Showing papers in "General Relativity and Gravitation in 1998"
TL;DR: A detailed study of the singularity theorems is presented in this article, where the authors discuss the plausibility and reasonability of their hypotheses, applicability and implications of singularity theories, as well as the theorem itself.
Abstract: A detailed study of the singularity theorems is presented. I discuss the plausibility and reasonability of their hypotheses, the applicability and implications of the theorems, as well as the theorems themselves. The consequences usually extracted from them, some of them without the necessary rigour, are widely and carefully analysed with many clarifying examples and alternative views.
283 citations
TL;DR: In this paper, an alternative to Einstein Gravity that satisfies the equivalence principle and automatically passes all classical weakfield tests (GM/r ≈ 10-6) was presented.
Abstract: Can we give the graviton a mass? Does it even make sense to speak of a massive graviton? In this essay I shall answer these questions in the affirmative. I shall outline an alternative to Einstein Gravity that satisfies the Equivalence Principle and automatically passes all classical weakfield tests (GM/r ≈ 10-6). It also passes medium-field tests (GM/r ≈ 1/5), but exhibits radically different strong-field behaviour (GM/r ≈ 1). Black holes in the usual sense do not exist in this theory, and large-scale cosmology is divorced from the distribution of matter. To do all this we have to sacrifice something: the theory exhibits prior geometry, and depends on a non-dynamical background metric.
148 citations
TL;DR: In this article, the geometry and geodesics of a class of spacetimes generalizing Robertson-Walker ones are studied under a global point-of-view, covering geodesic connectedness, geodeic completeness and stability of completeness.
Abstract: The geometry and, especially, the geodesics of a class of spacetimes generalizing Robertson-Walker ones (without any assumption on the fiber) is studied, under a global point of view. Our study covers geodesic connectedness, geodesic completeness and stability of completeness.
133 citations
TL;DR: A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action as mentioned in this paper, which is compatible with all present tests of general relativity and post-Newtonian gravity.
Abstract: A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action. On sub-horizon length scales the modified gravitational field equations seem compatible with all present tests of general relativity and post-Newtonian gravity. They induce a difference in the effective Newtonian constant between regions of space with vanishing or nonvanishing curvature scalar (or Ricci tensor). In cosmology they may lead to a value Ω < 1 for the critical density after inflation. The simplest model considered here appears to be in conflict with nucleosynthesis, but generalizations consistent with all cosmological observations seem conceivable.
100 citations
TL;DR: In this article, the authors used the standard statistical mechanical method of Gibbs to derive thermodynamic properties of the Schwarzschild black hole system from its microscopics and found that its microscopic (quantum) states are described by states of quantum Chern-Simons theory defined by sets of points on B with spins attached.
Abstract: Quantum theory of geometry, developed recently in the framework of non-perturbative quantum gravity, is used in an attempt to explain thermodynamics of Schwarzschild black holes on the basis of a microscopical (quantum) description of the system. We work with the formulation of thermodynamics in which the black hole is enclosed by a spherical surface B and a macroscopic state of the system is specified by two parameters: the area of the boundary surface and a quasilocal energy contained within it. To derive thermodynamical properties of the system from its microscopics we use the standard statistical mechanical method of Gibbs. Under a certain number of assumptions on the quantum behavior of the system, we find that its microscopic (quantum) states are described by states of quantum Chern-Simons theory defined by sets of points on B with spins attached. The level of the Chern-Simons theory turns out to be proportional to the horizon area of the black hole measured in Planck units. The statistical mechanical analysis turns out to be especially simple in the case when the entire interior of B is occupied by a black hole. We find in this case that the entropy contained within B, that is, the black hole entropy, is proportional to the horizon surface area.
88 citations
TL;DR: In this article, the curvature singularity of a radiation-dominated universe is regularized by the repulsive effects of spin interactions and the breaking of the local gravitational gauge symmetry.
