami, produced from a pattern consisting of a series of vertices where six creases meet, is one of the most widely used origami patterns. From a rigid origami viewpoint, it generally has multiple degrees of freedom, but when the pattern is folded symmetrically, the mobility reduces to one. This paper presents a thorough kinematic investigation on symmetric folding of the waterbomb pattern. It has been found that the pattern can have two folding paths under certain circumstance. Moreover, the pattern can be used to fold thick panels. Not only do the additional constraints imposed to fold the thick panels lead to single degree of freedom folding, but the folding process is also kinematically equivalent to the origami of zero-thickness sheets. The findings pave the way for the pattern being readily used to fold deployable structures ranging from flat roofs to large solar panels.
Rome, J.A.; Harris, J.H.
1984-01-01
A fusion reactor device is provided in which the magnetic fields for plasma confinement in a toroidal configuration is produced by a plurality of symmetrical modular coils arranged to form a symmetric modular torsatron referred to as a symmotron. Each of the identical modular coils is helically deformed and comprise one field period of the torsatron. Helical segments of each coil are connected by means of toroidally directed windbacks which may also provide part of the vertical field required for positioning the plasma. The stray fields of the windback segments may be compensated by toroidal coils. A variety of magnetic confinement flux surface configurations may be produced by proper modulation of the winding pitch of the helical segments of the coils, as in a conventional torsatron, winding the helix on a noncircular cross section and varying the poloidal and radial location of the windbacks and the compensating toroidal ring coils.
The Schenberg gravitational wave detector: status report
International Nuclear Information System (INIS)
Aguiar, O.D.; Barroso, J.J; Bessada, D.F.A.; Carvalho, N.C; Castro, P.J.; Montana, C.E. Cedeno; Costa, C.F. da Silva; Araujo, J.C.N de; Evangelista, E.F.D.; Furtado, S.R; Miranda, O.D.; Moraes, P.H.R.S.; Pereira, Eduardo S.; Silveira, P.R.; Stellati, C.; Weber, J.
2011-01-01
Full text: The quest for gravitational wave detection has been one of the toughest technological challenges ever faced by experimental physicists and engineers. Despite all difficulties, after four decades of research, the community involved in this area is continuously growing. One of the main reasons for this is because the first gravitational wave detection and the regular observation of gravitational waves are among the most important scientific goals for the beginning of this millennium. They will test one of the foundations of physics, Einstein's theory of general relativity, and will open a new window for the observation of the universe, which certainly will cause a revolution in our knowledge of physics and astrophysics. In this talk we present the status report of the Brazilian Schenberg gravitational wave detector, which started commissioning runs in September 2006 under the full support of FAPESP. We have been upgrading the detector since 2008, installing a dilution refrigerator, a new complete set of transducers, and a new suspension and vibration isolation system for the cabling and microstrip antennas, in order to restart operation with a higher sensitivity. We also have been studying an innovative approach, which could transform Schenberg into a broadband gravitational wave detector by the use of an ultra-high sensitivity non-resonant nanogap transducer, constructed by the application of recent achievements of nanotechnology. A spherical antenna, such as Schenberg or Mini-Grail, could add to this quality the advantage of wave position and polarity determination. (author)
Effect of scalar field mass on gravitating charged scalar solitons and black holes in a cavity
Energy Technology Data Exchange (ETDEWEB)
Ponglertsakul, Supakchai, E-mail: supakchai.p@gmail.com; Winstanley, Elizabeth, E-mail: E.Winstanley@sheffield.ac.uk
2017-01-10
We study soliton and black hole solutions of Einstein charged scalar field theory in cavity. We examine the effect of introducing a scalar field mass on static, spherically symmetric solutions of the field equations. We focus particularly on the spaces of soliton and black hole solutions, as well as studying their stability under linear, spherically symmetric perturbations of the metric, electromagnetic field, and scalar field.
Symmetric vectors and algebraic classification
International Nuclear Information System (INIS)
Leibowitz, E.
1980-01-01
The concept of symmetric vector field in Riemannian manifolds, which arises in the study of relativistic cosmological models, is analyzed. Symmetric vectors are tied up with the algebraic properties of the manifold curvature. A procedure for generating a congruence of symmetric fields out of a given pair is outlined. The case of a three-dimensional manifold of constant curvature (''isotropic universe'') is studied in detail, with all its symmetric vector fields being explicitly constructed
Theory of gravitational interactions
Gasperini, Maurizio
2017-01-01
This is the second edition of a well-received book that is a modern, self-contained introduction to the theory of gravitational interactions. The new edition includes more details on gravitational waves of cosmological origin, the so-called brane world scenario, and gravitational time-delay effects. The first part of the book follows the traditional presentation of general relativity as a geometric theory of the macroscopic gravitational field, while the second, more advanced part discusses the deep analogies (and differences) between a geometric theory of gravity and the “gauge” theories of the other fundamental interactions. This fills a gap within the traditional approach to general relativity which usually leaves students puzzled about the role of gravity. The required notions of differential geometry are reduced to the minimum, allowing room for aspects of gravitational physics of current phenomenological and theoretical interest, such as the properties of gravitational waves, the gravitational inter...
A new theory of space-time and gravitation
International Nuclear Information System (INIS)
Denisov, V.I.; Logunov, A.A.
1982-01-01
Field theory of gravitation is constructed. It uses a symmetrical second rank tensor field in pseudoeuclidean space-time for describing the gravitational field. The theory is based on the condition of the presence of conservation laws for gravitational field and matter taken together and on the geometrization principle. The field theory of gravitation has the same post-newtonian parame-- ters as the general relativity theory (GRT) which implies that both theories are indistinguishable from the viewpoint of any post- newtonian experiment. The description of the effects in strong gravitational fields as well as properties of gravitational waves in the field theory of gravitation and GRT differ significantly from each other. The distinctions between two theories include also the itational red shifti curving of light trajectories and timabsence in the field theory of gravitation of the effects of grav.. delay/ in processes of propagation of gravitational waves in external fields. These distinctions made it possible to suggest a number of experiments with gravitational waves in which the predictions of the field theory of gravitation can be compared with those of the GRT. Model of the Universe in the field theory of gravitation makes it possible to describe the cosmological red shift of the frequency. Character of the evolution in this mode is determined by the delay parameter q 0 : at q 0 0 >4-3/2xα the ''expansion'' at some moment will ''change'' to contraction'' and the Universe will return to the singular state, where α=8πepsilon 0 /3M 2 (H is the Hubble constant) [ru
Representations of locally symmetric spaces
International Nuclear Information System (INIS)
Rahman, M.S.
1995-09-01
Locally symmetric spaces in reference to globally and Hermitian symmetric Riemannian spaces are studied. Some relations between locally and globally symmetric spaces are exhibited. A lucid account of results on relevant spaces, motivated by fundamental problems, are formulated as theorems and propositions. (author). 10 refs
The gravitational shock wave of a massless particle
Hooft, G. 't; Dray, T
1985-01-01
The (spherical) gravitational shock wave due to a massless particle moving at the speed of light along the horizon of the Schwarzchild black hole is obtained. Special cases of our procedure yield previous results by Aichelburg and Sexl[1] for a photon in Minkowski vpace and by Penrose [2] for
Geometric inequalities for axially symmetric black holes
International Nuclear Information System (INIS)
Dain, Sergio
2012-01-01
A geometric inequality in general relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities play an important role in the characterization of the gravitational collapse; they are closely related with the cosmic censorship conjecture. Axially symmetric black holes are the natural candidates to study these inequalities because the quasi-local angular momentum is well defined for them. We review recent results in this subject and we also describe the main ideas behind the proofs. Finally, a list of relevant open problems is presented. (topical review)
Gravitational waves from inflation
International Nuclear Information System (INIS)
Guzzetti, M.C.; Bartolo, N.; Liguori, M.; Matarrese, S.
2016-01-01
The production of a stochastic background of gravitational waves is a fundamental prediction of any cosmological inflationary model. The features of such a signal encode unique information about the physics of the Early Universe and beyond, thus representing an exciting, powerful window on the origin and evolution of the Universe. We review the main mechanisms of gravitational-wave production, ranging from quantum fluctuations of the gravitational field to other mechanisms that can take place during or after inflation. These include e.g. gravitational waves generated as a consequence of extra particle production during inflation, or during the (p)reheating phase. Gravitational waves produced in inflation scenarios based on modified gravity theories and second-order gravitational waves are also considered. For each analyzed case, the expected power spectrum is given. We discuss the discriminating power among different models, associated with the validity/violation of the standard consistency relation between tensor-to-scalar ratio r and tensor spectral index ηT. In light of the prospects for (directly/indirectly) detecting primordial gravitational waves, we give the expected present-day gravitational radiation spectral energy-density, highlighting the main characteristics imprinted by the cosmic thermal history, and we outline the signatures left by gravitational waves on the Cosmic Microwave Background and some imprints in the Large-Scale Structure of the Universe. Finally, current bounds and prospects of detection for inflationary gravitational waves are summarized.
Gravitational agglomeration of post-HCDA LMFBR aerosols: nonspherical particles
International Nuclear Information System (INIS)
Tuttle, R.F.; Loyalka, S.K.
1982-12-01
Aerosol behavior analysis computer programs have shown that temporal aerosol size distributions in nuclear reactor containments are sensitive to shape factors. This research investigates shape factors by a detailed theoretical analysis of hydrodynamic interactions between a nonspherical particle and a spherical particle undergoing gravitational collisions in an LMFBR environment. First, basic definitions and expressions for settling speeds and collisional efficiencies of nonspherical particles are developed. These are then related to corresponding quantities for spherical particles through shape factors. Using volume equivalent diameter as the defining length in the gravitational collision kernel, the aerodynamic shape factor, the density correction factor, and the gravitational collision shape factor, are introduced to describe the collision kernel for collisions between aerosol agglomerates. The Navier-Stokes equation in oblate spheroidal coordinates is solved to model a nonspherical particle and then the dynamic equations for two particle motions are developed. A computer program (NGCEFF) is constructed, and the dynamical equations are solved by Gear's method
Anisotropic gravitational instability
International Nuclear Information System (INIS)
Polyachenko, V.L.; Fridman, A.M.
1988-01-01
Exact solutions of stability problems are obtained for two anisotropic gravitational systems of different geometries - a layer of finite thickness at rest and a rotating cylinder of finite radius. It is shown that the anisotropic gravitational instability which develops in both cases is of Jeans type. However, in contrast to the classical aperiodic Jeans instability, this instability is oscillatory. The physics of the anisotropic gravitational instability is investigated. It is shown that in a gravitating layer this instability is due, in particular, to excitation of previously unknown interchange-Jeans modes. In the cylinder, the oscillatory Jeans instability is associated with excitation of a rotational branch, this also being responsible for the beam gravitational instability. This is the reason why this instability and the anisotropic gravitational instability have so much in common
Nakedly singular non-vacuum gravitating equilibrium states
Woszczyna, Andrzej; Kutschera, Marek; Kubis, Sebastian; Czaja, Wojciech; Plaszczyk, Piotr; Golda, Zdzisław A.
2016-01-01
Non-vacuum static spherically symmetric spacetimes with central point-like repulsive gravity sources are investigated. Both the symmetries of spacetime and the degree of irregularity of curvature invariants, are the same as for the Schwarzschild case. The equilibrium configurations are modelled using the neutron star polytrope equation of state.
CERN. Geneva HR-RFA
2006-01-01
We will present a brief introduction to the physics of gravitational waves and their properties. We will review potential astrophysical sources of gravitational waves, and the physics and astrophysics that can be learned from their study. We will survey the techniques and technologies for detecting gravitational waves for the first time, including bar detectors and broadband interferometers, and give a brief status report on the international search effort.
CERN. Geneva
2006-01-01
Gravitational wave astronomy is expected to become an observational field within the next decade. First direct detection of gravitational waves is possible with existing terrestrial-based detectors, and highly probable with proposed upgrades. In this three-part lecture series, we give an overview of the field, including material on gravitional wave sources, detection methods, some details of interferometric detectors, data analysis methods, and current results from observational data-taking runs of the LIGO and GEO projects.
The energy-momentum problem and gravitation theory
International Nuclear Information System (INIS)
Logunov, A.A.; Folomeshkin, V.N.
