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Showing papers in "Classical and Quantum Gravity in 1999"


Journal ArticleDOI
TL;DR: In this paper, the authors summarize how quasinormal modes are defined and computed, see why they have been regarded as closely analogous to normal modes, and discover why they are actually quite different.
Abstract: Gravitational waves emitted by perturbed black holes or relativistic stars are dominated by `quasinormal ringing', damped oscillations at single frequencies which are characteristic of the underlying system. These quasinormal modes have been studied for a long time, often with the intent of describing the time evolution of a perturbation in terms of these modes in a way very similar to a normal-mode analysis. In this review, we summarize how quasinormal modes are defined and computed. We will see why they have been regarded as closely analogous to normal modes, and discover why they are actually quite different. We also discuss how quasinormal modes can be used in the analysis of a gravitational wave signal, such as will hopefully be detected in the near future.

836 citations


Journal ArticleDOI
TL;DR: In this article, a class of black hole solutions to Einstein's equations in d dimensions with a negative cosmological constant were considered, where the horizon is a (d − 2)-dimensional Einstein manifold of positive, zero or negative curvature.
Abstract: We consider a class of black hole solutions to Einstein's equations in d dimensions with a negative cosmological constant. These solutions have the property that the horizon is a (d - 2)-dimensional Einstein manifold of positive, zero or negative curvature. The mass, temperature and entropy are calculated. Using the correspondence with conformal field theory, the phase structure of the solutions is examined, and used to determine the correct mass dependence of the Bekenstein-Hawking entropy.

513 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the expected Bekenstein-Hawking entropy of black hole entropy can be fixed by symmetry arguments, independent of the details of quantum gravity.
Abstract: On a manifold with a boundary, the constraint algebra of general relativity may acquire a central extension, which can be computed using covariant phase space techniques. When the boundary is a (local) Killing horizon, a natural set of boundary conditions leads to a Virasoro subalgebra with a calculable central charge. Conformal field theory methods may then be used to determine the density of states at the boundary. I consider a number of cases - black holes, Rindler space, de Sitter space, Taub-NUT and Taub-bolt spaces and dilaton gravity - and show that the resulting density of states yields the expected Bekenstein-Hawking entropy. The statistical mechanics of black hole entropy may thus be fixed by symmetry arguments, independent of the details of quantum gravity.

341 citations


Journal ArticleDOI
TL;DR: In this article, it is argued that the so-called holographic principle will obstruct attempts to produce physically realistic models for the unification of general relativity with quantum mechanics, unless determinism in the latter is restored.
Abstract: It is argued that the so-called holographic principle will obstruct attempts to produce physically realistic models for the unification of general relativity with quantum mechanics, unless determinism in the latter is restored. The notion of time in GR is so different from the usual one in elementary particle physics that we believe that certain versions of hidden variable theories can -- and must -- be revived. A completely natural procedure is proposed, in which the dissipation of information plays an essential role. Unlike earlier attempts, it allows us to use strictly continuous and differentiable classical field theories as a starting point (although discrete variables, leading to fermionic degrees of freedom, are also welcome), and we show how an effective Hilbert space of quantum states naturally emerges when one attempts to describe the solutions statistically. Our theory removes some of the mysteries of the holographic principle; apparently non-local features are to be expected when the quantum degrees of freedom of the world are projected onto a lower-dimensional black hole horizon. Various examples and models illustrate the points we wish to make, notably a model showing that massless, non interacting neutrinos are deterministic.

300 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the horizon is a non-singular, non-rotating, null hypersurface whose intersection with a Cauchy surface is a squashed 3-sphere.
Abstract: We discuss some general features of black holes of five-dimensional supergravity, such as the first law of black hole mechanics. We also discuss some special features of rotating supersymmetric black holes. In particular, we show that the horizon is a non-singular, and {\sl non-rotating}, null hypersurface whose intersection with a Cauchy surface is a squashed 3-sphere. We find the Killing spinors of the near-horizon geometry and thereby determine the near-horizon isometry supergroup.

