Showing papers in "Classical and Quantum Gravity in 1998"
TL;DR: In this article, an anomaly-free spin-network operator corresponding to the Wheeler-DeWitt constraint of Lorentzian, four-dimensional, canonical, non-perturbative vacuum gravity is constructed in the continuum.
Abstract: An anomaly-free operator corresponding to the Wheeler - DeWitt constraint of Lorentzian, four-dimensional, canonical, non-perturbative vacuum gravity is constructed in the continuum. This operator is entirely free of factor-ordering singularities and can be defined in symmetric and non-symmetric form. We work in the real connection representation and obtain a well defined quantum theory. The action of the Wheeler - DeWitt constraint on spin-network states is by annihilating, creating and rerouting the quanta of angular momentum associated with the edges of the underlying graph while the ADM energy is essentially diagonalized by the spin-network states. We argue that the spin-network representation is the `nonlinear Fock representation' of quantum gravity, thus justifying the term `quantum spin dynamics (QSD)'. This paper is the first in a series of seven papers with the title `quantum spin dynamics (QSD)'.
776 citations
TL;DR: In this article, a pedagogical derivation of the Lagrangian equation for the velocity potential describing a sound wave is identical to that for a minimally coupled massless scalar field propagating in a (3 + 1)-dimensional Lorentzian geometry.
Abstract: It is a deceptively simple question to ask how acoustic disturbances propagate in a non-homogeneous flowing fluid. Subject to suitable restrictions, this question can be answered by invoking the language of Lorentzian differential geometry. This paper begins with a pedagogical derivation of the following result: if the fluid is barotropic and inviscid, and the flow is irrotational (though possibly time dependent), then the equation of motion for the velocity potential describing a sound wave is identical to that for a minimally coupled massless scalar field propagating in a (3 + 1)-dimensional Lorentzian geometry The acoustic metric governing the propagation of sound depends algebraically on the density, flow velocity, and local speed of sound. Even though the underlying fluid dynamics is Newtonian, non-relativistic, and takes place in flat space plus time, the fluctuations (sound waves) are governed by an effective (3 + 1)-dimensional Lorentzian spacetime geometry. This rather simple physical system exhibits a remarkable connection between classical Newtonian physics and the differential geometry of curved (3 + 1)-dimensional Lorentzian spacetimes, and is the basis underlying a deep and fruitful analogy between the black holes of Einstein gravity and supersonic fluid flows. Many results and definitions can be carried over directly from one system to another. For example, it will be shown how to define the ergosphere, trapped regions, acoustic apparent horizon, and acoustic event horizon for a supersonic fluid flow, and the close relationship between the acoustic metric for the fluid flow surrounding a point sink and the Painleve-Gullstrand form of the Schwarzschild metric for a black hole will be exhibited. This analysis can be used either to provide a concrete non-relativistic analogy for black-hole physics, or to provide a framework for attacking acoustics problems with the full power of Lorentzian differential geometry.
695 citations
TL;DR: In this paper, a unified first law of black-hole dynamics and relativistic thermodynamics is derived in spherically symmetric general relativity, which expresses the gradient of the active gravitational energy according to the Einstein equation, divided into energy-supply and work terms.
Abstract: A unified first law of black-hole dynamics and relativistic thermodynamics is derived in spherically symmetric general relativity. This equation expresses the gradient of the active gravitational energy E according to the Einstein equation, divided into energy-supply and work terms. Projecting the equation along the flow of thermodynamic matter and along the trapping horizon of a black hole yield, respectively, first laws of relativistic thermodynamics and black-hole dynamics. In the black-hole case, this first law has the same form as the first law of black-hole statics, with static perturbations replaced by the derivative along the horizon. In particular, there is the expected term involving the area and surface gravity, where the dynamic surface gravity is defined by substituting the Kodama vector and trapping horizon for the Killing vector and Killing horizon in the standard definition of static surface gravity. The remaining work term is consistent with, for instance, electromagnetic work in special relativity. The dynamic surface gravity vanishes for degenerate trapping horizons and satisfies certain inequalities involving the area and energy which have the same form as for stationary black holes. Turning to the thermodynamic case, the quasi-local first law has the same form, apart from a relativistic factor, as the classical first law of thermodynamics, involving heat supply and hydrodynamic work, but with E replacing the internal energy. Expanding E in the Newtonian limit shows that it incorporates the Newtonian mass, kinetic energy, gravitational potential energy and thermal energy (internal energy with fixed zero). There is also a weak type of unified zeroth law: a Gibbs-like definition of thermal equilibrium requires constancy of an effective temperature, generalizing the Tolman condition and the particular case of Hawking radiation, while gravithermal equilibrium further requires constancy of surface gravity. Finally, it is suggested that the energy operator of spherically symmetric quantum gravity is determined by the Kodama vector, which encodes a dynamic time related to E.