1977-01-01
General properties of geometrized gravitation theories are considered. A covariant formulation of conservation laws in an arbitrary Riemann space-time is presented. In the Einstein theory both symmetric and canonical energy-momentum tensors of the matter and gravitational field system and, in particular, energy-momentum of free gravitational waves prove to be equal to zero. Since gravitational waves carry the curvature and, consequently, affect the detector, this bears witness to an intrinsic contradiction of the Einstein theory. To realize the sources of difficulties concerning energy-momentum in the Einstein theory the gravitational field is treated in the same way as all the other physical fields, i.e. in terms of usual Lorentz-invariant field theory. Unification of this approach with the Einstein idea of geometrization enables to construct the geometrized theory, which is free from contradictions, has clearly defined the notions of gravitation field energy-momentum and satisfactorily describes all known experimental facts. To construct a logically consistent theory one should geometrize only the density of the matter Lagrangian. The gravitation field equations are formulated in terms of the Euclidean space-time with a metric tensor γsub(ik), while the matter motion may be completely described in terms of the non-Euclidean space-time with a metric tensor gsub(ik). For strong gravitational fields the predictions of the quasi-linear theory under consideration appriciably differ from those of the Einstein formulation of the gravitation theory. No black holes are present in the theory. The results of the calculation for the energy flow of gravitational waves are rigorously unambiguous and show that gravitational waves carry positively definite energy
Symmetric spaces and the Kashiwara-Vergne method
Rouvière, François
2014-01-01
Gathering and updating results scattered in journal articles over thirty years, this self-contained monograph gives a comprehensive introduction to the subject. Its goal is to: - motivate and explain the method for general Lie groups, reducing the proof of deep results in invariant analysis to the verification of two formal Lie bracket identities related to the Campbell-Hausdorff formula (the "Kashiwara-Vergne conjecture"); - give a detailed proof of the conjecture for quadratic and solvable Lie algebras, which is relatively elementary; - extend the method to symmetric spaces; here an obstruction appears, embodied in a single remarkable object called an "e-function"; - explain the role of this function in invariant analysis on symmetric spaces, its relation to invariant differential operators, mean value operators and spherical functions; - give an explicit e-function for rank one spaces (the hyperbolic spaces); - construct an e-function for general symmetric spaces, in the spirit of Kashiwara and Vergne's or...
International Nuclear Information System (INIS)
Ridgely, Charles T
2011-01-01
When two gravitating bodies reside in a material medium, Newton's law of universal gravitation must be modified to account for the presence of the medium. A modified expression of Newton's law is known in the literature, but lacks a clear connection with existing gravitational theory. Newton's law in the presence of a homogeneous material medium is herein derived on the basis of classical, Newtonian gravitational theory and by a general relativistic use of Archimedes' principle. It is envisioned that the techniques presented herein will be most useful to graduate students and those undergraduate students having prior experience with vector analysis and potential theory.
Hoffmann, William F
1964-01-01
Remarks on the observational basis of general relativity ; Riemannian geometry ; gravitation as geometry ; gravitational waves ; Mach's principle and experiments on mass anisotropy ; the many faces of Mach ; the significance for the solar system of time-varying gravitation ; relativity principles and the role of coordinates in physics ; the superdense star and the critical nucleon number ; gravitation and light ; possible effects on the solar system of φ waves if they exist ; the Lyttleton-Bondi universe and charge equality ; quantization of general relativity ; Mach's principle as boundary condition for Einstein's equations.
Hawking radiation from a spherical loop quantum gravity black hole
International Nuclear Information System (INIS)
Gambini, Rodolfo; Pullin, Jorge
2014-01-01
We introduce quantum field theory on quantum space-times techniques to characterize the quantum vacua as a first step toward studying black hole evaporation in spherical symmetry in loop quantum gravity and compute the Hawking radiation. We use as quantum space-time the recently introduced exact solution of the quantum Einstein equations in vacuum with spherical symmetry and consider a spherically symmetric test scalar field propagating on it. The use of loop quantum gravity techniques in the background space-time naturally regularizes the matter content, solving one of the main obstacles to back-reaction calculations in more traditional treatments. The discreteness of area leads to modifications of the quantum vacua, eliminating the trans-Planckian modes close to the horizon, which in turn eliminates all singularities from physical quantities, like the expectation value of the stress–energy tensor. Apart from this, the Boulware, Hartle–Hawking and Unruh vacua differ little from the treatment on a classical space-time. The asymptotic modes near scri are reproduced very well. We show that the Hawking radiation can be computed, leading to an expression similar to the conventional one but with a high frequency cutoff. Since many of the conclusions concern asymptotic behavior, where the spherical mode of the field behaves in a similar way as higher multipole modes do, the results can be readily generalized to non spherically symmetric fields. (paper)
Infinite order quantum-gravitational correlations
Knorr, Benjamin
2018-06-01
A new approximation scheme for nonperturbative renormalisation group equations for quantum gravity is introduced. Correlation functions of arbitrarily high order can be studied by resolving the full dependence of the renormalisation group equations on the fluctuation field (graviton). This is reminiscent of a local potential approximation in O(N)-symmetric field theories. As a first proof of principle, we derive the flow equation for the ‘graviton potential’ induced by a conformal fluctuation and corrections induced by a gravitational wave fluctuation. Indications are found that quantum gravity might be in a non-metric phase in the deep ultraviolet. The present setup significantly improves the quality of previous fluctuation vertex studies by including infinitely many couplings, thereby testing the reliability of schemes to identify different couplings to close the equations, and represents an important step towards the resolution of the Nielsen identity. The setup further allows one, in principle, to address the question of putative gravitational condensates.
High energy gravitational scattering: a numerical study
Marchesini, Giuseppe
2008-01-01
The S-matrix in gravitational high energy scattering is computed from the region of large impact parameters b down to the regime where classical gravitational collapse is expected to occur. By solving the equation of an effective action introduced by Amati, Ciafaloni and Veneziano we find that the perturbative expansion around the leading eikonal result diverges at a critical value signalling the onset of a new regime. We then discuss the main features of our explicitly unitary S-matrix down to the Schwarzschild's radius R=2G s^(1/2), where it diverges at a critical value b ~ 2.22 R of the impact parameter. The nature of the singularity is studied with particular attention to the scaling behaviour of various observables at the transition. The numerical approach is validated by reproducing the known exact solution in the axially symmetric case to high accuracy.
Gravitational Waves From a Dark (Twin) Phase Transition
Schwaller, Pedro
2015-01-01
In this work, we show that a large class of models with a composite dark sector undergo a strong first order phase transition in the early universe, which could lead to a detectable gravitational wave signal. We summarise the basic conditions for a strong first order phase transition for SU(N) dark sectors with n_f flavours, calculate the gravitational wave spectrum and show that, depending on the dark confinement scale, it can be detected at eLISA or in pulsar timing array experiments. The gravitational wave signal provides a unique test of the gravitational interactions of a dark sector, and we discuss the complementarity with conventional searches for new dark sectors. The discussion includes Twin Higgs and SIMP models as well as symmetric and asymmetric composite dark matter scenarios.
Preserving spherical symmetry in axisymmetric coordinates for diffusion problems
International Nuclear Information System (INIS)
Brunner, T. A.; Kolev, T. V.; Bailey, T. S.; Till, A. T.
2013-01-01
Persevering symmetric solutions, even in the under-converged limit, is important to the robustness of production simulation codes. We explore the symmetry preservation in both a continuous nodal and a mixed finite element method. In their standard formulation, neither method preserves spherical solution symmetry in axisymmetric (RZ) coordinates. We propose two methods, one for each family of finite elements, that recover spherical symmetry for low-order finite elements on linear or curvilinear meshes. This is a first step toward understanding achieving symmetry for higher-order elements. (authors)
Symmetric extendibility of quantum states
Nowakowski, Marcin L.
2015-01-01
Studies on symmetric extendibility of quantum states become especially important in a context of analysis of one-way quantum measures of entanglement, distilabillity and security of quantum protocols. In this paper we analyse composite systems containing a symmetric extendible part with a particular attention devoted to one-way security of such systems. Further, we introduce a new one-way monotone based on the best symmetric approximation of quantum state. We underpin those results with geome...
Gravitational lens effect and pregalactic halo objects
International Nuclear Information System (INIS)
Bontz, R.J.
1979-01-01
The changes in flux, position, and size of a distant extended (galaxy, etc.) source that result from the gravitational lens action of a massive opaque object are discussed. The flux increase is described by a single function of two parameters. One of these parameters characterizes the strength of the gravitational lens, the other describes the alignment of source and lens object. This function also describes the relative intensity of the images formed by lens. ( A similar formalism is discussed by Bourassa et al. for a point source). The formalism is applied to the problem of the galactic halo. It appears that a massive (10 1 2 M/sub sun/) spherical halo surrounding the visible part of the galaxy is consistent with the observable properties of extragalactic sources
International Nuclear Information System (INIS)
Burtraw, Dallas; Palmer, Karen; Kahn, Danny
2010-01-01
How to set policy in the presence of uncertainty has been central in debates over climate policy. Concern about costs has motivated the proposal for a cap-and-trade program for carbon dioxide, with a 'safety valve' that would mitigate against spikes in the cost of emission reductions by introducing additional emission allowances into the market when marginal costs rise above the specified allowance price level. We find two significant problems, both stemming from the asymmetry of an instrument that mitigates only against a price increase. One is that most important examples of price volatility in cap-and-trade programs have occurred not when prices spiked, but instead when allowance prices collapsed. Second, a single-sided safety valve may have unintended consequences for investment. We illustrate that a symmetric safety valve provides environmental and welfare improvements relative to the conventional one-sided approach.
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
Directory of Open Access Journals (Sweden)
Giuseppe Dattoli
1996-05-01
Full Text Available q analog of bessel functions, symmetric under the interchange of q and q^ −1 are introduced. The definition is based on the generating function realized as product of symmetric q-exponential functions with appropriate arguments. Symmetric q-Bessel function are shown to satisfy various identities as well as second-order q-differential equations, which in the limit q → 1 reproduce those obeyed by the usual cylindrical Bessel functions. A brief discussion on the possible algebraic setting for symmetric q-Bessel functions is also provided.
The Spherical Deformation Model
DEFF Research Database (Denmark)
Hobolth, Asgar
2003-01-01
Miller et al. (1994) describe a model for representing spatial objects with no obvious landmarks. Each object is represented by a global translation and a normal deformation of a sphere. The normal deformation is defined via the orthonormal spherical-harmonic basis. In this paper we analyse the s...
Relativistic gravitation theory
International Nuclear Information System (INIS)
Logunov, A.A.; Mestvirishvili, M.A.
1984-01-01
On the basis of the special relativity and geometrization principle a relativistic gravitation theory (RGT) is unambiguously constructed with the help of a notion of a gravitational field as a physical field in Faraday-Maxwell spirit, which posesses energy momentum and spins 2 and 0. The source of gravitation field is a total conserved energy-momentum tensor for matter and for gravitation field in Minkowski space. In the RGT conservation laws for the energy momentum and angular momentum of matter and gravitational field hold rigorously. The theory explains the whole set of gravitation experiments. Here, due to the geometrization principle the Riemannian space is of a field origin since this space arises effectively as a result of the gravitation field origin since this space arises effectively as a result of the gravitation field action on the matter. The RGT astonishing prediction is that the Universe is not closed but ''flat''. It means that in the Universe there should exist a ''missing'' mass in some form of matter
Those Elusive Gravitational Waves
MOSAIC, 1976
1976-01-01
The presence of gravitational waves was predicted by Einstein in his theory of General Relativity. Since then, scientists have been attempting to develop a detector sensitive enough to measure these cosmic signals. Once the presence of gravitational waves is confirmed, scientists can directly study star interiors, galaxy cores, or quasars. (MA)
Gravitationally coupled electroweak monopole
Energy Technology Data Exchange (ETDEWEB)
Cho, Y.M., E-mail: ymcho7@konkuk.ac.kr [Administration Building 310-4, Konkuk University, Seoul 143-701 (Korea, Republic of); School of Physics and Astronomy, Seoul National University, Seoul 151-742 (Korea, Republic of); Kimm, Kyoungtae [Faculty of Liberal Education, Seoul National University, Seoul 151-747 (Korea, Republic of); Yoon, J.H. [Department of Physics, College of Natural Sciences, Konkuk University, Seoul 143-701 (Korea, Republic of)
2016-10-10
We present a family of gravitationally coupled electroweak monopole solutions in Einstein–Weinberg–Salam theory. Our result confirms the existence of globally regular gravitating electroweak monopole which changes to the magnetically charged black hole as the Higgs vacuum value approaches to the Planck scale. Moreover, our solutions could provide a more accurate description of the monopole stars and magnetically charged black holes.
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)
High-intensification regions of gravitational lenses
International Nuclear Information System (INIS)
Benson, J.R.; Cooke, J.H.
1979-01-01
We examine the intensification, I, near the singular points in the object plane of an extended spherical gravitational lens. Geometrical optics predicts an infinite I for a point object located on a singularity. The function I, however, turns out to be integrable over the object plane. We make a detailed physical optics calculation for I. No singularities appear, and there are some interesting, marginally detectable diffraction phenomena. The two types of bright regions, the ''halo'' and the ''spike,'' behave very differently. Simple order-of-magnitude expressions give estimates for the brightness and duration of a high-intensification event
Gravitational physics of stellar and galactic systems
International Nuclear Information System (INIS)
Saslaw, W.C.
1985-01-01
The book concerns the gravitational interactions and evolution of astronomical systems on all scales, and is aimed at the graduate student of physics and astronomy. The text is divided into four parts, and each describes areas of the subject in order of decreasing symmetry. The four parts include: idealized homogeneous systems-basic ideas and gentle relaxation; infinite inhomogeneous systems and galaxy clustering; finite spherical systems including clusters of galaxies; galactic nuclei and globular clusters; and finite flattened systems and galaxies. (U.K.)
Normalization and Implementation of Three Gravitational Acceleration Models
Eckman, Randy A.; Brown, Aaron J.; Adamo, Daniel R.; Gottlieb, Robert G.
