Showing papers on "Gravitation published in 1994"
Book•
24 Jan 1994
TL;DR: In this paper, the authors provide a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time.
Abstract: The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time. In particular, these solutions are free of black holes and singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski space-time, in all directions. It thus provides the mathematical framework in which a rigorous derivation of the laws of gravitation proposed by Bondi can be given. Moreover, it establishes other important conclusions concerning the nonlinear character of gravitational radiation. The authors obtain their solutions as dynamic developments of all initial data sets, which are close, in a precise manner, to the flat initial data set corresponding to the Minkowski space-time. They thus establish the global dynamic stability of the latter.
1,047 citations
TL;DR: In this paper, it is pointed out that string-loop effects may generate matter couplings for the dilaton allowing this scalar partner of the tensorial graviton to stay massless while contributing to macroscopic gravity in a way naturally compatible with existing experimental data.
Abstract: It is pointed out that string-loop effects may generate matter couplings for the dilaton allowing this scalar partner of the tensorial graviton to stay massless while contributing to macroscopic gravity in a way naturally compatible with existing experimental data. Under a certain assumption of universality of the dilaton coupling functions, the cosmological evolution drives the dilaton towards values where it decouples from matter. At the present cosmological epoch, the coupling to matter of the dilaton should be very small, but non zero. This provides a new motivation for improving the experimental tests of Einstein's Equivalence Principle.
443 citations
TL;DR: This work studied the formation of compact bosonic objects through a dissipationless cooling mechanism and implications are discussed, including the abundance of bosonic stars in the universe, and the possibility of ruling out the axion as a dark matter candidate.
Abstract: We studied the formation of compact bosonic objects through a dissipationless cooling mechanism. Implications of the existence of this mechanism are discussed, including the abundance of bosonic stars in the Universe, and the possibility of ruling out the axion as a dark matter candidate.
282 citations
01 Jan 1994
TL;DR: Ohanian and Ruffini's Gravitation and Spacetime, Second Edition, the authors is the best book on the market today of 500 pages or less on gravitation and general relativity.
Abstract: Now more than ever, Gravitation and Spacetime, Second Edition, by Hans C. Ohanian and new coauthor Remo Ruffini, deserves John Wheeler's praise as "the best book on the market today of 500 pages or less on gravitation and general relativity." Gravitation and Spacetime has been thoroughly updated with the most exciting finds and hottest theoretical topics in general relativity and cosmology. Highlights of the revision include the rise and fall of the fifth force, principles and applications of gravitational lensing, COBE's spectacular confirmation of the blackbody spectrum of the cosmic thermal radiation, theories of dark matter and inflation, and the early universe as a testing ground for particle physicists' unification theories, and much, much more. The ideal choice for a graduate-level introduction to general relativity, Gravitation and Spacetime is also suitable for an advanced undergaduate course.
263 citations
TL;DR: In this paper, the authors argue that when measurement processes involve energies of the order of the Planck scale, the fundamental assumption of locality may no longer be a good approximation, and they argue that in fact, the assumption may not be the best approximation.
227 citations
TL;DR: The canonical Dirac quantization of gravity in terms of Ahtekar's new variables has already produced interesting results, although many important ingredients are still needed before we can say that the quantization has been successful as mentioned in this paper.
Abstract: The search for a theory of quantum gravity has for a long time been almost fruitless. A few years ago, however, Ashtekar found a reformulation of Hamiltonian gravity, which thereafter has given rise to a new promising quantization project: the canonical Dirac quantization of Einstein gravity in terms of Ahtekar's new variables. This project has already produced interesting results, although many important ingredients are still needed before we can say that the quantization has been successful. Related to the classical Ashtekar-Hamiltonian, there have been discoveries regarding new classical actions for gravity in (2+1) and (3+1) dimensions, and also generalizations of Einstein's theory of gravity. In the first type of generalization, one introduces infinitely many new parameters, similar to the conventional Einstein cosmological constant, into the theory. These generalizations are called `neighbours of Einstein's theory' or `cosmological constants generalizations', and the theory has the same number of degrees of freedom, per point in spacetime, as the conventional Einstein theory. The second type is a gauge group generalization of Ashtekar's Hamiltonian, and this theory has the correct number of degrees of freedom to function as a theory for a unification of gravity and Yang--Mills theory. In both types of generalizations, there are still important problems that are unresolved: e.g. the reality conditions, the metric-signature condition, the interpretation, etc. In this review, I will try to clarify the relations between the new and old actions for gravity, and also give a short introduction to the new generalizations. The new results/treatments in this review are: (1) a more detailed constraint analysis of the Hamiltonian formulation of the Hilbert--Palatini Lagrangian in (3+1) dimensions; (2) the canonical transformation relating the Ashtekar- and the ADM-Hamiltonian in (2+1) dimensions is given; (3) there is a discussion regarding the possibility of finding a higher-dimensional Ashtekar formulation. There are also two clarifying figures (at the beginning of sections 2 and 3, respectively) showing the relations between different action-formulations for Einstein gravity in (2+1) and (3+1) dimensions.