293 citations


Journal ArticleDOI
TL;DR: In this paper, a set of boundary conditions defining a non-rotating isolated horizon are given in Einstein-Maxwell theory, and the zeroth and first laws of black hole mechanics are established for isolated horizons.
Abstract: A set of boundary conditions defining a non-rotating isolated horizon are given in Einstein-Maxwell theory. A spacetime representing a black hole which itself is in equilibrium but whose exterior contains radiation admits such a horizon. Physically motivated, (quasi-)local definitions of the mass and surface gravity of an isolated horizon are introduced. Although these definitions do not refer to infinity, the quantities assume their standard values in Reissner-Nordstrom solutions. Finally, using these definitions, the zeroth and first laws of black hole mechanics are established for isolated horizons.

232 citations


Journal ArticleDOI
TL;DR: In this paper, the so(4) Plebanski action is shown to possess four phases, one of which is related to gravity and discuss the relation between this model and the model of Euclidean tetrad gravity.
Abstract: We study the correspondence between the `relativistic spin-foam' model introduced by Barrett, Crane and Baez and the so(4) Plebanski action. We argue that the so(4) Plebanski model is the continuum analogue of the relativistic spin-foam model. We prove that the so(4) Plebanski action possesses four phases, one of which is related to gravity and discuss the relation between this model and the model of Euclidean tetrad gravity. We also show that the so(4) Plebanski model possesses another natural discretization that can be associated with another, new, spin-foam model which appear to be the so(4) counterpart of the spin-foam model describing the self-dual formulation of gravity.

202 citations


Journal ArticleDOI
TL;DR: In this paper, the authors review the current state of the art in the field of gravitational radiation theory and astrophysics, and then look at the development of detector sensitivity over the next decade, both on the ground (such as LIGO) and in space (LISA).
Abstract: The first decade of the new millennium should see the first direct detections of gravitational waves. This will be a milestone or fundamental physics and it will open the new observational science of gravitational wave astronomy. But gravitational waves already play an important role in the modeling of astrophysical systems. I review here the present state of gravitational radiation theory in relativity and astrophysics, and I then look at the development of detector sensitivity over the next decade, both on the ground (such as LIGO) and in space (LISA). I review the sources of gravitational waves that are likely to play an imp rtant role in observations by first- and second-generation interferometers, including the astrophysical information that will c me from these observations. The review covers some 10 decades of gravitational wave frequency, from the high-frequency normal odes of neutron stars down to the lowest frequencies observable from space. The discussion of sources includes recent developments regarding binary black holes, spinning neutron stars, and the stochastic background.

194 citations


Journal ArticleDOI
TL;DR: In this paper, the authors discuss what is known at present about the global initial value problem for the vacuum Einstein equations with general asymptotically flat initial data and give precise formulations of cosmic censorship conjectures.
Abstract: In the first part of the paper we discuss what is known at present about the global initial value problem for the vacuum Einstein equations with general asymptotically flat initial data. We then give precise formulations of cosmic censorship conjectures. We also point out analogies with fluid dynamics and discuss possibilities suggested by these analogies. In the second part I discuss my work on the spherically symmetric Einstein equations with a real massless scalar field as the material model. I give an outline of the approach which has led to the proof of the conjectures in this context.

171 citations


Journal ArticleDOI
TL;DR: In this article, different kinds of self-similarity in general relativity are discussed, with special emphasis on similarity of the ''first'' kind, corresponding to spacetimes admitting a homothetic vector.
Abstract: The different kinds of self-similarity in general relativity are discussed, with special emphasis on similarity of the `first' kind, corresponding to spacetimes admitting a homothetic vector. We then survey the various classes of self-similar solutions to Einstein's field equations and the different mathematical approaches used in studying them. We focus mainly on spatially homogenous and spherically symmetric self-similar solutions, emphasizing their possible roles as asymptotic states for more general models. Perfect fluid spherically symmetric similarity solutions have recently been completely classified, and we discuss various astrophysical and cosmological applications of such solutions. Finally, we consider more general types of self-similar models.

157 citations


Journal ArticleDOI
TL;DR: In this paper, a geometric method to associate a Lie superalgebra with a large class of bosonic supergravity vacua of the type adS × X, corresponding to elementary branes in M-theory and type II string theory is presented.
Abstract: We present details of a geometric method to associate a Lie superalgebra with a large class of bosonic supergravity vacua of the type adS × X, corresponding to elementary branes in M-theory and type II string theory.