2016-01-01
Unlike the uniform density spherical shell approximations of Newton, the consequence of spaceflight in the real universe is that gravitational fields are sensitive to the asphericity of their generating central bodies. The gravitational potential of an aspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities that must be removed to generalize the method and solve for any possible orbit, including polar orbits. Samuel Pines, Bill Lear, and Robert Gottlieb developed three unique algorithms to eliminate these singularities. This paper documents the methodical normalization of two of the three known formulations for singularity-free gravitational acceleration (namely, the Lear and Gottlieb algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre polynomials and Associated Legendre Functions (ALFs) for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms.
Gravitational amplitudes in black hole evaporation: the effect of non-commutative geometry
International Nuclear Information System (INIS)
Grezia, Elisabetta Di; Esposito, Giampiero; Miele, Gennaro
2006-01-01
Recent work in the literature has studied the quantum-mechanical decay of a Schwarzschild-like black hole, formed by gravitational collapse, into almost-flat spacetime and weak radiation at a very late time. The relevant quantum amplitudes have been evaluated for bosonic and fermionic fields, showing that no information is lost in collapse to a black hole. On the other hand, recent developments in non-commutative geometry have shown that, in general relativity, the effects of non-commutativity can be taken into account by keeping the standard form of the Einstein tensor on the left-hand side of the field equations and introducing a modified energy-momentum tensor as a source on the right-hand side. The present paper, relying on the recently obtained non-commutativity effect on a static, spherically symmetric metric, considers from a new perspective the quantum amplitudes in black hole evaporation. The general relativity analysis of spin-2 amplitudes is shown to be modified by a multiplicative factor F depending on a constant non-commutativity parameter and on the upper limit R of the radial coordinate. Limiting forms of F are derived which are compatible with the adiabatic approximation here exploited. Approximate formulae for the particle emission rate are also obtained within this framework
Novel Remarks on Point Mass Sources, Firewalls, Null Singularities and Gravitational Entropy
Perelman, Carlos Castro
2016-01-01
A continuous family of static spherically symmetric solutions of Einstein's vacuum field equations with a spatial singularity at the origin r = 0 is found. These solutions are parametrized by a real valued parameter λ (ranging from 0 to 1) and such that the radial horizon's location is displaced continuously towards the singularity ( r = 0 ) as λ increases. In the extreme limit λ = 1, the location of the singularity and horizon merges leading to a null singularity. In this extreme case, any infalling observer hits the null singularity at the very moment he/she crosses the horizon. This fact may have important consequences for the resolution of the fire wall problem and the complementarity controversy in black holes. An heuristic argument is provided how one might avoid the Hawking particle emission process in this extreme case when the singularity and horizon merges. The field equations due to a delta-function point-mass source at r = 0 are solved and the Euclidean gravitational action corresponding to those solutions is evaluated explicitly. It is found that the Euclidean action is precisely equal to the black hole entropy (in Planck area units). This result holds in any dimensions D ≥ 3.
Bianchi, Eugenio; De Lorenzo, Tommaso; Smerlak, Matteo
2015-06-01
We study the dynamics of vacuum entanglement in the process of gravitational collapse and subsequent black hole evaporation. In the first part of the paper, we introduce a covariant regularization of entanglement entropy tailored to curved spacetimes; this regularization allows us to propose precise definitions for the concepts of black hole "exterior entropy" and "radiation entropy." For a Vaidya model of collapse we find results consistent with the standard thermodynamic properties of Hawking radiation. In the second part of the paper, we compute the vacuum entanglement entropy of various spherically-symmetric spacetimes of interest, including the nonsingular black hole model of Bardeen, Hayward, Frolov and Rovelli-Vidotto and the "black hole fireworks" model of Haggard-Rovelli. We discuss specifically the role of event and trapping horizons in connection with the behavior of the radiation entropy at future null infinity. We observe in particular that ( i) in the presence of an event horizon the radiation entropy diverges at the end of the evaporation process, ( ii) in models of nonsingular evaporation (with a trapped region but no event horizon) the generalized second law holds only at early times and is violated in the "purifying" phase, ( iii) at late times the radiation entropy can become negative (i.e. the radiation can be less correlated than the vacuum) before going back to zero leading to an up-down-up behavior for the Page curve of a unitarily evaporating black hole.
International Nuclear Information System (INIS)
Bianchi, Eugenio; Lorenzo, Tommaso De; Smerlak, Matteo
2015-01-01
We study the dynamics of vacuum entanglement in the process of gravitational collapse and subsequent black hole evaporation. In the first part of the paper, we introduce a covariant regularization of entanglement entropy tailored to curved spacetimes; this regularization allows us to propose precise definitions for the concepts of black hole “exterior entropy” and “radiation entropy.” For a Vaidya model of collapse we find results consistent with the standard thermodynamic properties of Hawking radiation. In the second part of the paper, we compute the vacuum entanglement entropy of various spherically-symmetric spacetimes of interest, including the nonsingular black hole model of Bardeen, Hayward, Frolov and Rovelli-Vidotto and the “black hole fireworks” model of Haggard-Rovelli. We discuss specifically the role of event and trapping horizons in connection with the behavior of the radiation entropy at future null infinity. We observe in particular that (i) in the presence of an event horizon the radiation entropy diverges at the end of the evaporation process, (ii) in models of nonsingular evaporation (with a trapped region but no event horizon) the generalized second law holds only at early times and is violated in the “purifying” phase, (iii) at late times the radiation entropy can become negative (i.e. the radiation can be less correlated than the vacuum) before going back to zero leading to an up-down-up behavior for the Page curve of a unitarily evaporating black hole.
On the energy-momentum density of gravitational plane waves
International Nuclear Information System (INIS)
Dereli, T; Tucker, R W
2004-01-01
By embedding Einstein's original formulation of general relativity into a broader context, we show that a dynamic covariant description of gravitational stress-energy emerges naturally from a variational principle. A tensor T G is constructed from a contraction of the Bel tensor with a symmetric covariant second degree tensor field Φ and has a form analogous to the stress-energy tensor of the Maxwell field in an arbitrary spacetime. For plane-fronted gravitational waves helicity-2 polarized (graviton) states can be identified carrying non-zero energy and momentum
Principle of equivalence and a theory of gravitation
International Nuclear Information System (INIS)
Shelupsky, D.
1985-01-01
We examine a well-known thought experiment often used to explain why we should expect a ray of light to be bent by gravity; according to this the light bends downward in the gravitational field because this is just what an observer would see if there were no field and he were accelerating upward instead. We show that this description of the action of Newtonian gravity in a flat space-time corresponds to an old two-index symmetric tensor field theory of gravitation
Relativistic theory of gravitation
International Nuclear Information System (INIS)
Logunov, A.A.; Mestvirishvilli, M.A.
1985-01-01
In the present paper a relativistic theory of gravitation (RTG) is constructed in a unique way on the basis of the special relativity and geometrization principle. In this, a gravitational field is treated as the Faraday-Maxwell spin-2 and spin-0 physical field possessing energy and momentum. The source of a gravitational field is the total conserved energy-momentum tensor of matter and of a gravitational field in Minkowski space. In the RTG, the conservation laws are strictly fulfilled for the energy-momentum and for the angular momentum of matter and a gravitational field. The theory explains the whole available set of experiments on gravitation. In virtue of the geometrization principle, the Riemannian space in our theory is of field origin, since it appears as an effective force space due to the action of a gravitational field on matter. The RTg leads to an exceptionally strong prediction: The Universe is not closed but just ''flat''. This suggests that in the Universe a ''hidden mass'' should exist in some form of matter
Spherical rhenium metal powder
International Nuclear Information System (INIS)
Leonhardt, T.; Moore, N.; Hamister, M.
2001-01-01
The development of a high-density, spherical rhenium powder (SReP) possessing excellent flow characteristics has enabled the use of advanced processing techniques for the manufacture of rhenium components. The techniques that were investigated were vacuum plasma spraying (VPS), direct-hot isostatic pressing (D-HIP), and various other traditional powder metallurgy processing methods of forming rhenium powder into near-net shaped components. The principal disadvantages of standard rhenium metal powder (RMP) for advanced consolidation applications include: poor flow characteristics; high oxygen content; and low and varying packing densities. SReP will lower costs, reduce processing times, and improve yields when manufacturing powder metallurgy rhenium components. The results of the powder characterization of spherical rhenium powder and the consolidation of the SReP are further discussed. (author)
International Nuclear Information System (INIS)
Berg, S.; Semmes, P.B.; Nazarewicz, W.
1997-01-01
Various theoretical approaches to proton emission from spherical nuclei are investigated, and it is found that all the methods employed give very similar results. The calculated decay widths are found to be qualitatively insensitive to the parameters of the proton-nucleus potential, i.e., changing the potential parameters over a fairly large range typically changes the decay width by no more than a factor of ∼3. Proton half-lives of observed heavy proton emitters are, in general, well reproduced by spherical calculations with the spectroscopic factors calculated in the independent quasiparticle approximation. The quantitative agreement with experimental data obtained in our study requires that the parameters of the proton-nucleus potential be chosen carefully. It also suggests that deformed proton emitters will provide invaluable spectroscopic information on the angular momentum decomposition of single-proton orbitals in deformed nuclei. copyright 1997 The American Physical Society
The Spherical Deformation Model
DEFF Research Database (Denmark)
Hobolth, Asgar
2003-01-01
Miller et al. (1994) describe a model for representing spatial objects with no obvious landmarks. Each object is represented by a global translation and a normal deformation of a sphere. The normal deformation is defined via the orthonormal spherical-harmonic basis. In this paper we analyse the s...... a single central section of the object. We use maximum-likelihood-based inference for this purpose and demonstrate the suggested methods on real data....
The homogeneous boundary value problem of the thick spherical shell
International Nuclear Information System (INIS)
Linder, F.
1975-01-01
With the aim to solve boundary value problems in the same manner as it is attained at thin shell theory (Superposition of Membrane solution to solution of boundary values), one has to search solutions of the equations of equilibrium of the three dimensional thick shell which produce tensions at the cut edge and are zero on the whole shell surface inside and outside. This problem was solved with the premissions of the linear theory of Elasticity. The gained solution is exact and contains the symmetric and non-symmetric behaviour and is described in relatively short analytical expressions for the deformations and tensions, after the problem of the coupled system had been solved. The static condition of the two surfaces (zero tension) leads to a homogeneous system of complex equations with the index of the Legendre spherical function as Eigenvalue. One symmetrical case is calculated numerically and is compared with the method of finite elements. This comparison results in good accordance. (Auth.)
International Nuclear Information System (INIS)
Tevikyan, R.V.
1986-01-01
This paper presents equations that describe particles with spins s = 0, 1/2, 1 completely and which also describe 2s + 2 limiting fields as E → ∞. It is shown that the ordinary Hilbert-Einstein action for the gravitation field must be augmented by the action for the Bose vacuum field. This means that one must introduce in the gravitational equations a cosmological term proportional to the square of the strength of the Bose vacuum field. It is shown that the theory of gravitation describes three realities: matter, field, and vacuum field. A new form of matter--the vacuum field--is introduced into field theory
Gravitational radiation reaction
International Nuclear Information System (INIS)
Tanaka, Takahiro
2006-01-01
We give a short personally-biased review on the recent progress in our understanding of gravitational radiation reaction acting on a point particle orbiting a black hole. The main motivation of this study is to obtain sufficiently precise gravitational waveforms from inspiraling binary compact starts with a large mass ratio. For this purpose, various new concepts and techniques have been developed to compute the orbital evolution taking into account the gravitational self-force. Combining these ideas with a few supplementary new ideas, we try to outline a path to our goal here. (author)
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
CSIR Research Space (South Africa)
Khawula, TNY
2016-03-01
Full Text Available Molybdenum disulfide-modified carbon nanospheres (MoS(sub2)/CNS) with two different morphologies (spherical and flower-like) have been synthesized using hydrothermal techniques and investigated as symmetric pseudocapacitors in an aqueous electrolyte...
Gravitational entropy and thermodynamics away from the horizon
Energy Technology Data Exchange (ETDEWEB)
Brustein, Ram, E-mail: ramyb@bgu.ac.il [Department of Physics, Ben-Gurion University, Beer-Sheva 84105 (Israel); CAS, Ludwig-Maximilians-Universitaet Muenchen, 80333 Muenchen (Germany); Medved, A.J.M., E-mail: j.medved@ru.ac.za [Department of Physics and Electronics, Rhodes University, Grahamstown 6140 (South Africa)
2012-08-29
We define, by an integral of geometric quantities over a spherical shell of arbitrary radius, an invariant gravitational entropy. This definition relies on defining a gravitational energy and pressure, and it reduces at the horizon of both black branes and black holes to Wald's Noether charge entropy. We support the thermodynamic interpretation of the proposed entropy by showing that, for some cases, the field theory duals of the entropy, energy and pressure are the same as the corresponding quantities in the field theory. In this context, the Einstein equations are equivalent to the field theory thermodynamic relation TdS=dE+PdV supplemented by an equation of state.