Abstract: I present two examples in which the curvature singularity of a radiation-dominated Universe is regularized by (a) the repulsive effects of spin interactions, and (b) the repulsive effects arising from a breaking of the local gravitational gauge symmetry. In both cases the collapse of an initial, asymptotically flat state is stopped, and the Universe bounces towards a state of decelerated expansion. The emerging picture is typical of the pre-big bang scenario, with the main difference that the string cosmology dilaton is replaced by a classical radiation fluid, and the solutions are not duality-invariant.
86 citations
TL;DR: In this paper, the authors derived the field equations and equa tions of motion for 5-dimensional relativity in the general case where the metric can depend on all 5 coordinates (i.e., Kaluza-Klein theory without the cylinder restriction).
Abstract: Using a novel coordinate system, we rederive the field equations and equa tions of motion for 5-dimensional relativity in the general case where the metric can depend on all 5 coordinates (i.e., Kaluza-Klein theory without the cylinder restriction). We show that in general the fifth dimension produces a new dynamical force in 4-dimensional spacetime. This timelike fifth force is proportional to the 4-velocity of a particle and is thus unlike any known 4-force. We briefly examine the properties of some simple models, and suggest that the detection of the fifth force is the most promising way to investigate the existence of an extra dimension in nature.
79 citations
TL;DR: In this article, the effect of the global rotation of the universe on the formation of galaxies is investigated, and it is found that the local rotation provides a natural origin for the rotation of galaxies, and the morphology of the objects formed from gravitational instability in a rotating and expanding universe depends on the amplitude of the density fluctuation.
Abstract: The effect of the global rotation of the universe on the formation of galaxies is investigated. It is found that the global rotation provides a natural origin for the rotation of galaxies, and the morphology of the objects formed from gravitational instability in a rotating and expanding universe depends on the amplitude of the density fluctuation, different values of the amplitude of the fluctuation lead to the formation of elliptical galaxies, spiral galaxies, and walls. The global rotation gives a natural explanation of the empirical relation between the angular momentum and mass of galaxies: J ∝ M5/3. The present angular velocity of the universe is estimated at ∼10-13rad yr-1.
73 citations
TL;DR: In this article, it was shown that any shear-free perfect fluid with the acceleration proportional to the vorticity vector must be either nonexpanding or nonrotating.
Abstract: In this paper we provide fully covariant proofs of some theorems on shear-free perfect fluids. In particular, we explicitly show that any shear-free perfect fluid with the acceleration proportional to the vorticity vector (including the simpler case of vanishing acceleration) must be either non-expanding or non-rotating. We also show that these results are not necessarily true in the Newtonian case, and present an explicit comparison of shear-free dust in Newtonian and relativistic theories in order to see where and why the differences appear.
71 citations
TL;DR: In this paper, the cosmological constant arises from the degrees of freedom of the vacuum regarded as a dynamical entity, and a time variable can naturally be naturally introduced, which is the case in our case.
Abstract: By regarding the vacuum as a perfect fluid with equation of state p = -ρ, de Sitter's cosmological model is quantized. Our treatment differs from previous ones in that it endows the vacuum with dynamical degrees of freedom, following modern ideas that the cosmological term is a manifestation of the vacuum energy. Instead of being postulated from the start, the cosmological constant arises from the degrees of freedom of the vacuum regarded as a dynamical entity, and a time variable can be naturally introduced. Taking the scale factor as the sole degree of freedom of the gravitational field, stationary and wave-packet solutions to the Wheeler-DeWitt equation are found, whose properties are studied. It is found that states of the Universe with a definite value of the cosmological constant do not exist. For the wave packets investigated, quantum effects are noticeable only for small values of the scale factor, a classical regime being attained at asymptotically large times.
63 citations
TL;DR: In this paper, the authors study the collapse of a self-gravitating charged scalar field and find a null, weak, mass-inflation singularity along the Cauchy horizon, which is a precursor of a strong, spacelike singularity.