Journal ArticleDOI
TL;DR: In this article, a covariant boundary expression for the quasilocal quantities of general relativity and other geometric gravity theories was derived from a covariance Hamiltonian formulation. But the choice of the boundary condition is dependent on the selected type of boundary condition.
Abstract: From a covariant Hamiltonian formulation, by using symplectic ideas, we obtain certain covariant boundary expressions for the quasilocal quantities of general relativity and other geometric gravity theories. The contribution from each of the independent dynamic geometric variables (the frame, metric or connection) has two possible covariant forms associated with the selected type of boundary condition. The quasilocal expressions also depend on a reference value for each dynamic variable and a displacement vector field. Integrating over a closed 2-surface with suitable choices for the vector field gives the quasilocal energy, momentum and angular momentum. For the special cases of Einstein's theory and the Poincare gauge theory our expressions are similar to some previously known expressions and give good values for the total ADM and Bondi quantities. We apply our formalism to black hole thermodynamics obtaining the first law and an associated entropy expression for these general gravity theories. For Einstein's theory our quasilocal expressions are evaluated on static spherically symmetric solutions and compared with the findings of some other researchers. The choices needed for the formalism to associate a quasilocal expression with the boundary of a region are discussed.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the Stackel-Killing tensor of the rotating extreme black hole is Liouville integrable and may be integrated by additively separating the Hamilton-Jacobi equation.
Abstract: The geodesics of the rotating extreme black hole in five spacetime dimensions found by Breckenridge, Myers, Peet and Vafa are Liouville integrable and may be integrated by additively separating the Hamilton-Jacobi equation. This allows us to obtain the Stackel-Killing tensor. We use these facts to give the maximal analytic extension of the spacetime and discuss some aspects of its causal structure. In particular, we exhibit a `repulson'-like behaviour occurring when there are naked closed timelike curves. In this case we find that the spacetime is geodesically complete (with respect to causal geodesics) and free of singularities. When a partial Cauchy surface exists, we show, by solving the Klein-Gordon equation, that the absorption cross section for massless waves at small frequencies is given by the area of the hole. At high frequencies a dependence on the angular quantum numbers of the wave develops. We comment on some aspects of `inertial time travel' and argue that such time machines cannot be constructed by spinning up a black hole with no naked closed timelike curves.

Journal ArticleDOI
TL;DR: The global structure of McVittie's solution representing a point mass embedded in a spatially flat Robertson-Walker universe is investigated in this article, where the scalar curvature singularity at proper radius R = 2m, where m (constant) is the Schwarzschild mass, and the apparent horizon which surrounds it are studied.
Abstract: The global structure of McVittie's solution representing a point mass embedded in a spatially flat Robertson-Walker universe is investigated. The scalar curvature singularity at proper radius R=2m, where m (constant) is the Schwarzschild mass, and the apparent horizon which surrounds it are studied. The conformal diagram for the spacetime is obtained via a qualitative analysis of the radial null geodesics. Particular attention is paid to the physical interpretation of this spacetime; previous work on this issue is reviewed, and to how recent quasi-local definitions of black and white holes relate to this spacetime.

Journal ArticleDOI
TL;DR: In this paper, the authors considered black holes in EYM theory with a negative cosmological constant and showed that the solutions obtained are somewhat different from those for which the cosmology constant is either positive or zero.
Abstract: We consider black holes in Einstein-Yang-Mills theory with a negative cosmological constant. The solutions obtained are somewhat different from those for which the cosmological constant is either positive or zero. Firstly, regular black hole solutions exist for continuous intervals of the parameter space, rather than discrete points. Secondly, there are non-trivial solutions in which the gauge field has no nodes. We show that these solutions are linearly stable.