Design and Transmission Analysis of an Asymmetrical Spherical Parallel Manipulator
DEFF Research Database (Denmark)
Wu, Guanglei; Caro, Stéphane; Wang, Jiawei
2015-01-01
analysis and optimal design of the proposed manipulator based on its kinematic analysis. The input and output transmission indices of the manipulator are defined for its optimum design based on the virtual coefficient between the transmission wrenches and twist screws. The sets of optimal parameters......This paper presents an asymmetrical spherical parallel manipulator and its transmissibility analysis. This manipulator contains a center shaft to both generate a decoupled unlimited-torsion motion and support the mobile platform for high positioning accuracy. This work addresses the transmission...... are identified and the distribution of the transmission index is visualized. Moreover, a comparative study regarding to the performances with the symmetrical spherical parallel manipulators is conducted and the comparison shows the advantages of the proposed manipulator with respect to its spherical parallel...
International Nuclear Information System (INIS)
Yilmaz, H.
1975-01-01
Schwinger's source theory is applied to the problem of gravitation and its quantization. It is shown that within the framework of a flat-space the source theory implementation leads to a violation of probability. To avoid the difficulty one must introduce a curved space-time hence the source concept may be said to necessitate the transition to a curved-space theory of gravitation. It is further shown that the curved-space theory of gravitation implied by the source theory is not equivalent to the conventional Einstein theory. The source concept leads to a different theory where the gravitational field has a stress-energy tensor t/sup nu//sub mu/ which contributes to geometric curvatures
Gravitational lensing of quasars
Eigenbrod, Alexander
2013-01-01
The universe, in all its richness, diversity and complexity, is populated by a myriad of intriguing celestial objects. Among the most exotic of them are gravitationally lensed quasars. A quasar is an extremely bright nucleus of a galaxy, and when such an object is gravitationally lensed, multiple images of the quasar are produced – this phenomenon of cosmic mirage can provide invaluable insights on burning questions, such as the nature of dark matter and dark energy. After presenting the basics of modern cosmology, the book describes active galactic nuclei, the theory of gravitational lensing, and presents a particular numerical technique to improve the resolution of astronomical data. The book then enters the heart of the subject with the description of important applications of gravitational lensing of quasars, such as the measurement of the famous Hubble constant, the determination of the dark matter distribution in galaxies, and the observation of the mysterious inner parts of quasars with much higher r...
Gravitational Waves and Neutrinos
Sturani, Riccardo
2018-01-01
We give an overview about the recent detection of gravitational waves by the Advanced LIGO first and second observing runs and by Advanced Virgo, with emphasis on the prospects for multi-messenger astronomy involving neutrinos detections.
CERN. Geneva
2016-01-01
In the past year, the LIGO-Virgo Collaboration announced the first secure detection of gravitational waves. This discovery heralds the beginning of gravitational wave astronomy: the use of gravitational waves as a tool for studying the dense and dynamical universe. In this talk, I will describe the full spectrum of gravitational waves, from Hubble-scale modes, through waves with periods of years, hours and milliseconds. I will describe the different techniques one uses to measure the waves in these bands, current and planned facilities for implementing these techniques, and the broad range of sources which produce the radiation. I will discuss what we might expect to learn as more events and sources are measured, and as this field matures into a standard part of the astronomical milieu.
Listening music of gravitation
International Nuclear Information System (INIS)
Anon.
2001-01-01
Achievements of precision experiments in Japan (TAMA project) and USA (LIGO Laboratory) in the field of registration of gravitation waves using interferometric gravitational wave detectors are described. Works of the GEO groups in Hannover (Germany) and Vigro (Italy) are noted. Interferometer operation in synchronization during 160 hours demonstrating viability of the technique and its reliability is recorded. Advances in the field of the data analysis with the aim of recording of cosmic signal from noise of the interferometer are noted [ru
Romero, Gustavo E.
2017-01-01
I discuss the recent claims made by Mario Bunge on the philosophical implications of the discovery of gravitational waves. I think that Bunge is right when he points out that the detection implies the materiality of spacetime, but I reject his identification of spacetime with the gravitational field. I show that Bunge's analysis of the spacetime inside a hollow sphere is defective, but this in no way affects his main claim.
Relativistic theory of gravitation
International Nuclear Information System (INIS)
Logunov, A.A.; Mestvirishvili, M.A.
1986-01-01
In the present paper a relativistic theory of gravitation (RTG) is unambiguously constructed on the basis of the special relativity and geometrization principle. In this a gravitational field is treated as the Faraday--Maxwell spin-2 and spin-0 physical field possessing energy and momentum. The source of a gravitational field is the total conserved energy-momentum tensor of matter and of a gravitational field in Minkowski space. In the RTG the conservation laws are strictly fulfilled for the energy-moment and for the angular momentum of matter and a gravitational field. The theory explains the whole available set of experiments on gravity. By virtue of the geometrization principle, the Riemannian space in our theory is of field origin, since it appears as an effective force space due to the action of a gravitational field on matter. The RTG leads to an exceptionally strong prediction: The universe is not closed but just ''flat.'' This suggests that in the universe a ''missing mass'' should exist in a form of matter
Gravitating discs around black holes
International Nuclear Information System (INIS)
Karas, V; Hure, J-M; Semerak, O
2004-01-01
Fluid discs and tori around black holes are discussed within different approaches and with the emphasis on the role of disc gravity. First reviewed are the prospects of investigating the gravitational field of a black hole-disc system using analytical solutions of stationary, axially symmetric Einstein equations. Then, more detailed considerations are focused to the middle and outer parts of extended disc-like configurations where relativistic effects are small and the Newtonian description is adequate. Within general relativity, only a static case has been analysed in detail. Results are often very inspiring. However, simplifying assumptions must be imposed: ad hoc profiles of the disc density are commonly assumed and the effects of frame-dragging are completely lacking. Astrophysical discs (e.g. accretion discs in active galactic nuclei) typically extend far beyond the relativistic domain and are fairly diluted. However, self-gravity is still essential for their structure and evolution, as well as for their radiation emission and the impact on the surrounding environment. For example, a nuclear star cluster in a galactic centre may bear various imprints of mutual star-disc interactions, which can be recognized in observational properties, such as the relation between the central mass and stellar velocity dispersion. (topical review)
Axially symmetric Lorentzian wormholes in general relativity
International Nuclear Information System (INIS)
Schein, F.
1997-11-01
The field equations of Einstein's theory of general relativity, being local, do not fix the global structure of space-time. They admit topologically non-trivial solutions, including spatially closed universes and the amazing possibility of shortcuts for travel between distant regions in space and time - so-called Lorentzian wormholes. The aim of this thesis is to (mathematically) construct space-times which contain traversal wormholes connecting arbitrary distant regions of an asymptotically flat or asymptotically de Sitter universe. Since the wormhole mouths appear as two separate masses in the exterior space, space-time can at best be axially symmetric. We eliminate the non-staticity caused by the gravitational attraction of the mouths by anchoring them by strings held at infinity or, alternatively, by electric repulsion. The space-times are obtained by surgically grafting together well-known solutions of Einstein's equations along timelike hypersurfaces. This surgery naturally concentrates a non-zero stress-energy tensor on the boundary between the two space-times which can be investigated by using the standard thin shell formalism. It turns out that, when using charged black holes, the provided constructions are possible without violation of any of the energy conditions. In general, observers living in the axially symmetric, asymptotically flat (respectively asymptotically de Sitter) region axe able to send causal signals through the topologically non-trivial region. However, the wormhole space-times contain closed timelike curves. Because of this explicit violation of global hyperbolicity these models do not serve as counterexamples to known topological censorship theorems. (author)
Cooperstock's counterexample to the gravitational-radiation quadrupole formula
International Nuclear Information System (INIS)
Walker, M.
1986-01-01
Cooperstock has recently modified the axially symmetric gravitational two-body problem previously analyzed by himself, Lim, and Hobill by introducing a new assumption, that ''The system undergoes a smooth transition from the static state to free-fall and the motion. . .consists of the two bodies accelerating towards each other while undergoing slow tidal deformation.'' This assumption is inconsistent with his solution of the field equations. The quadrupole formula correctly describes the radiation emitted
Singularities and horizons in the collisions of gravitational waves
International Nuclear Information System (INIS)
Yurtsever, U.H.
1989-01-01
This thesis presents a study of the dynamical, nonlinear interaction of colliding gravitational waves, as described by classical general relativity. In the work on the collisions of exactly-plane waves, it is shown that Killing horizons in any plane-symmetric spacetime are unstable against small plane-symmetric perturbations. It is thus concluded that the Killing-Cauchy horizons produced by the collisions of some exactly plane gravitational waves are nongeneric, and the generic initial data for the colliding plane waves always produce pure spacetime singularities without such horizons. This conclusion is later proved rigorously (using the full nonlinear theory rather than perturbation theory), in connection with an analysis of the asymptotic singularity structure of a general colliding plane-wave spacetime. This analysis also proves that asymptotically the singularities created by colliding plane waves are of inhomogeneous-Kasner type; the asymptotic Kasner axes and exponents of these singularities in general depend on the spatial coordinate that runs tangentially to the singularity in the non-plane-symmetric direction. In the work on collisions of almost-plane gravitational waves, first some general properties of single almost-plane gravitational-wave spacetimes are explored. It is shown that, by contrast with an exact plane wave, an almost-plane gravitational wave cannot have a propagation direction that is Killing; i.e., it must diffract and disperse as it propagates. It is also shown that an almost-plane wave cannot be precisely sandwiched between two null wave-fronts; i.e., it must leave behind tails in the spacetime region through which is passes
Mesotherapy for benign symmetric lipomatosis.
Hasegawa, Toshio; Matsukura, Tomoyuki; Ikeda, Shigaku
2010-04-01
Benign symmetric lipomatosis, also known as Madelung disease, is a rare disorder characterized by fat distribution around the shoulders, arms, and neck in the context of chronic alcoholism. Complete excision of nonencapsulated lipomas is difficult. However, reports describing conservative therapeutic measures for lipomatosis are rare. The authors present the case of a 42-year-old man with a diagnosis of benign symmetric lipomatosis who had multiple, large, symmetrical masses in his neck. Multiple phosphatidylcholine injections in the neck were administered 4 weeks apart, a total of seven times to achieve lipolysis. The patient's lipomatosis improved in response to the injections, and he achieved good cosmetic results. Intralesional injection, termed mesotherapy, using phosphatidylcholine is a potentially effective therapy for benign symmetric lipomatosis that should be reconsidered as a therapeutic option for this disease.
Looking for symmetric Bell inequalities
Bancal, Jean-Daniel; Gisin, Nicolas; Pironio, Stefano
2010-01-01
Finding all Bell inequalities for a given number of parties, measurement settings and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full Bell polytope. As an illustration of our method, we generate 238 885 new Bell inequalities and 1085 new Svetlichny inequalities. We find, in particular, facet inequalities for Bell e...
Numerical relativity in spherical coordinates with the Einstein Toolkit
Mewes, Vassilios; Zlochower, Yosef; Campanelli, Manuela; Ruchlin, Ian; Etienne, Zachariah B.; Baumgarte, Thomas W.
2018-04-01
Numerical relativity codes that do not make assumptions on spatial symmetries most commonly adopt Cartesian coordinates. While these coordinates have many attractive features, spherical coordinates are much better suited to take advantage of approximate symmetries in a number of astrophysical objects, including single stars, black holes, and accretion disks. While the appearance of coordinate singularities often spoils numerical relativity simulations in spherical coordinates, especially in the absence of any symmetry assumptions, it has recently been demonstrated that these problems can be avoided if the coordinate singularities are handled analytically. This is possible with the help of a reference-metric version of the Baumgarte-Shapiro-Shibata-Nakamura formulation together with a proper rescaling of tensorial quantities. In this paper we report on an implementation of this formalism in the Einstein Toolkit. We adapt the Einstein Toolkit infrastructure, originally designed for Cartesian coordinates, to handle spherical coordinates, by providing appropriate boundary conditions at both inner and outer boundaries. We perform numerical simulations for a disturbed Kerr black hole, extract the gravitational wave signal, and demonstrate that the noise in these signals is orders of magnitude smaller when computed on spherical grids rather than Cartesian grids. With the public release of our new Einstein Toolkit thorns, our methods for numerical relativity in spherical coordinates will become available to the entire numerical relativity community.
Mostert, W.; Pullin, D. I.; Wheatley, V.; Samtaney, Ravi
2017-01-01
We present numerical simulations of ideal magnetohydrodynamics showing suppression of the Richtmyer-Meshkov instability in spherical implosions in the presence of an octahedrally symmetric magnetic field. This field configuration is of interest owing to its high degree of spherical symmetry in comparison with previously considered dihedrally symmetric fields. The simulations indicate that the octahedral field suppresses the instability comparably to the other previously considered candidate fields for light-heavy interface accelerations while retaining a highly symmetric underlying flow even at high field strengths. With this field, there is a reduction in the root-mean-square perturbation amplitude of up to approximately 50% at representative time under the strongest field tested while maintaining a homogeneous suppression pattern compared to the other candidate fields.
Mostert, W.