517 citations
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TL;DR: In this paper, the authors define the concept of a ''spin foam'' going from one spin network to another, and present a spin foam model of four-dimensional Euclidean quantum gravity, closely related to the state sum model of Barrett and Crane.
Abstract: While the use of spin networks has greatly improved our understanding of the kinematical aspects of quantum gravity, the dynamical aspects remain obscure. To address this problem, we define the concept of a `spin foam' going from one spin network to another. Just as a spin network is a graph with edges labelled by representations and vertices labelled by intertwining operators, a spin foam is a two-dimensional complex with faces labelled by representations and edges labelled by intertwining operators. Spin foams arise naturally as higher-dimensional analogues of Feynman diagrams in quantum gravity and other gauge theories in the continuum, as well as in lattice gauge theory. When formulated as a `spin foam model', such a theory consists of a rule for computing amplitudes from spin foam vertices, faces and edges. The product of these amplitudes gives the amplitude for the spin foam, and the transition amplitude between spin networks is given as a sum over spin foams. After reviewing how spin networks describe `quantum 3-geometries', we describe how spin foams describe `quantum 4-geometries'. We conclude by presenting a spin foam model of four-dimensional Euclidean quantum gravity, closely related to the state sum model of Barrett and Crane, but not assuming the presence of an underlying spacetime manifold.
440 citations
TL;DR: In this paper, it is shown that the Hamiltonian of the standard model supports a representation in which finite linear combinations of Wilson loop functionals around closed loops, as well as along open lines with fermionic and Higgs field insertions at the end points, are densely defined operators.
Abstract: It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague quantum field theories in a background metric. We demonstrate that at least part of this idea is implemented in a precise sense within the framework of four-dimensional canonical Lorentzian quantum gravity in the continuum. Specifically, we show that the Hamiltonian of the standard model supports a representation in which finite linear combinations of Wilson loop functionals around closed loops, as well as along open lines with fermionic and Higgs field insertions at the end points, are densely defined operators. This Hamiltonian, surprisingly, does not suffer from any singularities, it is completely finite without renormalization. This property is shared by string theory. In contrast to string theory, however, we are dealing with a particular phase of the standard model coupled to gravity which is entirely non-perturbatively defined and second quantized. Of course, to show that the entire theory is finite requires more: one would need to know what the physical observables are, apart from the Hamiltonian constraint, and whether they are also finite. However, with the results given in this paper this question can now be answered, at least in principle.
423 citations
TL;DR: In this article, the Schrodinger-Newton equations for the spherically-symmetric case are considered and numerical evidence for a discrete family of solutions, everywhere regular, and with normalizable wavefunctions.
Abstract: As part of a programme in which quantum state reduction is understood as a gravitational phenomenon, we consider the Schrodinger-Newton equations. For a single particle, this is a coupled system consisting of the Schrodinger equation for the particle moving in its own gravitational field, where this is generated by its own probability density via the Poisson equation. Restricting to the spherically-symmetric case, we find numerical evidence for a discrete family of solutions, everywhere regular, and with normalizable wavefunctions. The solutions are labelled by the non-negative integers, the nth solution having n zeros in the wavefunction. Furthermore, these are the only globally defined solutions. Analytical support is provided for some of the features found numerically.
401 citations
TL;DR: In this article, the running of the cosmological constant and Newton's constant at sub-Planckian energies, taking into account the effect of quantum fields with any spin between 0 and 2, was studied.