Journal ArticleDOI
TL;DR: In this paper, the authors consider the problem of evolving the state of a quantum field between any two (in general, curved) Cauchy surfaces and show that functional evolution of the quantum state can be satisfactorily described using algebraic quantum field theory.
Abstract: We consider the problem of evolving the state of a quantum field between any two (in general, curved) Cauchy surfaces. Classically, this dynamical evolution is represented by a canonical transformation on the phase space for the field theory. We show that this canonical transformation cannot, in general, be unitarily implemented on the Fock space for free quantum fields on flat spacetimes of dimension greater than 2. We do this by considering time evolution of a free Klein-Gordon field on a flat spacetime (with toroidal Cauchy surfaces) starting from a flat initial surface and ending on a generic final surface. The associated Bogolubov transformation is computed; it does not correspond to a unitary transformation on the Fock space. This means that functional evolution of the quantum state as originally envisioned by Tomonaga, Schwinger and Dirac is not a viable concept. Nevertheless, we demonstrate that functional evolution of the quantum state can be satisfactorily described using the formalism of algebraic quantum field theory. We discuss possible implications of our results for canonical quantum gravity.

Journal ArticleDOI
TL;DR: In this article, the authors explore the generality of a particular interpretation of the Dirac procedure known as refined algebraic quantization, and find technical conditions under which refined algebras can reproduce the general implementation of Dirac scheme for systems whose constraints form a Lie algebra with structure constants.
Abstract: The Dirac quantization `procedure' for constrained systems is well known to have many subtleties and ambiguities. Within this ill-defined framework, we explore the generality of a particular interpretation of the Dirac procedure known as refined algebraic quantization. We find technical conditions under which refined algebraic quantization can reproduce the general implementation of the Dirac scheme for systems whose constraints form a Lie algebra with structure constants. The main result is that, under appropriate conditions, the choice of an inner product on the physical states is equivalent to the choice of a `rigging map' in refined algebraic quantization.

Journal ArticleDOI
TL;DR: In this article, an explicit solution to the Einstein equations is presented, describing the collapse of two massless particles into a non-rotating black hole, and general arguments imply that massive particles can be used as well, and the creation of rotating black holes is also possible.
Abstract: When two point particles, coupled to three-dimensional gravity with a negative cosmological constant, approach each other with a sufficiently large centre-of-mass energy, then a BTZ black hole is created. An explicit solution to the Einstein equations is presented, describing the collapse of two massless particles into a non-rotating black hole. Some general arguments imply that massive particles can be used as well, and the creation of a rotating black hole is also possible.

Journal ArticleDOI
TL;DR: In this article, the authors studied the late-time evolution of a class of exact anisotropic cosmological solutions of Einstein's equations, namely spatially homogeneous cosmologies of Bianchi type VII0 with a perfect fluid source.
Abstract: We study the late-time evolution of a class of exact anisotropic cosmological solutions of Einstein's equations, namely spatially homogeneous cosmologies of Bianchi type VII0 with a perfect fluid source. We show that, in contrast to models of Bianchi type VIIh which are asymptotically self-similar at late times, Bianchi VII0 models undergo a complicated type of self-similarity breaking. This symmetry breaking affects the late-time isotropization that occurs in these models in a significant way: if the equation of state parameter satisfies (4/3) the models isotropize as regards the shear but not as regards the Weyl curvature. Indeed, these models exhibit a new dynamical feature that we refer to as Weyl curvature dominance: the Weyl curvature dominates the dynamics at late times. By viewing the evolution from a dynamical systems perspective we show that, despite the special nature of the class of models under consideration, this behaviour has implications for more general models.

Journal ArticleDOI
TL;DR: In this paper, the Geroch-Wald-Jang-Huisken-Ilmanen approach was extended to give a negative lower bound for the mass of asymptotically anti-de Sitter spacetimes containing horizons with exotic topologies having ends or infinities of the form g ×, in terms of the cosmological constant.
Abstract: The Geroch-Wald-Jang-Huisken-Ilmanen approach to the positive energy problem may be extended to give a negative lower bound for the mass of asymptotically anti-de Sitter spacetimes containing horizons with exotic topologies having ends or infinities of the form g × , in terms of the cosmological constant. We also show how the method gives a lower bound for the mass of time-symmetric initial data sets for black holes with vectors and scalars in terms of the mass, |Z(Q,P)| of the double-extreme black hole with the same charges. I also give a lower bound for the area of an apparent horizon, and hence a lower bound for the entropy in terms of the same function |Z(Q,P)|. This shows that the so-called attractor behaviour extends beyond the static spherically symmetric case. and underscores the general importance of the function |Z(Q,P)|. There are hints that higher-dimensional generalizations may involve the Yamabe conjectures.