2017-01-27
We present numerical simulations of ideal magnetohydrodynamics showing suppression of the Richtmyer-Meshkov instability in spherical implosions in the presence of an octahedrally symmetric magnetic field. This field configuration is of interest owing to its high degree of spherical symmetry in comparison with previously considered dihedrally symmetric fields. The simulations indicate that the octahedral field suppresses the instability comparably to the other previously considered candidate fields for light-heavy interface accelerations while retaining a highly symmetric underlying flow even at high field strengths. With this field, there is a reduction in the root-mean-square perturbation amplitude of up to approximately 50% at representative time under the strongest field tested while maintaining a homogeneous suppression pattern compared to the other candidate fields.
Equations of motion derived from a generalization of Einstein's equation for the gravitational field
International Nuclear Information System (INIS)
Mociutchi, C.
1980-01-01
The extended Einstein's equation, combined with a vectorial theory of maxwellian type of the gravitational field, leads to: a) the equation of motion; b) the equation of the trajectory for the static case of spherical symmetry, the test particle having a rest mass other than zero, and c) the propagation of light on null geodesics. All the basic tests of the theory given by Einstein's extended equation. Thus, the new theory of gravitation suggested by us is competitive. (author)
Evolution of the spherical clusters
International Nuclear Information System (INIS)
Surdin, V.G.
1978-01-01
The possible processes of the Galaxy spherical clusters formation and evolution are described on a popular level. The orbits of spherical cluster motion and their spatial velocities are determined. Given are the distrbutions of spherical cluster stars according to their velocities and the observed distribution of spherical clusters in the area of the Galaxy slow evolution. The dissipation and dynamic friction processes destructing clusters with the mass less than 10 4 of solar mass and bringing about the reduction of clusters in the Galaxy are considered. The paradox of forming mainly X-ray sources in spherical clusters is explained. The schematic image of possible ways of forming X-ray sources in spherical clusters is given
The Role of Orthogonal Polynomials in Tailoring Spherical Distributions to Kurtosis Requirements
Directory of Open Access Journals (Sweden)
Luca Bagnato
2016-08-01
Full Text Available This paper carries out an investigation of the orthogonal-polynomial approach to reshaping symmetric distributions to fit in with data requirements so as to cover the multivariate case. With this objective in mind, reference is made to the class of spherical distributions, given that they provide a natural multivariate generalization of univariate even densities. After showing how to tailor a spherical distribution via orthogonal polynomials to better comply with kurtosis requirements, we provide operational conditions for the positiveness of the resulting multivariate Gram–Charlier-like expansion, together with its kurtosis range. Finally, the approach proposed here is applied to some selected spherical distributions.
Spherical tokamak development in Brazil
Energy Technology Data Exchange (ETDEWEB)
Ludwig, Gerson Otto; Bosco, Edson Del; Ferreira, Julio Guimaraes [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma] (and others)
2003-07-01
The general characteristics of spherical tokamaks, or spherical tori, with a brief view of work in this area already performed or in progress at several institutions worldwide are described. The paper presents also the steps in the development of the ETE (Experiment Tokamak spheric) project, its research program, technical characteristics and operating conditions as of December, 2002 a the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)
Spherical tokamak development in Brazil
International Nuclear Information System (INIS)
Ludwig, Gerson Otto; Bosco, Edson Del; Ferreira, Julio Guimaraes
2003-01-01
The general characteristics of spherical tokamaks, or spherical tori, with a brief view of work in this area already performed or in progress at several institutions worldwide are described. The paper presents also the steps in the development of the ETE (Experiment Tokamak spheric) project, its research program, technical characteristics and operating conditions as of December, 2002 a the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)
Gravitational theory in atomic scale units in Dirac cosmology
International Nuclear Information System (INIS)
Davidson, W.
1984-01-01
The implication of Dirac's large numbers hypothesis (LNH) that there are two cosmological space-time metrics, gravitational (E) and atomic (A), is used to formulate the gravitational laws for a general mass system in atomic scale units within such a cosmology. The gravitational laws are illustrated in application to the case of a single spherical mass immersed in the smoothed out expanding universe. The condition is determined for such a metric to apply approximately just outside a typical member of a cosmic distribution of such masses. Conversely, the condition is given when the influence of the universe as a whole can be neglected outside such a mass. In the latter situation, which applies in particular to stars, a Schwarzschild-type metric is derived which incorporates variable G in accordance with the LNH. The dynamics of freely moving particles and photons in such a metric are examined according to the theory and observational tests are formulated. (author)
Gravitational waves and antennas
CERN. Geneva
2003-01-01
Gravitational waves and their detection represent today a hot topic, which promises to play a central role in astrophysics, cosmology and theoretical physics. Technological developments have enabled the construction of such sensitive detectors that the detection of gravitational radiation and the start of a new astronomy could become a reality during the next few years. This is expected to bring a revolution in our knowledge of the universe by allowing the observation of hiterto unseen phenomena such as coalescence of compact objects (neutron stars and black holes) fall of stars into supermassive black holes, stellar core collapses, big bang relics and the new and unexpected. In these lectures I give a brief overview of this challenging field of modern physics. Topics : Basic properties of gravitational radiation. Astrophysical sources. Principle of operation of detectors. Interferometers (both ground based and space-based), bars and spheres. Present status of the experiments, their recent results and their f...
Ohanian, Hans C
2013-01-01
The third edition of this classic textbook is a quantitative introduction for advanced undergraduates and graduate students. It gently guides students from Newton's gravitational theory to special relativity, and then to the relativistic theory of gravitation. General relativity is approached from several perspectives: as a theory constructed by analogy with Maxwell's electrodynamics, as a relativistic generalization of Newton's theory, and as a theory of curved spacetime. The authors provide a concise overview of the important concepts and formulas, coupled with the experimental results underpinning the latest research in the field. Numerous exercises in Newtonian gravitational theory and Maxwell's equations help students master essential concepts for advanced work in general relativity, while detailed spacetime diagrams encourage them to think in terms of four-dimensional geometry. Featuring comprehensive reviews of recent experimental and observational data, the text concludes with chapters on cosmology an...
Spherical grating spectrometers
O'Donoghue, Darragh; Clemens, J. Christopher
2014-07-01
We describe designs for spectrometers employing convex dispersers. The Offner spectrometer was the first such instrument; it has almost exclusively been employed on satellite platforms, and has had little impact on ground-based instruments. We have learned how to fabricate curved Volume Phase Holographic (VPH) gratings and, in contrast to the planar gratings of traditional spectrometers, describe how such devices can be used in optical/infrared spectrometers designed specifically for curved diffraction gratings. Volume Phase Holographic gratings are highly efficient compared to conventional surface relief gratings; they have become the disperser of choice in optical / NIR spectrometers. The advantage of spectrometers with curved VPH dispersers is the very small number of optical elements used (the simplest comprising a grating and a spherical mirror), as well as illumination of mirrors off axis, resulting in greater efficiency and reduction in size. We describe a "Half Offner" spectrometer, an even simpler version of the Offner spectrometer. We present an entirely novel design, the Spherical Transmission Grating Spectrometer (STGS), and discuss exemplary applications, including a design for a double-beam spectrometer without any requirement for a dichroic. This paradigm change in spectrometer design offers an alternative to all-refractive astronomical spectrometer designs, using expensive, fragile lens elements fabricated from CaF2 or even more exotic materials. The unobscured mirror layout avoids a major drawback of the previous generation of catadioptric spectrometer designs. We describe laboratory measurements of the efficiency and image quality of a curved VPH grating in a STGS design, demonstrating, simultaneously, efficiency comparable to planar VPH gratings along with good image quality. The stage is now set for construction of a prototype instrument with impressive performance.
Kelly, Bernard J.
2010-01-01
Einstein's General Theory of Relativity is our best classical description of gravity, and informs modern astronomy and astrophysics at all scales: stellar, galactic, and cosmological. Among its surprising predictions is the existence of gravitational waves -- ripples in space-time that carry energy and momentum away from strongly interacting gravitating sources. In my talk, I will give an overview of the properties of this radiation, recent breakthroughs in computational physics allowing us to calculate the waveforms from galactic mergers, and the prospect of direct observation with interferometric detectors such as LIGO and LISA.
Supersymmetry and gravitational duality
International Nuclear Information System (INIS)
Argurio, Riccardo; Dehouck, Francois; Houart, Laurent
2009-01-01
We study how the supersymmetry algebra copes with gravitational duality. As a playground, we consider a charged Taub-Newman-Unti-Tamburino(NUT) solution of D=4, N=2 supergravity. We find explicitly its Killing spinors, and the projection they obey provides evidence that the dual magnetic momenta necessarily have to appear in the supersymmetry algebra. The existence of such a modification is further supported using an approach based on the Nester form. In the process, we find new expressions for the dual magnetic momenta, including the NUT charge. The same expressions are then rederived using gravitational duality.
Formation of solar-type stars in spherical symmetry. II. Effects of detailed constitutive relations
International Nuclear Information System (INIS)
Winkler, K.A.; Newman, M.J.
1980-01-01
A time-dependent hydrodynamical calculation of the spherically symmetric self-gravitational collapse and accretion of a homogeneous Jeans unstable 1 M/sub sun/ protostellar cloud has been performed using the detailed equation-of-state tables of Fontaine, Graboske, and Van Horn. It is found that the inner 0.03 M/sub sun/ of the core enters a partially degenerate region during the main accretion phase. A well-pronounced off-center temperature maximum develops under the combined influences of electron degeneracy and pressure ionization. A hydrogen ionization zone within the quasi-hydrostatic core drives core oscillations with typical periods of a few months in the transition phase from the second (final) collpase to the accretion stage. A third collapse does not occur, because of the gradual (''soft'') ionization of hydrogen at high density (rhoapprox. =1 g cm -3 ). Gas opacities were taken from the King IVa tables of Cox and Tabor, and dust opacities from Bertout and Yorke. Energy transport by radiation was treated by solution of the time-dependent moment equations with an Eddington factor f derived from the static transport equation. The diffusion approximation with f=1/3 would offer an adequate description of the protostellar core, but the intensity of the constant luminosity radiation field becomes highly anisotropic in local optically thin regions of the envelope. The degree of anisotropy in optically thick regions is determined by the temperature dependence of the dust opacity and the depletion of matter from the envelope. Near the end of the accretion phase the entire envelope is characterized by complete anisotropy f=1
International Nuclear Information System (INIS)
Sussman, Roberto A.
2009-01-01
A numerical approach is considered for spherically symmetric spacetimes that generalize Lemaitre-Tolman-Bondi dust solutions to nonzero pressure ('LTB spacetimes'). We introduce quasilocal (QL) variables that are covariant LTB objects satisfying evolution equations of Friedman-Lemaitre-Robertson-Walker (FLRW) cosmologies. We prove rigorously that relative deviations of the local covariant scalars from the QL scalars are nonlinear, gauge invariant and covariant perturbations on a FLRW formal background given by the QL scalars. The dynamics of LTB spacetimes is completely determined by the QL scalars and these exact perturbations. Since LTB spacetimes are compatible with a wide variety of ''equations of state,'' either single fluids or mixtures, a large number of known solutions with dark matter and dark energy sources in a FLRW framework (or with linear perturbations) can be readily examined under idealized but nontrivial inhomogeneous conditions. Coordinate choices and initial conditions are derived for a numerical treatment of the perturbation equations, allowing us to study nonlinear effects in a variety of phenomena, such as gravitational collapse, nonlocal effects, void formation, dark matter and dark energy couplings, and particle creation. In particular, the embedding of inhomogeneous regions can be performed by a smooth matching with a suitable FLRW solution, thus generalizing the Newtonian 'top hat' models that are widely used in astrophysical literature. As examples of the application of the formalism, we examine numerically the formation of a black hole in an expanding Chaplygin gas FLRW universe, as well as the evolution of density clumps and voids in an interactive mixture of cold dark matter and dark energy.
International Nuclear Information System (INIS)
Manoff, S.
1979-07-01
By utilization of the method of Lagrangians with covariant derivatives (MLCD) the different energy-momentum tensors (canonical, generalized canonical, symmetrical) and the relations between them are considered. On this basis, Einstein's theory of gravitation is studied as a field theory with a Lagrangian density of the type Lsub(g)=√-g.Lsub(g)(gsub(ij),Rsub(A)), (Rsub(A)=Rsub(ijkl)). It is shown that the energy-momentum tensors of the gravitational field can be defined for this theory. The symmetrical energy-momentum tensor of the gravitational field sub(gs)Tsub(k)sup(i), which in the general case is not a local conserved quantity (sub(gs)Tsub(k)sup(i)sub(;i) unequal 0) (in contrast to the material fields satisfying condition sub(Ms)Tsub(k)sup(i)sub(;i) = 0), is equal to zero for the gravitational field in vacuum (cosmological constant Λ = 0). Equations of the gravitational field of a new type are suggested, leading to equations of motion (sub(Ms)Tsub(k)sup(i) + sub(gs)Tsub(k)sup(i))sub(;i) = 0. The equations corresponding to the Lagrangian density Lsub(g)=(√-g/kappasub(o)) (R - lambda approximately), lambda approximately = const., are considered. The equations of Einstein Rsub(ij) = 0 are obtained in the case of gravitational field in vacuum. Some particular cases are examined as an illustration to material fields and the corresponding gravitational equations. (author)
Spherical collapse of small masses in the ghost-free gravity
International Nuclear Information System (INIS)
Frolov, Valeri P.; Zelnikov, Andrei; Netto, Tibério de Paula
2015-01-01
We discuss some properties of recently proposed models of a ghost-free gravity. For this purpose we study solutions of linearized gravitational equations in the framework of such a theory. We mainly focus on the version of the ghost-free theory with the exponential modification exp (◻/μ 2 )◻ −1 of the free propagator. The following three problems are discussed: (i) gravitational field of a point mass; (ii) Penrose limit of a point source boosted to the speed of light; and (iii) spherical gravitational collapse of null fluid. For the first problem we demonstrate that it can be solved by using the method of heat kernels and obtain a solution in a spacetime with arbitrary number of dimensions. For the second problem we also find the corresponding gyraton-type solutions of the ghost-free gravitational equations for any number of dimensions. For the third problem we obtain solutions for the gravitational field for the collapse of both “thin" and “thick" spherical null shells. We demonstrate how the ghost-free modification of the gravitational equations regularize the solutions of the linearized Einstein equations and smooth out their singularities.