Abstract: We study the gravitational collapse of a self-gravitating charged scalar-field. Starting with a regular spacetime, we follow the evolution through the formation of an apparent horizon, a Cauchy horizon and a final central singularity. We find a null, weak, mass-inflation singularity along the Cauchy horizon, which is a precursor of a strong, spacelike singularity along the r = 0 hypersurface. The inner black hole region is bounded (in the future) by singularities. This resembles the classical inner structure of a Schwarzschild black hole and it is remarkably different from the inner structure of a charged static Reissner-Nordstrom or a stationary rotating Kerr black holes.
TL;DR: In this article, the meaning of a time-dependent cosmological constant is discussed and a set of conditions to recover an asymptotic de Sitter behavior for a class of extended gravity models independently of initial data is given.
Abstract: In the framework of extended gravity theories, we discuss the meaning of a time-dependent “cosmological constant” and give a set of conditions to recover an asymptotic de Sitter behaviour for a class of cosmological models independently of initial data. To this purpose we introduce a time-dependent (effective) quantity which asymptotically becomes the true cosmological constant. We will deal with scalar-tensor, fourth and higher than fourth-order theories.
TL;DR: In this paper, a new formulation for General Relativity is developed; it is a canonical, global and geometrically well posed formalism in which gravity is described using only variables related to spin structures.
Abstract: A new formulation for General Relativity is developed; it is a canonical, global and geometrically well posed formalism in which gravity is described using only variables related to spin structures. It does not require any background metric fixing and it applies to quite general manifolds, i.e. it does not need particular symmetries requirement or global frames. A global Lagrangian framework for Dirac spinors is also provided; conserved quantities and superpotentials are given. The interaction between gravity and spinors is described in a minimal coupling fashion with respect to the new variables and the Hilbert stress tensor of spinor fields is computed, providing the gravitational field generated by spinors. Finally differences and analogies between this formalism and gauge theories are discussed.
TL;DR: In this article, a master formula for the Hodge star commutator is proposed and a detailed discussion of the Kaniel-Itin model is given. But the model belongs to the teleparallelism class of gravitational gauge theories.
Abstract: Recently Kaniel and Itin proposed a gravitational model with the wave type equation
$$\left[ { + \lambda \left( x \right)} \right]\vartheta ^\alpha = 0$$
as vacuum field equation, where
$$\vartheta ^\alpha$$
denotes the coframe of spacetime. They found that the viable Yilmaz-Rosen metric is an exact solution of the tracefree part of their field equation. This model belongs to the teleparallelism class of gravitational gauge theories. Of decisive importance for the evaluation of the Kaniel-Itin model is the question whether the variation of the coframe commutes with the Hodge star. We find a master formula for this commutator and rectify some corresponding mistakes in the literature. Then we turn to a detailed discussion of the Kaniel-Itin model.
TL;DR: The general solution of the field equations is represented in an exact closed parametric form and corresponds to a transition between two Minkowskian space-times connected by an inflationary period as mentioned in this paper.
Abstract: The general exact solution of the gravitational field equations for a homogeneous flat Friedmann-Robertson-Walker universe filled with a causal bulk viscous fluid with bulk viscosity coefficient proportional to the Hubble function is obtained in the framework of the full causal Israel-Stewart-Hiscock theory. The general solution of the field equations is represented in an exact closed parametric form and corresponds to a transition between two Minkowskian space-times connected by an inflationary period. The evolution of the temperature, entropy, deceleration parameter and bulk viscosity coefficient are considered in the general case. Particular solutions corresponding to a particular choice of parameters and leading to a non-inflationary evolution of the universe are presented too.
TL;DR: In this paper, the analytic spherically symmetric solution of the Einstein equations, which has de Sitter asymptotics for both r → ∞ and r → 0, is presented.
Abstract: We present the analytic spherically symmetric solution of the Einstein equations, which has de Sitter asymptotics for both r → ∞ and r → 0. This two-lambda spherically symmetric solution is globally regular. At the range of mass parameter Mcr1 Mcr2 another one-horizon configuration which can be called “de Sitter bag”. The solutions with M = Mcr1 and M = Mcr2 represent two extreme states of a neutral nonsingular cosmological black hole.