Abstract: We compute the running of the cosmological constant and Newton's constant at sub-Planckian energies, taking into account the effect of quantum fields with any spin between 0 and 2. We find that Newton's constant does not vary appreciably but the cosmological constant can change by many orders of magnitude when one goes from cosmological scales to typical elementary particle scales. In the extreme infrared, zero modes drive a positive cosmological constant to zero.
304 citations
TL;DR: In this article, the authors present physical requirements on gravitational avatars of nonlinear electrodynamics and illustrate them with explicit determinantal Born - Infeld - Einstein models.
Abstract: We present some obvious physical requirements on gravitational avatars of nonlinear electrodynamics and illustrate them with explicit determinantal Born - Infeld - Einstein models. A related procedure, using compensating Weyl scalars, permits us to formulate conformally invariant versions of these systems as well.
264 citations
TL;DR: In this paper, the authors review some of the unresolved problems and suggest avenues for their solution, but none is completely satisfactory, and many questions remain open: there is no consensus as to what fields provide the relevant degrees of freedom or where these excitations live.
Abstract: With the recent discovery that many aspects of black hole thermodynamics can be effectively reduced to problems in three spacetime dimensions, it has become increasingly important to understand the `statistical mechanics' of the (2 + 1)-dimensional black hole of Banados, Teitelboim, and Zanelli (BTZ). Several conformal field theoretic derivations of the BTZ entropy exist, but none is completely satisfactory, and many questions remain open: there is no consensus as to what fields provide the relevant degrees of freedom or where these excitations live. In this paper, I review some of the unresolved problems and suggest avenues for their solution.
248 citations
TL;DR: In this article, it was shown that the microwave background can be identified at the intersections of the surface of last scattering as seen by different copies of the observer, regardless of the background geometry or topology.
Abstract: If the universe is finite and smaller than the distance to the surface of last scatter, then the signature of the topology of the universe is writ large on the microwave background sky. We show that the microwave background will be identified at the intersections of the surface of last scattering as seen by different `copies' of the observer. Since the surface of last scattering is a 2-sphere, these intersections will be circles, regardless of the background geometry or topology. We therefore propose a statistic that is sensitive to all small, locally homogeneous topologies. Here, small means that the distance to the surface of last scatter is smaller than the `topology scale' of the universe.
225 citations
TL;DR: In this article, the complete and rigorous kernel of the Wheeler-DeWitt constraint operator for four-dimensional, Lorentzian, non-perturbative, canonical vacuum quantum gravity in the continuum was determined.
Abstract: We determine the complete and rigorous kernel of the Wheeler - DeWitt constraint operator for four-dimensional, Lorentzian, non-perturbative, canonical vacuum quantum gravity in the continuum. We do this for the non-symmetric version of the operator constructed previously in this series. We also construct a symmetric, regulated constraint operator. For the regulated Euclidean Wheeler - DeWitt operator as well as for the regulated generator of the Wick transform from the Euclidean to the Lorentzian regime we prove existence of self-adjoint extensions and based on these we propose a method of proof of self-adjoint extensions for the regulated Lorentzian operator. Both constraint operators evaluated at unit lapse as well as the generator of the Wick transform can be shown to have regulator-independent and symmetric duals on the diffeomorphism-invariant Hilbert space. Finally, we comment on the status of the Wick rotation transform in the light of the present results and give an intuitive description of the action of the Hamiltonian constraint.
TL;DR: In this paper, the authors extend the kinematical framework for diffeomorphism-invariant theories of connections for compact gauge groups to the case of a diffeomorphic invariant quantum field theory which includes, besides connections, also fermions and Higgs fields.
Abstract: We extend the recently developed kinematical framework for diffeomorphism-invariant theories of connections for compact gauge groups to the case of a diffeomorphism-invariant quantum field theory which includes, besides connections, also fermions and Higgs fields. This framework is appropriate for coupling matter to quantum gravity. The presence of diffeomorphism invariance forces us to choose a representation which is a rather non-Fock-like one: the elementary excitations of the connection are along open or closed strings, while those of the fermions or Higgs fields are at the end points of the string. Nevertheless we are able to promote the classical reality conditions to quantum adjointness relations which, in turn, uniquely fixes the gauge- and diffeomorphism-invariant probability measure that underlies the Hilbert space. Most of the fermionic part of this work is independent of the recent preprint by Baez and Krasnov and earlier work by Rovelli and Morales-Tecotl because we use new canonical fermionic variables, so-called Grassman-valued half-densities, which enable us to solve the difficult fermionic adjointness relations.