Spherical collapse of small masses in the ghost-free gravity
Energy Technology Data Exchange (ETDEWEB)
Frolov, Valeri P.; Zelnikov, Andrei [Theoretical Physics Institute, Department of Physics, University of Alberta,Edmonton, AB, T6G 2E1 (Canada); Netto, Tibério de Paula [Theoretical Physics Institute, Department of Physics, University of Alberta,Edmonton, AB, T6G 2E1 (Canada); Departamento de Fisica - ICE, Universidade Federal de Juiz de Fora,Campus da UFJF, CEP: 36036-900, Juiz de Fora, MG (Brazil)
2015-06-17
We discuss some properties of recently proposed models of a ghost-free gravity. For this purpose we study solutions of linearized gravitational equations in the framework of such a theory. We mainly focus on the version of the ghost-free theory with the exponential modification exp (◻/μ{sup 2})◻{sup −1} of the free propagator. The following three problems are discussed: (i) gravitational field of a point mass; (ii) Penrose limit of a point source boosted to the speed of light; and (iii) spherical gravitational collapse of null fluid. For the first problem we demonstrate that it can be solved by using the method of heat kernels and obtain a solution in a spacetime with arbitrary number of dimensions. For the second problem we also find the corresponding gyraton-type solutions of the ghost-free gravitational equations for any number of dimensions. For the third problem we obtain solutions for the gravitational field for the collapse of both “thin' and “thick' spherical null shells. We demonstrate how the ghost-free modification of the gravitational equations regularize the solutions of the linearized Einstein equations and smooth out their singularities.
Einstein-Rosen gravitational waves
International Nuclear Information System (INIS)
Astefanoaei, Iordana; Maftei, Gh.
2001-01-01
In this paper we analyse the behaviour of the gravitational waves in the approximation of the far matter fields, considering the indirect interaction between the matter sources and the gravitational field, in a cosmological model based on the Einstein-Rosen solution, Because the properties of the gravitational waves obtained as the solutions of Einstein fields equations (the gravitational field equations) are most obvious in the weak gravitational fields we consider here, the gravitational field in the linear approximation. Using the Newman-Penrose formalism, we calculate in the null-tetradic base (e a ), the spin coefficients, the directional derivates and the tetradic components of Ricci and Weyl tensors. From the Einstein field equations we obtained the solution for b(z, t) what described the behaviour of gravitational wave in Einstein-Rosen Universe and in the particular case, when t → ∞, p(z, t) leads us to the primordial gravitational waves in the Einstein-Rosen Universe. (authors)
Gravitational Waves: The Evidence Mounts
Wick, Gerald L.
1970-01-01
Reviews the work of Weber and his colleagues in their attempts at detecting extraterrestial gravitational waves. Coincidence events recorded by special detectors provide the evidence for the existence of gravitational waves. Bibliography. (LC)
Directory of Open Access Journals (Sweden)
Igor Salom
2017-07-01
Full Text Available We construct the three-body permutation symmetric hyperspherical harmonics to be used in the non-relativistic three-body Schrödinger equation in three spatial dimensions (3D. We label the state vectors according to the S3⊗SO(3rot⊂O(2⊗SO(3rot⊂U(3⋊S2⊂O(6 subgroup chain, where S3 is the three-body permutation group and S2 is its two element subgroup containing transposition of first two particles, O(2 is the “democracy transformation”, or “kinematic rotation” group for three particles; SO(3rot is the 3D rotation group, and U(3,O(6 are the usual Lie groups. We discuss the good quantum numbers implied by the above chain of algebras, as well as their relation to the S3 permutation properties of the harmonics, particularly in view of the SO(3rot⊂SU(3 degeneracy. We provide a definite, practically implementable algorithm for the calculation of harmonics with arbitrary finite integer values of the hyper angular momentum K, and show an explicit example of this construction in a specific case with degeneracy, as well as tables of K≤6 harmonics. All harmonics are expressed as homogeneous polynomials in the Jacobi vectors (λ,ρ with coefficients given as algebraic numbers unless the “operator method” is chosen for the lifting of the SO(3rot⊂SU(3 multiplicity and the dimension of the degenerate subspace is greater than four – in which case one must resort to numerical diagonalization; the latter condition is not met by any K≤15 harmonic, or by any L≤7 harmonic with arbitrary K. We also calculate a certain type of matrix elements (the Gaunt integrals of products of three harmonics in two ways: 1 by explicit evaluation of integrals and 2 by reduction to known SU(3 Clebsch–Gordan coefficients. In this way we complete the calculation of the ingredients sufficient for the solution to the quantum-mechanical three-body bound state problem.
Harmonic analysis on symmetric spaces
Terras, Audrey
This text explores the geometry and analysis of higher rank analogues of the symmetric spaces introduced in volume one. To illuminate both the parallels and differences of the higher rank theory, the space of positive matrices is treated in a manner mirroring that of the upper-half space in volume one. This concrete example furnishes motivation for the general theory of noncompact symmetric spaces, which is outlined in the final chapter. The book emphasizes motivation and comprehensibility, concrete examples and explicit computations (by pen and paper, and by computer), history, and, above all, applications in mathematics, statistics, physics, and engineering. The second edition includes new sections on Donald St. P. Richards’s central limit theorem for O(n)-invariant random variables on the symmetric space of GL(n, R), on random matrix theory, and on advances in the theory of automorphic forms on arithmetic groups.
Gravitation radiation observations
Glass, E. N.
2017-01-01
The notion of gravitational radiation begins with electromagnetic radiation. In 1887 Heinrich Hertz, working in one room, generated and received electromagnetic radiation. Maxwell's equations describe the electromagnetic field. The quanta of electromagnetic radiation are spin 1 photons. They are fundamental to atomic physics and quantum electrodynamics.
Alternative equations of gravitation
International Nuclear Information System (INIS)
Pinto Neto, N.
1983-01-01
It is shown, trough a new formalism, that the quantum fluctuation effects of the gravitational field in Einstein's equations are analogs to the effects of a continuum medium in Maxwell's Electrodynamics. Following, a real example of the applications of these equations is studied. Qunatum fluctuations effects as perturbation sources in Minkowski and Friedmann Universes are examined. (L.C.) [pt
Glitches and gravitational waves
Indian Academy of Sciences (India)
A M Srivastava
2017-10-09
Oct 9, 2017 ... We also discuss gravitational wave production due to rapidly changing ... efficient source of energy loss during the cooling of the neutron star. ..... [3] U S Gupta, R K Mohapatra, A M Srivastava and V K. Tiwari, Phys. Rev. D 82 ...
Extragalactic Gravitational Collapse
Rees, Martin J.
After some introductory "numerology", routes towards black hole formation are briefly reviewed; some properties of black holes relevant to theories for active galactic nuclei are then described. Applications are considered to specific models for energy generation and the production of relativistic beams. The paper concludes with a discussion of extragalactic sources of gravitational waves.
Indian Academy of Sciences (India)
Keywords. General relativity; gravitational waves; astrophysics; interferometry. Author Affiliations. P Ajith1 K G Arun2. LIGO Laboratory and Theoretical Astrophysics California Institute of Technology MS 18-34, Pasadena CA 91125, USA. Chennai Mathematical Institute Plot H1, SIPCOT IT Park Siruseri, Padur Post Chennai ...
International Nuclear Information System (INIS)
Kikkawa, Keiji; Nakanishi, Noboru; Nariai, Hidekazu
1983-01-01
These proceedings contain the articles presented at the named symposium. They deal with geometrical aspects of gauge theory and gravitation, special problems in gauge theories, quantum field theory in curved space-time, quantum gravity, supersymmetry including supergravity, and grand unification. See hints under the relevant topics. (HSI)
Looking for symmetric Bell inequalities
International Nuclear Information System (INIS)
Bancal, Jean-Daniel; Gisin, Nicolas; Pironio, Stefano
2010-01-01
Finding all Bell inequalities for a given number of parties, measurement settings and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full Bell polytope. As an illustration of our method, we generate 238 885 new Bell inequalities and 1085 new Svetlichny inequalities. We find, in particular, facet inequalities for Bell experiments involving two parties and two measurement settings that are not of the Collins-Gisin-Linden-Massar-Popescu type.
Symmetric normalisation for intuitionistic logic
DEFF Research Database (Denmark)
Guenot, Nicolas; Straßburger, Lutz
2014-01-01
We present two proof systems for implication-only intuitionistic logic in the calculus of structures. The first is a direct adaptation of the standard sequent calculus to the deep inference setting, and we describe a procedure for cut elimination, similar to the one from the sequent calculus......, but using a non-local rewriting. The second system is the symmetric completion of the first, as normally given in deep inference for logics with a DeMorgan duality: all inference rules have duals, as cut is dual to the identity axiom. We prove a generalisation of cut elimination, that we call symmetric...
Diagrams for symmetric product orbifolds
International Nuclear Information System (INIS)
Pakman, Ari; Rastelli, Leonardo; Razamat, Shlomo S.
2009-01-01
We develop a diagrammatic language for symmetric product orbifolds of two-dimensional conformal field theories. Correlation functions of twist operators are written as sums of diagrams: each diagram corresponds to a branched covering map from a surface where the fields are single-valued to the base sphere where twist operators are inserted. This diagrammatic language facilitates the study of the large N limit and makes more transparent the analogy between symmetric product orbifolds and free non-abelian gauge theories. We give a general algorithm to calculate the leading large N contribution to four-point correlators of twist fields.
Looking for symmetric Bell inequalities
Energy Technology Data Exchange (ETDEWEB)
Bancal, Jean-Daniel; Gisin, Nicolas [Group of Applied Physics, University of Geneva, 20 rue de l' Ecole-de Medecine, CH-1211 Geneva 4 (Switzerland); Pironio, Stefano, E-mail: jean-daniel.bancal@unige.c [Laboratoire d' Information Quantique, Universite Libre de Bruxelles (Belgium)
2010-09-24
Finding all Bell inequalities for a given number of parties, measurement settings and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full Bell polytope. As an illustration of our method, we generate 238 885 new Bell inequalities and 1085 new Svetlichny inequalities. We find, in particular, facet inequalities for Bell experiments involving two parties and two measurement settings that are not of the Collins-Gisin-Linden-Massar-Popescu type.
Symmetric autocompensating quantum key distribution
Walton, Zachary D.; Sergienko, Alexander V.; Levitin, Lev B.; Saleh, Bahaa E. A.; Teich, Malvin C.
2004-08-01
We present quantum key distribution schemes which are autocompensating (require no alignment) and symmetric (Alice and Bob receive photons from a central source) for both polarization and time-bin qubits. The primary benefit of the symmetric configuration is that both Alice and Bob may have passive setups (neither Alice nor Bob is required to make active changes for each run of the protocol). We show that both the polarization and the time-bin schemes may be implemented with existing technology. The new schemes are related to previously described schemes by the concept of advanced waves.
First results of spherical GEMs
Pinto, Serge Duarte; Brock, Ian; Croci, Gabriele; David, Eric; de Oliveira, Rui; Ropelewski, Leszek; van Stenis, Miranda; Taureg, Hans; Villa, Marco
2010-01-01
We developed a method to make GEM foils with a spherical geometry. Tests of this procedure and with the resulting spherical GEMs are presented. Together with a spherical drift electrode, a spherical conversion gap can be formed. This eliminates the parallax error for detection of x-rays, neutrons or UV photons when a gaseous converter is used. This parallax error limits the spatial resolution at wide scattering angles. Besides spherical GEMs, we have developed curved spacers to maintain accurate spacing, and a conical field cage to prevent edge distortion of the radial drift field up to the limit of the angular acceptance of the detector. With these components first tests are done in a setup with a spherical entrance window but a planar readout structure; results will be presented and discussed. A flat readout structure poses difficulties, however. Therefore we will show advanced plans to make a prototype of an entirely spherical double-GEM detector, including a spherical 2D readout structure. This detector w...