TL;DR: In this article, exact solutions for an anisotropic Bianchi type I model with bulk viscosity and variable G and Λ were obtained, where the anisotropy energy decreases exponentially with time.
Abstract: Exact solutions for an anisotropic Bianchi type I model with bulk viscosity and variable G and Λ are obtained We have found some solutions that correspond to our earlier work for the isotropic one Unlike Kalligas et al, an inflationary solution with a variable energy density has been found where the anisotropy energy decreases exponentially with time There is a period of hyper-inflation during which the energy density remains constant
TL;DR: In this paper, the cosmological term varies inversely with the square of time of the time taken to compute the energy momentum tensor in the presence of bulk viscosity for the spatially flat homogeneous and isotropic universe.
Abstract: Einstein's equations with variable gravitational and cosmological “constants” are considered in the presence of bulk viscosity for the spatially flat homogeneous and isotropic universe in a way which conserves the energy momentum tensor. A solution is found in which the cosmological term varies inversely with the square of time. Our approach is compared with that of Arbab.
TL;DR: In this paper, a new cosmological equation (48) is obtained by space-time averaging of all the terms of Eq. (7) and taking into account the fluctuations of the gravitational field due to nonuniformities in the distribution of matter.
Abstract: Existing cosmological theories are based on Einstein's law of gravitation (7). In this equation the average is taken only in the right-hand side by a substitution of the energy momentum tensor corresponding to uniform and continuous distribution of matter. In this paper a new cosmological equation (48), which is more correct from the physical and mathematical point of view, is obtained by space-time averaging of all the terms of Eq. (7) and taking into account the fluctuations of the gravitational field due to nonuniformities in the distribution of matter. An estimate of these fluctuations within the framework of Newton's approximation leads to the cosmological equations (51), (52) and (53) for flat space and positive and negative curvature. The solutions of these equations, in distinction from all the variants of Friedman's theory, do not have a singular point for some initial moment of time with an infinitely large density of matter. However, this result follows when the relations obtained are extrapolated beyond the range of their applicability, and therefore final conclusions can be made on the basis of the solutions of the new cosmological equations (48) when we go beyond the Newtonian approximation.
TL;DR: In this paper, a comparative study between the metric and the teleparallel descriptions of gravitation is made for the case of a scalar field and it is shown that scalar fields can not only feel anyone of these geometries, but also produce torsion.
Abstract: A comparative study between the metric and the teleparallel descriptions of gravitation is made for the case of a scalar field In contrast to the current belief that only spin matter could detect the teleparallel geometry, scalar matter being able to feel the metric geometry only, we show that a scalar field is able not only to feel anyone of these geometries, but also to produce torsion Furthermore, both descriptions are found to be completely equivalent, which means that in fact, besides coupling to curvature, a scalar field couples also to torsion
TL;DR: In this article, a criterion given by Castejon-Amenedo and MacCallum for the existence of (locally) hypersurface-orthogonal generators of an orthogonallytransitive two-parameter Abelian group of motions (a G2I) in spacetime is re-expressed as a test for linear dependence with constant coefficients between the three components of the metric in the orbits in canonical coordinates.
Abstract: A criterion given by Castejon-Amenedo and MacCallum for the existence of (locally) hypersurface-orthogonal generators of an orthogonallytransitive two-parameter Abelian group of motions (a G2I) in spacetime is re-expressed as a test for linear dependence with constant coefficients between the three components of the metric in the orbits in canonical coordinates. In general, it is shown that such a relation implies that the metric is locally diagonalizable in canonical coordinates, or has a null Killing vector, or can locally be written in a generalized form of the “windmill” solutions characterized by McIntosh. If the orbits of the G2I have cylindrical or toroidal topology and a periodic coordinate is used, these metric forms cannot in general be realized globally as they would conflict with the topological identification. The geometry then has additional essential parameters, which specify the topological identification. The physical significance of these parameters is shown by their appearance in global holonomy and by examples of exterior solutions where they have been related to characteristics of physical sources. These results lead to some remarks about the definition of cylindrical symmetry.