TL;DR: In this paper, the authors studied the phase space structure and quantization of a point-like particle in (2 + 1)-dimensional gravity by adding boundary terms to the first-order Einstein-Hilbert action, and removing all redundant gauge degrees of freedom.
Abstract: We study the phase space structure and the quantization of a pointlike particle in (2 + 1)-dimensional gravity. By adding boundary terms to the first-order Einstein-Hilbert action, and removing all redundant gauge degrees of freedom, we arrive at a reduced action for a gravitating particle in 2 + 1 dimensions, which is invariant under Lorentz transformations and a group of generalized translations. The momentum space of the particle turns out to be the group manifold SL(2). Its position coordinates have non-vanishing Poisson brackets, resulting in a non-commutative quantum spacetime. We use the representation theory of SL(2) to investigate its structure. We find a discretization of time, and some semi-discrete structure of space. An uncertainty relation forbids a fully localized particle. The quantum dynamics is described by a discretized Klein-Gordon equation.
TL;DR: In this article, the quantum versions of Riemannian structures such as triad and area operators exhibit a non-commutativity, which is surprising because it implies that the framework does not admit a triad representation.
Abstract: The basic framework for a systematic construction of a quantum theory of Riemannian geometry was introduced recently. The quantum versions of Riemannian structures - such as triad and area operators - exhibit a non-commutativity. At first sight, this feature is surprising because it implies that the framework does not admit a triad representation. To better understand this property and to reconcile it with intuition, we analyse its origin in detail. In particular, a careful study of the underlying phase space is made and the feature is traced back to the classical theory; there is no anomaly associated with quantization. We also indicate why the uncertainties associated with this non-commutativity become negligible in the semiclassical regime.
TL;DR: In this paper, the U-duality invariant conditions on the quantized charges which specify the number of supersymmetries preserved with a particular charge configuration were analyzed for all extended supergravities with 16 or 32 supersymmetries in various dimensions.
Abstract: In extended supergravity theories there are p-brane solutions preserving different numbers of supersymmetries, depending on the charges, the spacetime dimension and the number of original supersymmetries (8, 16 or 32). We find U-duality invariant conditions on the quantized charges which specify the number of supersymmetries preserved with a particular charge configuration. These conditions relate U-duality invariants to the picture of intersecting branes. The analysis is carried out for all extended supergravities with 16 or 32 supersymmetries in various dimensions.
TL;DR: In this paper, the Fuchsian algorithm was used to construct singular solutions of Einstein's equations which belong to the class of Gowdy spacetimes and provided precise asymptotics at the singularity which is Kasner-like.
Abstract: We use the Fuchsian algorithm to construct singular solutions of Einstein's equations which belong to the class of Gowdy spacetimes. The solutions have the maximum number of arbitrary functions. Special cases correspond to polarized or other known solutions. The method provides precise asymptotics at the singularity, which is Kasner-like. All of these solutions are asymptotically velocity-dominated. The results account for the fact that solutions with velocity parameter uniformly greater than one are not observed numerically. They also provide a justification of formal expansions proposed by Grubisic and Moncrief.
TL;DR: In this paper, the classical theory of locally "anti-de-Sitter" spaces is treated in an elementary way, using visualizable models, including black holes, spaces with multiple black holes and closed universes.
Abstract: Vacuum Einstein theory in three spacetime dimensions is locally trivial, but admits many solutions that are globally different, particularly if there is a negative cosmological constant. The classical theory of such locally “anti-de Sitter” spaces is treated in an elementary way, using visualizable models. Among the objects discussed are black holes, spaces with multiple black holes, their horizon structure, closed universes, and the topologies that are possible.
TL;DR: In this paper, the authors studied the local consequences of gauge invariance and formulated a vanishing theorem for the superpotential and the current when there is a (Killing) global isometry or its generalization.