Spherical Torus Center Stack Design
International Nuclear Information System (INIS)
C. Neumeyer; P. Heitzenroeder; C. Kessel; M. Ono; M. Peng; J. Schmidt; R. Woolley; I. Zatz
2002-01-01
The low aspect ratio spherical torus (ST) configuration requires that the center stack design be optimized within a limited available space, using materials within their established allowables. This paper presents center stack design methods developed by the National Spherical Torus Experiment (NSTX) Project Team during the initial design of NSTX, and more recently for studies of a possible next-step ST (NSST) device
Position Control of a 3-CPU Spherical Parallel Manipulator
Directory of Open Access Journals (Sweden)
Massimo Callegari
2013-01-01
Full Text Available The paper presents the first experimental results on the control of a prototypal robot designed for the orientation of parts or tools. The innovative machine is a spherical parallel manipulator actuated by 3 linear motors; several position control schemes have been tested and compared with the final aim of designing an interaction controller. The relative simplicity of machine kinematics allowed to test algorithms requiring the closed-loop evaluation of both inverse and direct kinematics; the compensation of gravitational terms has been experimented as well.
Towards Gravitating Discs around Stationary Black Holes
Semerák, Oldřich
This article outlines the search for an exact general relativistic description of the exterior(vacuum) gravitational field of a rotating spheroidal black hole surrounded by a realistic axially symmetric disc of matter. The problem of multi-body stationary spacetimes is first exposed from the perspective of the relativity theory (section 1) and astrophysics (section 2), listing the basic methods employed and results obtained. Then (in section 3) basic formulas for stationary axisymmetric solutions are summarized. Sections 4 and 5 review what we have learnt with Miroslav Žáček and Tomáš Zellerin about certain static and stationary situations recently. Concluding remarks are given in section 6. Although the survey part is quite general, the list of references cannot be complete.Our main desideratum was the informative value rather than originality — novelties have been preferred, mainly reviews and those with detailed introductions.
Symmetric relations of finite negativity
Kaltenbaeck, M.; Winkler, H.; Woracek, H.; Forster, KH; Jonas, P; Langer, H
2006-01-01
We construct and investigate a space which is related to a symmetric linear relation S of finite negativity on an almost Pontryagin space. This space is the indefinite generalization of the completion of dom S with respect to (S.,.) for a strictly positive S on a Hilbert space.
Tilting-connected symmetric algebras
Aihara, Takuma
2010-01-01
The notion of silting mutation was introduced by Iyama and the author. In this paper we mainly study silting mutation for self-injective algebras and prove that any representation-finite symmetric algebra is tilting-connected. Moreover we give some sufficient conditions for a Bongartz-type Lemma to hold for silting objects.
Symmetric group representations and Z
Adve, Anshul; Yong, Alexander
2017-01-01
We discuss implications of the following statement about the representation theory of symmetric groups: every integer appears infinitely often as an irreducible character evaluation, and every nonnegative integer appears infinitely often as a Littlewood-Richardson coefficient and as a Kronecker coefficient.
Symmetric Key Authentication Services Revisited
Crispo, B.; Popescu, B.C.; Tanenbaum, A.S.
2004-01-01
Most of the symmetric key authentication schemes deployed today are based on principles introduced by Needham and Schroeder [15] more than twenty years ago. However, since then, the computing environment has evolved from a LAN-based client-server world to include new paradigms, including wide area
Quantum systems and symmetric spaces
International Nuclear Information System (INIS)
Olshanetsky, M.A.; Perelomov, A.M.
1978-01-01
Certain class of quantum systems with Hamiltonians related to invariant operators on symmetric spaces has been investigated. A number of physical facts have been derived as a consequence. In the classical limit completely integrable systems related to root systems are obtained
The symmetric longest queue system
van Houtum, Geert-Jan; Adan, Ivo; van der Wal, Jan
1997-01-01
We derive the performance of the exponential symmetric longest queue system from two variants: a longest queue system with Threshold Rejection of jobs and one with Threshold Addition of jobs. It is shown that these two systems provide lower and upper bounds for the performance of the longest queue
Sirius-T, a symmetrically illuminated ICF tritium production facility
International Nuclear Information System (INIS)
Sviatoslavsky, I.N.; Sawan, M.E.; Moses, G.A.; Kulcinski, G.L.; Engelstad, R.L.; Larsen, E.; Lovell, E.; MacFarlane, J.; Peterson, R.R.; Wittenberg, L.J.
1989-01-01
A scoping study of a symmetrically illuminated ICF tritium production facility utilizing a KrF laser is presented. A single shell ICF target is illuminated by 92 beams symmetrically distributed around a spherical cavity filled with xenon gas at 1.0 torr. The driver energy and target gain are taken to be 2 MJ and 50 for the optimistic case and 1 MJ and 100 for the conservative case. Based on a graphite dry wall evaporation rate of 0.1 cm/y for a 100 MJ yield, the authors estimate a cavity radius of 3.5 m for a rep-rate of 10 Hz and 3.0 m for 5 Hz. A spherical structural frame has been scoped out capable of supporting 92 blanket modules, each with a beam port in the center. They have selected liquid lithium in vanadium structure as the primary breeding concept utilizing beryllium as a neutron multiplier. A tritium breeding ratio of 1.83 can be achieved in the 3 m radius cavity which at 10 Hz and an availability of 75% provides an annual tritium surplus of 32.6 kg. Assuming 100% debt financing over a 30 year reactor lifetime, the production cost of T 2 for the 2 MJ driver case is $7,325/g for a 5% interest rate and $12,370/g for a 10% interest rate. 8 refs., 3 figs., 4 tabs
Projective relativity, cosmology and gravitation
International Nuclear Information System (INIS)
Arcidiacono, G.
1986-01-01
This book describes the latest applications of projective geometry to cosmology and gravitation. The contents of the book are; the Poincare group and Special Relativity, the thermodynamics and electromagnetism, general relativity, gravitation and cosmology, group theory and models of universe, the special projective relativity, the Fantappie group and Big-Bang cosmology, a new cosmological projective mechanics, the plasma physics and cosmology, the projective magnetohydrodynamics field, projective relativity and waves propagation, the generalizations of the gravitational field, the general projective relativity, the projective gravitational field, the De Sitter Universe and quantum physics, the conformal relativity and Newton gravitation
Symmetric imaging findings in neuroradiology
International Nuclear Information System (INIS)
Zlatareva, D.
2015-01-01
Full text: Learning objectives: to make a list of diseases and syndromes which manifest as bilateral symmetric findings on computed tomography and magnetic resonance imaging; to discuss the clinical and radiological differential diagnosis for these diseases; to explain which of these conditions necessitates urgent therapy and when additional studies and laboratory can precise diagnosis. There is symmetry in human body and quite often we compare the affected side to the normal one but in neuroradiology we might have bilateral findings which affected pair structures or corresponding anatomic areas. It is very rare when clinical data prompt diagnosis. Usually clinicians suspect such an involvement but Ct and MRI can reveal symmetric changes and are one of the leading diagnostic tool. The most common location of bilateral findings is basal ganglia and thalamus. There are a number of diseases affecting these structures symmetrically: metabolic and systemic diseases, intoxication, neurodegeneration and vascular conditions, toxoplasmosis, tumors and some infections. Malformations of cortical development and especially bilateral perisylvian polymicrogyria requires not only exact report on the most affected parts but in some cases genetic tests or combination with other clinical symptoms. In the case of herpes simplex encephalitis bilateral temporal involvement is common and this finding very often prompt therapy even before laboratory results. Posterior reversible encephalopathy syndrome (PReS) and some forms of hypoxic ischemic encephalopathy can lead to symmetric changes. In these acute conditions MR plays a crucial role not only in diagnosis but also in monitoring of the therapeutic effect. Patients with neurofibromatosis type 1 or type 2 can demonstrate bilateral optic glioma combined with spinal neurofibroma and bilateral acoustic schwanoma respectively. Mirror-image aneurysm affecting both internal carotid or middle cerebral arteries is an example of symmetry in
Simple Analytic Models of Gravitational Collapse
Energy Technology Data Exchange (ETDEWEB)
Adler, R.
2005-02-09
Most general relativity textbooks devote considerable space to the simplest example of a black hole containing a singularity, the Schwarzschild geometry. However only a few discuss the dynamical process of gravitational collapse, by which black holes and singularities form. We present here two types of analytic models for this process, which we believe are the simplest available; the first involves collapsing spherical shells of light, analyzed mainly in Eddington-Finkelstein coordinates; the second involves collapsing spheres filled with a perfect fluid, analyzed mainly in Painleve-Gullstrand coordinates. Our main goal is pedagogical simplicity and algebraic completeness, but we also present some results that we believe are new, such as the collapse of a light shell in Kruskal-Szekeres coordinates.
Legendre Duality of Spherical and Gaussian Spin Glasses
International Nuclear Information System (INIS)
Genovese, Giuseppe; Tantari, Daniele
2015-01-01
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model
Legendre Duality of Spherical and Gaussian Spin Glasses
Energy Technology Data Exchange (ETDEWEB)
Genovese, Giuseppe, E-mail: giuseppe.genovese@math.uzh.ch [Universität Zürich, Institut für Mathematik (Switzerland); Tantari, Daniele, E-mail: daniele.tantari@sns.it [Scuola Normale Superiore di Pisa, Centro Ennio de Giorgi (Italy)
2015-12-15
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model.
Near spherical illumination of ion-beam and laser targets
International Nuclear Information System (INIS)
Mark, J.W.K.
1985-01-01
A procedure is developed for reducing energy-deposition asymmetry in spherical targets driven directly by ion or laser beams. This work is part of a strategy for achieving illumination symmetry in such targets, which is proposed as an alternative to those in the literature. This strategy allows an axially symmetric placement of beamlets, which would be convenient for some driven or reactor scenarios. It also allows the use of beam currents or energy fluxes and beam transverse profiles to help reduce deposition asymmetry with fewer beamlets. In the ideal limit of thin deposition layers and controlled beam profiles, at most six beamlets are needed for target symmetry
Measuring Gravitational Flexion in ACS Clusters
Goldberg, David
2005-07-01
We propose measurement of the gravitational "Flexion" signal in ACS cluster images. The flexion, or "arciness" of a lensed background galaxy arises from variations in the lensing field. As a result, it is extremely sensitive to small scale perturbations in the field, and thus, to substructure in clusters. Moreover, because flexion represents gravitationally induced asymmetries in the lensed image, it is completely separable from traditional measurements of shear, which focus on the induced ellipticity of the image, and thus, the two signals may be extracted simultaneously. Since typical galaxies are roughly symmetric upon 180 degree rotation, even a small induced flexion can potentially produce a noticeable effect {Goldberg & Bacon, 2005}. We propose the measurement of substructure within approximately 4 clusters with high-quality ACS data, and will further apply a test of a new tomographic technique whereby comparisons of lensed arcs at different redshifts may be used to estimate the background cosmology, and thus place constraints on the equation of state of dark energy.
Global gravitational anomalies
International Nuclear Information System (INIS)
Witten, E.
1985-01-01
A general formula for global gauge and gravitational anomalies is derived. It is used to show that the anomaly free supergravity and superstring theories in ten dimensions are all free of global anomalies that might have ruined their consistency. However, it is shown that global anomalies lead to some restrictions on allowed compactifications of these theories. For example, in the case of O(32) superstring theory, it is shown that a global anomaly related to π 7 (O(32)) leads to a Dirac-like quantization condition for the field strength of the antisymmetric tensor field. Related to global anomalies is the question of the number of fermion zero modes in an instanton field. It is argued that the relevant gravitational instantons are exotic spheres. It is shown that the number of fermion zero modes in an instanton field is always even in ten dimensional supergravity. (orig.)
Gravitational properties of antimatter
International Nuclear Information System (INIS)
Goldman, T.; Nieto, M.M.
1985-01-01
Quantum gravity is at the forefront of modern particle physics, yet there are no direct tests, for antimatter, of even the principle of equivalence. We note that modern descriptions of gravity, such as fibre bundles and higher dimensional spacetimes, allow violations of the commonly stated form of the principle of equivalence, and of CPT. We review both indirect arguments and experimental tests of the expected gravitational properties of CPT-conjugate states. We conclude that a direct experimental test of the gravitational properties of antimatter, at the 1% (or better) level, would be of great value. We identify some experimental reasons which make the antiproton a prime candidate for this test, and we strongly urge that such an experiment be done at LEAR. 21 references
Gravitation and electromagnetism
Apsel, D
1979-01-01
Through an examination of the Bohm-Aharonov experiment, a new theory of gravitation and electromagnetism is proposed. The fundamental assumption of the theory is that the motion of a particle in a combination of gravitational and electromagnetic fields is determined from a variational principle of the form delta integral /sub A//sup B /d tau =0. The form of the physical time is determined from an examination of the Maxwell-Einstein action function. The field and motion equations are formally identical to those of Maxwell-Einstein theory. The theory predicts that even in a field-free region of space, electromagnetic potentials can alter the phase of a wave function and the lifetime of a charged particle. The phase alteration has been observed in the Bohm-Aharonov experiment. There is an indication that the lifetime alteration has shown up in a recent CERN storage ring experiment. Experimental tests are proposed. (11 refs).
Kopczyński, W.; Trautman, A.