TL;DR: Yang's pure space equations generalize Einstein's gravitational equations, while coming from gauge theory as discussed by the authors, and they are studied from a number of vantage points: summarizing the work done previously, comparing them with the Einstein equations and investigating their properties.
Abstract: Yang's pure space equations generalize Einstein's gravitational equations, while coming from gauge theory. We study these equations from a number of vantage points: summarizing the work done previously, comparing them with the Einstein equations and investigating their properties. In particular, the initial value problem is discussed and a number of results are presented for these equations with common energy-momentum tensors.
TL;DR: In this paper, the authors propose that a radiation is created whenever a relative acceleration between the charge and its own electric field exists, and the work done to overcome the stress force is the source of energy carried by the radiation.
Abstract: The emission of radiation by a uniformly accelerated charge is analyzed. According to the standard approach, a radiation is observed whenever there is a relative acceleration between the charge and the observer. Analyzing difficulties that arose in the standard approach, we propose that a radiation is created whenever a relative acceleration between the charge and its own electric field exists. The electric field induced by a charge accelerated by an external (nongravitational) force is not accelerated with the charge. Hence the electric field is curved in the instantaneous rest frame of the accelerated charge. This curvature gives rise to a stress force, and the work done to overcome the stress force is the source of the energy carried by the radiation. In this way, the “energy balance paradox” finds its solution.
TL;DR: In this paper, two relativistic models for collapsing spheres at different stages of evolution, which include pre-relaxation processes, are presented and the influence of relaxation time on the outcome of evolution in both cases is exhibited and established.
Abstract: Two relativistic models for collapsing spheres at different stages of evolution, which include pre-relaxation processes, are presented. The influence of relaxation time on the outcome of evolution in both cases is exhibited and established. It is shown that relaxation processes can drastically change the final state of the collapsing system. In particular, there are cases in which the value of the relaxation time determines the bounce or the collapse of the sphere.
TL;DR: In this paper, the authors considered spherically symmetric perfect equat ions with zero shear and showed that equat ion can be solved in terms of elementary funct ions only for some special forms of the funct ion f (x), as later research showed.
Abstract: Although the authors did not provide (and were probably not aware of) an invariant de® nit ion of the problem they considered, such a de® nit ion exists: they considered spherically symmetric perfect ̄ uid solut ions of Einstein’ s equat ions with zero shear. The zero shear appears unannounced in the ® rst sentence of the paper together with the assumpt ion that the coordinat es are isot ropic and comoving at the same time. The main result of the paper is the reduction of the Einstein equat ions in the nonstatic case to the single ordinary diŒerential equat ion, eq. (12) . Just because this result has such a neat invariant de® nit ion, it was bound to reappear in several contexts. In consequence, it was independently rediscovered by other authors 17 times altogether (see Ref. 1 for the full list). The paper contains one more valuable result . Equat ion (12) can be solved in terms of elementary funct ions only for some special forms of the funct ion f (x) , as later research showed, and a few speci® c solut ions in terms of ellipt ic funct ions are known today [see again Ref. 1, and also Ref. 2 in which a serious eŒort was undertaken to ® nd a general solut ion of eq. (12) ]. Kustaanheimo and Qvist were the ® rst to note that solut ions expressible in elementary funct ions exist when f (x) = (ax + bx + c) 5 / 2 . They classi® ed and found all but one of these solut ions (the missing case is when the trinomial f 2 / 5 has no real roots). Nevertheless, each of the cases was rediscovered lat er; the number of rediscoveries ranges from 1 to 8 for each conformally non ̄ at case (f / = 0), and the total number, including simpler subcases, is 22 (see Ref. 1). The conformally ̄ at case ( f = 0) was rediscovered 21 times. The authors of
TL;DR: It is well known that any scalar can be promoted to a Jordan-Brans-Dicke type scalar coupling to the Einstein-Hilbert term through a field dependent Weyl transformation of the metric as mentioned in this paper.