Abstract: Noether's general analysis of conservation laws has to be completed in a Lagrangian theory with local gauge invariance. Bulk charges are replaced by fluxes at a suitable singularity (in general, at infinity) of so-called superpotentials, namely local functions of the gauge fields (or more generally of the gauge forms). Some gauge-invariant bulk charges and current densities may subsist when distinguished one-dimensional subgroups are present. We shall study mostly local consequences of gauge invariance. Quite generally there exist local superpotentials analogous to those of Freud or Bergmann for general relativity. They are parametrized by infinitesimal gauge transformations, but are afflicted by topological ambiguities which one must handle on a case-by-case basis. The choice of variational principle: variables, surface terms and boundary conditions is crucial. As a first illustration we propose a new affine action that reduces to general relativity upon gauge fixing the dilatation (Weyl-1918-like) part of the connection and elimination of auxiliary fields. We can also reduce it by similar considerations either to the Palatini action or to the Cartan-Weyl moving frame action and compare the associated superpotentials. This illustrates the concept of Noether identities. We formulate a vanishing theorem for the superpotential and the current when there is a (Killing) global isometry or its generalization. We distinguish between asymptotic symmetries and symmetries defined in the bulk. A second and independent application is a geometrical reinterpretation of the convection of vorticity in barotropic non-viscous fluids first established by Helmholtz-Kelvin, Eckart and Ertel. In the homentropic case it can be seen to follow by a general theorem from the vanishing of the superpotential corresponding to the time-independent relabelling symmetry. The special diffeomorphism symmetry is, in the absence of dynamical gauge field and spin, associated with a vanishing internal transverse momentum flux density. We also consider the non-homentropic case. We identify the one-dimensional subgroups responsible for the bulk charges and thus propose an impulsive forcing for creating or destroying selectively helicity (respectively enstrophies) in odd (respectively even) dimensions. This is an example of a new and general forcing rule.
TL;DR: In this paper, a non-perturbative four-dimensional Lorentzian canonical quantum gravity in the continuum has been studied in connection with the recently constructed Wheeler-DeWitt quantum constraint operator.
Abstract: This paper deals with several technical issues of non-perturbative four-dimensional Lorentzian canonical quantum gravity in the continuum that arose in connection with the recently constructed Wheeler-DeWitt quantum constraint operator. The Wheeler-DeWitt constraint of quantum general relativity mixes the diffeomorphism superselection sectors for diffeomorphism-invariant theories of connections that were previously discussed in the literature. From it one can construct diffeomorphism-invariant operators which do not necessarily commute with the Hamiltonian constraint but which still mix those sectors and which, at the diffeomorphism-invariant level, encode physical information. Thus, if one adopts, as before in the literature, the strategy to solve the diffeomorphism constraint before the Hamiltonian constraint then those sectors become spurious. The inner product for diffeomorphism-invariant states can be fixed by requiring that diffeomorphism group averaging is a partial isometry. The established non-anomalous constraint algebra is clarified by computing commutators of duals of constraint operators. The full classical constraint algebra is faithfully implemented on the diffeomorphism-invariant Hilbert space in an appropriate sense. The Hilbert space of diffeomorphism-invariant states can be made separable if a natural new superselection principle is satisfied. We propose a natural physical scalar product for quantum general relativity by extending the group-average approach to the case of non-self-adjoint constraint operators like the Wheeler-DeWitt constraint. Equipped with this inner product, the construction of physical observables is straightforward.
TL;DR: A very brief review of some of the developments leading to our current understanding of black holes in string theory is given in this article, followed by a discussion of two possible misconceptions in this subject - one involving the stability of small black holes and the other involving scale radius duality.
Abstract: A very brief review is given of some of the developments leading to our current understanding of black holes in string theory. This is followed by a discussion of two possible misconceptions in this subject - one involving the stability of small black holes and the other involving scale radius duality. Finally, I describe some recent results concerning quasinormal modes of black holes in anti-de Sitter spacetime, and their implications for strongly coupled conformal field theories (in various dimensions).
TL;DR: In this article, the authors studied the geometrical and topological aspects of the generalized dimensional reduction of supergravities in D = 11 and D = 10 dimensions, which give rise to massive theories in lower dimensions.