Journal ArticleDOI
TL;DR: In this article, a relativistic perfect fluid with a non-homogeneous isentropic flow is studied in terms of acoustic geometry, and the sound wave equation turns out to be equivalent to the equation of motion for a massless scalar field propagating in a curved spacetime geometry.
Abstract: Sound wave propagation in a relativistic perfect fluid with a non-homogeneous isentropic flow is studied in terms of acoustic geometry. The sound wave equation turns out to be equivalent to the equation of motion for a massless scalar field propagating in a curved spacetime geometry. The geometry is described by the acoustic metric tensor which depends locally on the equation of state and the 4-velocity of the fluid. For a relativistic supersonic flow in curved spacetime the ergosphere and acoustic horizon may be defined in a way analogous to the non-relativistic case. A general-relativistic expression for the acoustic analogue of surface gravity has been found.

Journal ArticleDOI
TL;DR: In this article, the authors investigate the space of so-called rigging maps associated with refined algebraic quantization, a particular realization of the Dirac scheme and provide a condition under which the rigging map is unique, in which case it is given by group-averaging techniques.
Abstract: This work addresses certain ambiguities in the Dirac approach to constrained systems. Specifically, we investigate the space of so-called `rigging maps' associated with refined algebraic quantization, a particular realization of the Dirac scheme. Our main result is to provide a condition under which the rigging map is unique, in which case we also show that it is given by group-averaging techniques. Our results comprise all cases where the gauge group is a finite-dimensional Lie group.

Journal ArticleDOI
TL;DR: In this article, the flatness and quasi-flatness problems in cosmological models with varying speed of light were studied and perturbative, non-perturbative and asymptotic solutions were found using both numerical and analytical methods.
Abstract: We define the flatness and quasi-flatness problems in cosmological models. We seek solutions to both problems in homogeneous and isotropic Brans-Dicke cosmologies with a varying speed of light. We formulate this theory and find perturbative, non-perturbative and asymptotic solutions using both numerical and analytical methods. For a particular range of variations of the speed of light the flatness problem can be solved. Under other conditions there exists a late-time attractor with a constant value of that is smaller than, but of the order of unity. Thus these theories may solve the quasi-flatness problem, a considerably more challenging problem than the flatness problem. We also discuss the related and quasi- problem in these theories. We conclude with an appraisal of the difficulties these theories may face.

Journal ArticleDOI
Abstract: A classical continuum theory corresponding to Barrett and Crane's model of Euclidean simplicial quantum gravity is presented The fields in this classical theory are those of SO(4) BF theory, a simple topological theory of an so(4)-algebra-valued 2-form field, , and an SO(4) connection The left-handed (self-dual) and right-handed (anti-self-dual) components of B define a left-handed and a, generally distinct, right-handed area for each spacetime 2-surface The theory presented is obtained by adding to the BF action a Lagrange multiplier term which enforces the constraint that the left- and the right-handed areas should be be equal The solution space of the theory has six branches, two of which reproduce Euclidean general relativity (GR) The other four branches are also characterized and it is shown that the GR branches are stable in the sense that non-degenerate initial data of a solution in one of the GR branches does not, except in special cases, admit an alternative development in another branch Finally, the path-integral quantization of the theory is discussed at a formal level and a heuristic argument is given suggesting that in the semiclassical limit the path integral is dominated by solutions in one of the non-GR sectors, which would mean that the theory quantized in this way is not a quantization of GR

Journal ArticleDOI
TL;DR: In this paper, it was shown that given an arbitrary regular distribution of matter at the initial epoch, there always exists an evolution from this initial data which would result either in a black hole or a naked singularity, depending on the allowed choice of free functions available in the solution.
Abstract: Generalizing earlier results on the initial data and the final fate of dust collapse, we study here the relevance of the initial state of a spherically symmetric matter cloud towards determining its end state in the course of a continuing gravitational collapse. It is shown that given an arbitrary regular distribution of matter at the initial epoch, there always exists an evolution from this initial data which would result either in a black hole or a naked singularity, depending on the allowed choice of free functions available in the solution. It follows that given any initial density and pressure profiles for the cloud, there is a non-zero measure set of configurations leading either to black holes or naked singularities, subject to the usual energy conditions ensuring the positivity of energy density. We also characterize here wide new families of black hole solutions resulting from spherically symmetric collapse without requiring the cosmic censorship assumption.