Abstract: It is well-known that any scalar can be promoted to a Jordan-Brans-Dicke type scalar coupling to the Einstein-Hilbert term through a field dependent Weyl transformation of the metric The Weyl rescaling also transforms mass terms into coupling constants between matter and the scalar It is pointed out that there exists a distinguished metric where all scalars decouple from an arbitrary fiducial fermion, eg the nucleon If bound states of this fermion are used to define distances and to probe the interior of the forward light cone, it seems reasonable to say that the metric in that particular frame defines the local geometry of space-time at low energies, as probed by experimental gravity and cosmology
TL;DR: The canonical quantization of diffeomorphism invariant theories of connections in terms of loop variables is revisited in this paper, which yields a representation of the algebra of observables in a separable Hilbert space.
Abstract: The canonical quantization of diffeomorphism invariant theories of connections in terms of loop variables is revisited. Such theories include general relativity described in terms of Ashtekar-Barbero variables and extension to Yang-Mills fields (with or without fermions) coupled to gravity. It is argued that the operators induced by classical diffeomorphism invariant or covariant functions are respectively invariant or covariant under a suitable completion of the diffeomorphism group. The canonical quantization in terms of loop variables described here, yields a representation of the algebra of observables in a separable Hilbert space. Furthermore, the resulting quantum theory is equivalent to a model for diffeomorphism invariant gauge theories which replaces space with a manifestly combinatorial object.
TL;DR: The recent interest in the study of symme tries in general relativity and its purpose is to discuss the mathematical foundations required for such a study as mentioned in this paper, where general (formal and informal) ideas of what constitutes a symmetry of space-time are discussed and developed and the idea of a Lie algebra of symmetry vector fields is studied in detail.
Abstract: The motivation for this paper is the recent interest in the study of symme tries in general relativity and its purpose is to discuss the mathematical foundations required for such a study The general (formal and informal) ideas of what constitutes a symmetry of space-time are discussed and developed and the idea of a Lie algebra of symmetry vector fields is studied in detail The relationship between such Lie algebras and the ideas of Lie transformation group theory (Palais' theorems) is stated and a general theorem regarding the orbits of such symmetries is given Finally some specific symmetries in general relativity are explored and some of their similarities and differences noted
TL;DR: In this paper, the authors analyzed the local versus global visibility of a singularity that forms in gravitational collapse of a dust cloud, which has important implications for the weak and strong versions of the cosmic censorship hypothesis.
Abstract: We analyze here the issue of local versus global visibility of a singularity that forms in gravitational collapse of a dust cloud, which has important implications for the weak and strong versions of the cosmic censorship hypothesis. We find conditions for when a singularity will be only locally naked, rather than being globally visible, thus preserving the weak censorship hypothesis. The conditions for the formation of a black hole or a naked singularity in the Szekeres quasi-spherical collapse models are worked out. The causal behaviour of the singularity curve is studied by examining the outgoing radial null geodesics, and the final outcome of collapse is related to the nature of the regular initial data specified on an initial hypersurface from which the collapse evolves. An interesting feature that emerges is that the singularity in Szekeres spacetimes can be “directionally naked”.
TL;DR: In this article, the use of Lax pair tensors as a unifying framework for Killing tensors of arbitrary rank is discussed, and some properties of the tensorial Lax Pair formulation are stated.
Abstract: The use of Lax pair tensors as a unifying framework for Killing tensors of arbitrary rank is discussed. Some properties of the tensorial Lax pair formulation are stated. A mechanical system with a well-known Lax representation—the three-particle open Toda lattice—is geometrized by a suitable canonical transformation. In this way the Toda lattice is realized as the geodesic system of a certain Riemannian geometry. By using different canonical transformations we obtain two inequivalent geometries which both represent the original system. Adding a timelike dimension gives four-dimensional spacetimes which admit two Killing vector fields and are completely integrable.