This book is a revised translation of the Polish original "Czasoprzestrzeń i grawitacja", Warszawa (Poland), Państwowe Wydawnictwo Naukowe, 1984. Ideas about space and time are at the root of one's understanding of nature, both at the intuitive level of everyday experience and in the framework of sophisticated physical theories. These ideas have led to the development of geometry and its applications to physics. The contemporary physical theory of space and time, including its extention to the phenomena of gravitation, is Einstein's theory of relativity. The book is a short introduction to this theory. A great deal of emphasis is given to the geometrical aspects of relativity theory and its comparison with the Newtonian view of the world. There are short chapters on the origins of Einstein's theory, gravitational waves, cosmology, spinors and the Einstein-Cartan theory.
Linearized vector radiative transfer model MCC++ for a spherical atmosphere
International Nuclear Information System (INIS)
Postylyakov, O.V.
2004-01-01
Application of radiative transfer models has shown that optical remote sensing requires extra characteristics of radiance field in addition to the radiance intensity itself. Simulation of spectral measurements, analysis of retrieval errors and development of retrieval algorithms are in need of derivatives of radiance with respect to atmospheric constituents under investigation. The presented vector spherical radiative transfer model MCC++ was linearized, which allows the calculation of derivatives of all elements of the Stokes vector with respect to the volume absorption coefficient simultaneously with radiance calculation. The model MCC++ employs Monte Carlo algorithm for radiative transfer simulation and takes into account aerosol and molecular scattering, gas and aerosol absorption, and Lambertian surface albedo. The model treats a spherically symmetrical atmosphere. Relation of the estimated derivatives with other forms of radiance derivatives: the weighting functions used in gas retrieval and the air mass factors used in the DOAS retrieval algorithms, is obtained. Validation of the model against other radiative models is overviewed. The computing time of the intensity for the MCC++ model is about that for radiative models treating sphericity of the atmosphere approximately and is significantly shorter than that for the full spherical models used in the comparisons. The simultaneous calculation of all derivatives (i.e. with respect to absorption in all model atmosphere layers) and the intensity is only 1.2-2 times longer than the calculation of the intensity only
Neutrinos from gravitational collapse
International Nuclear Information System (INIS)
Mayle, R.; Wilson, J.R.; Schramm, D.N.
1986-05-01
Detailed calculations are made of the neutrino spectra emitted during gravitational collapse events (Type II supernovae). Those aspects of the neutrino signal which are relatively independent of the collapse model and those aspects which are sensitive to model details are discussed. The easier-to-detect high energy tail of the emitted neutrinos has been calculated using the Boltzmann equation which is compared with the result of the traditional multi-group flux limited diffusion calculations. 8 figs., 28 refs
Energy Technology Data Exchange (ETDEWEB)
Goldoni, R
1980-11-22
A bimetric theory of gravitation within a Machian framework is developed on the basis of considerations which are completely divorced from Newton's theory. The theory is assumed to hold in any conceivable cosmos and possesses the Machian properties of being singular in the absence of matter and of explicitly incorporating the idea that properties of space-time are determined not only by local matter, but also by the average distribution of cosmological matter.
Gravitation, Symmetry and Undergraduates
Jorgensen, Jamie
2001-04-01
This talk will discuss "Project Petrov" Which is designed to investigate gravitational fields with symmetry. Project Petrov represents a collaboration involving physicists, mathematicians as well as graduate and undergraduate math and physics students. An overview of Project Petrov will be given, with an emphasis on students' contributions, including software to classify and generate Lie algebras, to classify isometry groups, and to compute the isometry group of a given metric.
International Nuclear Information System (INIS)
Penrose, R.
1986-01-01
The author's definition for the mass-momentum/angular momentum surrounded by a spacelike 2-surface with S/sup 2/ topology is presented. This definition is motivated by some ideas from twistor theory in relation to linearized gravitational theory. The status of this definition is examined in relation to many examples which have been worked out. The reason for introducing a slight modification of the original definition is also presented
General Relativity and Gravitation
Ehlers, J.; Murdin, P.
2000-11-01
The General Theory of Relativity (GR), created by Albert Einstein between 1907 and 1915, is a theory both of gravitation and of spacetime structure. It is based on the assumption that matter, via its energy-momentum, interacts with the metric of spacetime, which is considered (in contrast to Newtonian physics and SPECIAL RELATIVITY) as a dynamical field having degrees of freedom of its own (GRAVI...
Fivebrane gravitational anomalies
International Nuclear Information System (INIS)
Becker, Katrin; Becker, Melanie
2000-01-01
Freed, Harvey, Minasian and Moore (FHMM) have proposed a mechanism to cancel the gravitational anomaly of the M-theory fivebrane coming from diffeomorphisms acting on the normal bundle. This procedure is based on a modification of the conventional M-theory Chern-Simons term. We apply the FHMM mechanism in the ten-dimensional type IIA theory. We then analyze the relation to the anomaly cancellation mechanism for the type IIA fivebrane proposed by Witten
Gravitational light deflection in the Solar System
International Nuclear Information System (INIS)
Cowling, S.A.
1984-01-01
The problems of defining the bending of a light path in general stationary space-times are discussed. It is shown how in situations of axial symmetry the use of 'triangulation lines' leads to a coordinate invariant definition of the bending angle between arbitrary points on a light path. An exact expression is derived for the bending angle in a static, spherically symmetric space-time of arbitrarily strong curvature. This formulation is used to calculate, to second PPN order, the apparent positional shift which is measured when observing, for example, an asteroid or a spacecraft situated close to superior conjunction with the Sun. The possibilities of measuring light deflection effects using modern observational facilities are considered. (author)
2017 Updates: Earth Gravitational Model 2020
Barnes, D. E.; Holmes, S. A.; Ingalls, S.; Beale, J.; Presicci, M. R.; Minter, C.
2017-12-01
The National Geospatial-Intelligence Agency [NGA], in conjunction with its U.S. and international partners, has begun preliminary work on its next Earth Gravitational Model, to replace EGM2008. The new `Earth Gravitational Model 2020' [EGM2020] has an expected public release date of 2020, and will retain the same harmonic basis and resolution as EGM2008. As such, EGM2020 will be essentially an ellipsoidal harmonic model up to degree (n) and order (m) 2159, but will be released as a spherical harmonic model to degree 2190 and order 2159. EGM2020 will benefit from new data sources and procedures. Updated satellite gravity information from the GOCE and GRACE mission, will better support the lower harmonics, globally. Multiple new acquisitions (terrestrial, airborne and shipborne) of gravimetric data over specific geographical areas (Antarctica, Greenland …), will provide improved global coverage and resolution over the land, as well as for coastal and some ocean areas. Ongoing accumulation of satellite altimetry data as well as improvements in the treatment of this data, will better define the marine gravity field, most notably in polar and near-coastal regions. NGA and partners are evaluating different approaches for optimally combining the new GOCE/GRACE satellite gravity models with the terrestrial data. These include the latest methods employing a full covariance adjustment. NGA is also working to assess systematically the quality of its entire gravimetry database, towards correcting biases and other egregious errors. Public release number 15-564
JUST: Joint Upgraded Spherical Tokamak
International Nuclear Information System (INIS)
Azizov, E.A.; Dvorkin, N.Ya.; Filatov, O.G.
1997-01-01
The main goals, ideas and the programme of JUST, spherical tokamak (ST) for the plasma burn investigation, are presented. The place and prospects of JUST in thermonuclear investigations are discussed. (author)
Spherical tokamak development in Brazil
International Nuclear Information System (INIS)
Ludwig, G.O.; Del Bosco, E.; Ferreira, J.G.; Berni, L.A.; Oliveira, R.M.; Andrade, M.C.R.; Shibata, C.S.; Ueda, M.; Barroso, J.J.; Castro, P.J.; Barbosa, L.F.W.; Patire Junior, H.; The high-power microwave sources group
2003-01-01
This paper describes the general characteristics of spherical tokamaks, or spherical tori, with a brief overview of work in this area already performed or in progress at several institutions worldwide. The paper presents also the steps in the development of the ETE (Experimento Tokamak Esferico) project, its research program, technical characteristics and operating conditions as of December, 2002 at the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)
Miniaturization of Spherical Magnetodielectric Antennas
DEFF Research Database (Denmark)
Hansen, Troels Vejle
; Arbitrary order of the spherical wave, arbitrary radius of the spherical antenna, as well as arbitrarily large core permeability and/or permittivity, given an inversely proportional frequency variation of the imaginary part(s) and an arbitrary dispersion of the real part(s) - thus describing both lossless...... with a magnetic loss tangent of 1 and relative permeability of 300 yield Q/e equal 65% of the Chu lower bound, with a simultaneous e of 71%....
Spherical tokamak development in Brazil
Energy Technology Data Exchange (ETDEWEB)
Ludwig, G.O.; Del Bosco, E.; Ferreira, J.G.; Berni, L.A.; Oliveira, R.M.; Andrade, M.C.R.; Shibata, C.S.; Ueda, M.; Barroso, J.J.; Castro, P.J. [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma; Barbosa, L.F.W. [Universidade do Vale do Paraiba (UNIVAP), Sao Jose dos Campos, SP (Brazil). Faculdade de Engenharia, Arquitetura e Urbanismo; Patire Junior, H. [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Div. de Mecanica Espacial e Controle; The high-power microwave sources group
2003-12-01
This paper describes the general characteristics of spherical tokamaks, or spherical tori, with a brief overview of work in this area already performed or in progress at several institutions worldwide. The paper presents also the steps in the development of the ETE (Experimento Tokamak Esferico) project, its research program, technical characteristics and operating conditions as of December, 2002 at the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)
Parity-Time Symmetric Photonics
Zhao, Han
2018-01-17
The establishment of non-Hermitian quantum mechanics (such as parity-time (PT) symmetry) stimulates a paradigmatic shift for studying symmetries of complex potentials. Owing to the convenient manipulation of optical gain and loss in analogy to the complex quantum potentials, photonics provides an ideal platform for visualization of many conceptually striking predictions from the non-Hermitian quantum theory. A rapidly developing field has emerged, namely, PT symmetric photonics, demonstrating intriguing optical phenomena including eigenstate coalescence and spontaneous PT symmetry breaking. The advance of quantum physics, as the feedback, provides photonics with brand-new paradigms to explore the entire complex permittivity plane for novel optical functionalities. Here, we review recent exciting breakthroughs in PT symmetric photonics while systematically presenting their underlying principles guided by non-Hermitian symmetries. The potential device applications for optical communication and computing, bio-chemical sensing, and healthcare are also discussed.
Homotheties of cylindrically symmetric static spacetimes
International Nuclear Information System (INIS)
Qadir, A.; Ziad, M.; Sharif, M.
1998-08-01
In this note we consider the homotheties of cylindrically symmetric static spacetimes. We find that we can provide a complete list of all metrics that admit non-trivial homothetic motions and are cylindrically symmetric static. (author)
Studies on radiation symmetrization in heavy-ion driven hohlraum targets
International Nuclear Information System (INIS)
Temporal, M.; Atzeni, S.
1993-01-01
Radiation symmetrization within spherical, ellipsoidal and cylindral hohlraum targets for heavy ion inertial confinement fusion (ICF) is studied by means of a 3-D numerical, static model, in which realistic assumptions are made concerning the geometry of the system and, particularly, of the radiation converters. Among the systems so far studied, only spherical hohlraums with six converters achieve the illumination symmetry of the fusion capsule considered necessary for ICF applications. A parametric study of cylindrical hohlraums enlightens the effect of several parameter changes, and suggests directions for further studies, aiming at the design of two-converter targets
Maximally Symmetric Composite Higgs Models.
Csáki, Csaba; Ma, Teng; Shu, Jing
2017-09-29
Maximal symmetry is a novel tool for composite pseudo Goldstone boson Higgs models: it is a remnant of an enhanced global symmetry of the composite fermion sector involving a twisting with the Higgs field. Maximal symmetry has far-reaching consequences: it ensures that the Higgs potential is finite and fully calculable, and also minimizes the tuning. We present a detailed analysis of the maximally symmetric SO(5)/SO(4) model and comment on its observational consequences.
On symmetric structures of order two
Directory of Open Access Journals (Sweden)
Michel Bousquet
2008-04-01
Full Text Available Let (ω n 0 < n be the sequence known as Integer Sequence A047749 http://www.research.att.com/ njas/sequences/A047749 In this paper, we show that the integer ω n enumerates various kinds of symmetric structures of order two. We first consider ternary trees having a reflexive symmetry and we relate all symmetric combinatorial objects by means of bijection. We then generalize the symmetric structures and correspondences to an infinite family of symmetric objects.
On gravitational wave energy in Einstein gravitational theory
International Nuclear Information System (INIS)
Folomeshkin, V.N.; Vlasov, A.A.
1978-01-01
By the example of precise wave solutions for the Einstein equations it is shown that a standard commonly adopted formulation of energy-momentum problem with pseudotensors provides us either with a zero or sign-variable values for the energy of gravitational waves. It is shown that if in the Einstein gravitational theory a strict transition to the limits of weak fields is realised then the theory gives us an unambiguous zero result for weak gravitational waves. The well-known non-zero result arises due to incorrect transition to weak field approximation in the Einstein gravitation theory