Journal ArticleDOI
TL;DR: In this article, it was shown that static electrovacuum black hole spacetimes containing an asymptotically flat spacelike hypersurface with compact interior and with both degenerate and non-degenerate components of the event horizon do not exist.
Abstract: We show that static electrovacuum black hole spacetimes containing an asymptotically flat spacelike hypersurface with compact interior and with both degenerate and non-degenerate components of the event horizon do not exist, under the supplementary hypothesis that all degenerate components of the event horizon have charges of the same sign. This extends previous uniqueness theorems of Simon and Masood-ul-Alam (where only non-degenerate horizons were allowed) and Heusler (where only degenerate horizons were allowed).

Journal ArticleDOI
TL;DR: In this paper, a minor modification of the Alcubierre geometry can dramatically improve the total energy requirements for a "warp bubble" that can be used to transport macroscopic objects, and a spacetime for which the total negative mass needed is of the order of a few solar masses, accompanied by a comparable amount of positive energy.
Abstract: I show how a minor modification of the Alcubierre geometry can dramatically improve the total energy requirements for a 'warp bubble' that can be used to transport macroscopic objects. A spacetime is presented for which the total negative mass needed is of the order of a few solar masses, accompanied by a comparable amount of positive energy. This puts the warp drive in the mass scale of large traversable wormholes. The new geometry satisfies the quantum inequality concerning WEC violations and has the same advantages as the original Alcubierre spacetime.

Journal ArticleDOI
TL;DR: In this article, the existence of static, electrically charged, perfect fluid spheres that have a regular interior and are arbitrarily close to a maximally charged black-hole state was shown.
Abstract: We present new results concerning the existence of static, electrically charged, perfect fluid spheres that have a regular interior and are arbitrarily close to a maximally charged black-hole state. These configurations are described by exact solutions of Einstein's field equations. A family of these solutions had already been found (de Felice et al 1995 Mon. Not. R. Astron. Soc. 277 L17) but here we generalize that result to cases with different charge distributions within the spheres and show, in an appropriate parameter space, that the set of such physically reasonable solutions has a non-zero measure. We also perform a perturbation analysis and identify the solutions which are stable against adiabatic radial perturbations. We then suggest that the stable configurations can be considered as classic models of charged particles. Finally, our results are used to show that a conjecture of Kristiansson et al (1998 Gen. Rel. Grav. 30 275) is incorrect.

Journal ArticleDOI
TL;DR: The energy spectra of GWs produced in quintessential inflationary models increase in frequency and exhibit a sharp spike around 170 GHz where the associated fraction of critical energy density presently stored in relic gravitons is of the order of 10-6.
Abstract: The energy spectra of gravitational waves (GWs) produced in quintessential inflationary models increase in frequency and exhibit a sharp spike around 170 GHz where the associated fraction of critical energy density presently stored in relic gravitons is of the order of 10-6. The maximal energy density present (today) in the stochastic GW background of quintessential origin is mainly constrained by the consistency with the (homogeneous and isotropic) big-bang nucleosynthesis scenario. We contrast our findings with the spectra of ordinary inflationary models and we comment on possible detection strategies for the spike.

Journal ArticleDOI
TL;DR: In this paper, it is shown that including singular metrics into general relativity has more, and in fact a quite counter-intuitive, impact on the theory than one naively expects.
Abstract: A simple example is given to show that the gauge equivalence classes of physical states in Chern-Simons theory are not in one-to-one correspondence with those of Einstein gravity in three spacetime dimensions. The two theories are therefore not equivalent. It is shown that including singular metrics into general relativity has more, and in fact a quite counter-intuitive, impact on the theory than one naively expects.