Abstract: We study some geometrical and topological aspects of the generalized dimensional reduction of supergravities in D = 11 and D = 10 dimensions, which give rise to massive theories in lower dimensions. In these reductions, a global symmetry is used in order to allow some of the fields to have a non-trivial dependence on the compactifying coordinates. Global consistency in the internal space imposes topological restrictions on the parameters of the compactification as well as the structure of the space itself. Examples that we consider include the generalized reduction of the type IIA and IIB theories on a circle, and also the massive ten-dimensional theory obtained by the generalized reduction of D = 11 supergravity.
TL;DR: In this article, the boundary conditions associated with extended supersymmetric Maxwell theory in five-dimensional anti-de Sitter space were examined, and the possibility of a connection between this phenomenon and the world-volume theory of 3-branes in IIB string theory was discussed.
Abstract: We examine the boundary conditions associated with extended supersymmetric Maxwell theory in five-dimensional anti-de Sitter space. Excitations on the boundary are identical to those of ordinary four-dimensional conformal invariant superelectrodynamics. Extrapolations of these excitations give rise to a five-dimensional topological gauge theory of the singleton type. The possibility of a connection between this phenomenon and the world-volume theory of 3-branes in IIB string theory is discussed.
TL;DR: In this paper, the authors studied the quantization of Euclidean 2 + 1 gravity for an arbitrary genus of the spacelike hypersurface with new, classically equivalent constraints that maximally probe the Lorentzian 3 + 1 situation.
Abstract: The quantization of Lorentzian or Euclidean 2 + 1 gravity by canonical methods is a well studied problem. However, the constraints of 2 + 1 gravity are those of a topological field theory and therefore resemble very little those of the corresponding Lorentzian 3 + 1 constraints. In this paper we canonically quantize Euclidean 2 + 1 gravity for an arbitrary genus of the spacelike hypersurface with new, classically equivalent constraints that maximally probe the Lorentzian 3 + 1 situation. We choose the signature to be Euclidean because this implies that the gauge group is, as in the 3 + 1 case, SU(2) rather than . We employ, and carry out to full completion, the new quantization method introduced in preceding papers of this series which resulted in a finite 3 + 1 Lorentzian quantum field theory for gravity. The space of solutions to all constraints turns out to be much larger than that obtained by traditional approaches, however, it is fully included. Thus, by a suitable restriction of the solution space, we can recover all former results which gives confidence in the new quantization methods. The meaning of the remaining `spurious solutions' is discussed.
TL;DR: A review of recent progress in string theory concerning the Bekenstein formula for black hole entropy is given in this article, which includes p-branes, D-brane and supersymmetry.
Abstract: A review of recent progress in string theory concerning the Bekenstein formula for black hole entropy is given. Topics discussed include p-branes, D-branes and supersymmetry; the correspondence principle; the D- and M-brane approach to black hole entropy; the D-brane analogue of Hawking radiation and information loss; D-branes as probes of black holes and the matrix theory approach to charged and neutral black holes. Some introductory material is included, as are some very brief remarks on the AdS/CFT correspondence.
TL;DR: In this article, the non-flat factor of the Godel metric belongs to a one-parameter family of (2 + 1)-dimensional geometries that also includes the anti-de Sitter metric.
Abstract: We show that the non-flat factor of the Godel metric belongs to a one-parameter family of (2 + 1)-dimensional geometries that also includes the anti-de Sitter metric. The elements of this family allow a generalization a la Kaluza-Klein of the usual (3 + 1)-dimensional Godel metric. Their lightcones can be viewed as deformations of the anti-de Sitter ones, involving tilting and squashing. This provides a simple geometric picture of the causal structure of these spacetimes, anti-de Sitter geometry appearing as the boundary between causally safe and causally pathological spaces. Furthermore, we construct a global algebraic isometric embedding of these metrics in (4 + 3)- or (3 + 4)-dimensional flat spaces, thereby illustrating in another way the occurrence of the closed timelike curves.
TL;DR: In this article, the authors analyzed several aspects of the five-dimensional anti-de-Sitter black hole, including its relation to thermal anti-desitter space, its embedding in a Chern-Simons supergravity theory, its global charges and holonomies and the existence of Killing spinors.
Abstract: Anti-de Sitter space with identified points give rise to black-hole structures. This was first pointed out in three dimensions and generalized to higher dimensions by Aminneborg et al. In this paper, we analyse several aspects of the five-dimensional anti-de Sitter black hole, including its relation to thermal anti-de Sitter space, its embedding in a Chern - Simons supergravity theory, its global charges and holonomies and the existence of Killing spinors.
TL;DR: In this article, a simple exact model of radiating stellar collapse, with a shear-free and non-accelerating interior matched to a Vaidya exterior, is presented.
Abstract: We find a simple exact model of radiating stellar collapse, with a shear-free and non-accelerating interior matched to a Vaidya exterior. The heat flux is subject to causal thermodynamics, leading to self-consistent determination of the temperature T. We solve for T exactly when the mean collision time is constant, and perturbatively in a more realistic case of variable . Causal thermodynamics predicts temperature behaviour that can differ significantly from the predictions of non-causal theory. In particular, the causal theory gives a higher central temperature and greater temperature gradient.
TL;DR: In this article, a post-Newtonian expansion of the gravitational field generated by a slowly moving isolated source is constructed, and the source moments parametrize the linearized approximation of the gravity field exterior to the source, as computed by a specific post-Minkowskian algorithm defined in a previous work.
Abstract: The multipole expansion (in general relativity) of the gravitational field generated by a slowly-moving isolated source is constructed. We introduce some definitions for the source multipole moments, valid to all orders in a post-Newtonian expansion, and depending in a well defined way on the total stress-energy pseudo-tensor of the material and gravitational fields. The source moments parametrize the linearized approximation of the gravitational field exterior to the source, as computed by means of a specific post-Minkowskian algorithm defined in a previous work. Since the radiative multipole moments parametrizing the radiation field far from the source can be obtained as nonlinear functionals of the source moments, the present paper allows one to relate the radiation field far from a slowly-moving source to the stress-energy pseudo-tensor of the source. This should be useful when comparing theory with the future observations of gravitational radiation by the LIGO and VIRGO experiments.
TL;DR: In this paper, the diagonal values of the first five heat kernel coefficients associated with a general Laplace-type operator on a compact Riemannian space without boundary are presented.
Abstract: Using index-free notation, we present the diagonal values of the first five heat kernel coefficients associated with a general Laplace-type operator on a compact Riemannian space without boundary. The fifth coefficient appears here for the first time. For the special case of a flat space, but with a gauge connection, the sixth coefficient is given too. Also provided are the leading terms for any coefficient, both in ascending and descending powers of the Yang-Mills and Riemann curvatures, to the same order as required for the fourth coefficient. These results are obtained by directly solving the relevant recursion relations, working in the Fock-Schwinger gauge and Riemann normal coordinates. Our procedure is thus non-covariant, but we show that for any coefficient the `gauged', respectively `curved', version is found from the corresponding `non-gauged', respectively `flat', coefficient by making some simple covariant substitutions. These substitutions being understood, the coefficients retain their `flat' form and size. In this sense the fifth and sixth coefficient have only 26 and 75 terms, respectively, allowing us to write them down. Using index-free notation also clarifies the general structure of the heat kernel coefficients. In particular, in flat space we find that from the fifth coefficient onward, certain scalars are absent. This may be relevant for the anomalies of quantum field theories in ten or more dimensions.
TL;DR: In this paper, the Siklos class of solutions of Einstein's field equations is investigated by analytical methods and it is concluded that the spacetimes represent exact gravitational waves propagating in the anti-de Sitter universe.
Abstract: The Siklos class of solutions of Einstein's field equations is investigated by analytical methods. By studying the behaviour of free particles we reach the conclusion that the spacetimes represent exact gravitational waves propagating in the anti-de Sitter universe. The presence of a negative cosmological constant implies that the `background' space is not asymptotically flat and requires `rotating' reference frames in order to fully simplify and view the behaviour of nearby test particles. The Kaigorodov spacetime, which is the simplest representative of the Siklos class, is analysed in more detail. It is argued that it may serve as a `cosmological' analogue of the well known homogeneous pp-waves in the flat universe.