222 citations
TL;DR: In this paper, it was shown that no causal Green's function can give the correct linearized response to certain bilocalized distributions, even though these distributions obey the constraints of linearization stability.
Abstract: Classical gravitation on de Sitter space suffers from a linearization instability. One consequence is that the causal response to a spatially localized distribution of positive energy cannot be globally regular. We use this fact to show that no causal Green's function can give the correct linearized response to certain bilocalized distributions, even though these distributions obey the constraints of linearization stability. We avoid the problem by working on the open submanifold spanned by conformal coordinates. The retarded Green's function is first computed in a simple gauge, then the rest of the propagator is inferred by analyticity — up to the usual ambiguity about real, analytic and homogeneous terms. We show that the latter can be chosen so as to give a propagator which does not grow in any direction. The ghost propagator is also given and the interaction vertices are worked out.
176 citations
TL;DR: The old framework of semiclassical gravity is extended to that based on a Langevin-type equation, where the dynamics of the fluctuations of spacetime is driven by the quantum fluctuations of the matter field, useful for the investigation of quantum processes in the early Universe involving fluctuations, vacuum instability, and phase transition phenomena as well as the nonequilibrium thermodynamics of black holes.
Abstract: We continue our earlier investigation of the back reaction problem in semiclassical gravity with the Schwinger-Keldysh or closed-time-path (CTP) functional formalism using the language of the decoherent history formulation of quantum mechanics. Making use of its intimate relation with the Feynman-Vernon influence functional method, we examine the statistical mechanical meaning and show the interrelation of the many quantum processes involved in the back reaction problem, such as particle creation, decoherence, and dissipation. We show how noise and fluctuation arise naturally from the CTP formalism. We derive an expression for the CTP effective action in terms of the Bogoliubov coefficients and show how noise is related to the fluctuations in the number of particles created. In so doing we have extended the old framework of semiclassical gravity, based on the mean field theory of Einstein equation with a source given by the expectation value of the energy-momentum tensor, to that based on a Langevin-type equation, where the dynamics of the fluctuations of spacetime is driven by the quantum fluctuations of the matter field. This generalized framework is useful for the investigation of quantum processes in the early Universe involving fluctuations, vacuum instability, and phase transition phenomena as well as the nonequilibrium thermodynamics of black holes. It is also essential to an understanding of the transition from any quantum theory of gravity to classical general relativity.
172 citations
172 citations
TL;DR: This work considers the coupled evolution of density, (scalar) metric and dilaton perturbations in the transition from a “stringy” phase of growing curvature and gravitational coupling to the standard radiation-dominated cosmology and shows that dilaton production, with a spectrum tilted towards large frequencies, emerges as a general property of this scenario.
Abstract: We consider the coupled evolution of density, (scalar) metric and dilaton perturbations in the transition from a “stringy” phase of growing curvature and gravitational coupling to the standard radiation-dominated cosmology. We show that dilaton production, with a spectrum tilted towards large frequencies, emerges as a general property of this scenario. We discuss the frame-independence of the dilaton spectrum and of the inflationary properties of the metric background by using, as model of source, a pressureless gas of weakly interacting strings, which is shown to provide an approximate but consistent solution to the full system of background equations and string equations of motion. We combine various cosmological bounds on a growing dilaton spectrum with the bound on the dilaton mass obtained from tests of the equivalence principle, and we find allowed windows compatible with a universe presently dominated by a relic background of dilatonic dark matter.
157 citations
TL;DR: In this paper, it was shown that the instantonic soliton of five-dimensional Yang-Mills theory and the closely related BPS monopole of four-dimensional BPS/Higgs theory continue to be exact static, and stable, solutions of these field theories even after the inclusion of gravitational, electromagnetic and, in the four dimensional case, dilatonic interactions, provided that certain nonminimal interactions are included.
TL;DR: This work analyzes inspiralling compact binaries in the context of the scalar-tensor theory of Jordan, Fierz, Brans, and Dicke, focusing on the effect on the inspiral of energy lost to dipole gravitational radiation, whose source is the gravitational self-binding energy of the inspiralling bodies.
Abstract: Observations of gravitational waves from inspiralling compact binaries using laser-interferometric detectors can provide accurate measures of parameters of the source. They can also constrain alternative gravitation theories. We analyze inspiralling compact binaries in the context of the scalar-tensor theory of Jordan, Fierz, Brans, and Dicke, focusing on the effect on the inspiral of energy lost to dipole gravitational radiation, whose source is the gravitational self-binding energy of the inspiralling bodies. Using a matched-filter analysis we obtain a bound on the coupling constant ${\mathrm{\ensuremath{\omega}}}_{\mathrm{BD}}$ of Brans-Dicke theory. For a neutron-star--black-hole binary, we find that the bound could exceed the current bound of ${\mathrm{\ensuremath{\omega}}}_{\mathrm{BD}}$g500 from solar-system experiments, for sufficiently low-mass systems. For a 0.7${\mathit{M}}_{\mathrm{\ensuremath{\bigodot}}}$ neutron star and a 3${\mathit{M}}_{\mathrm{\ensuremath{\bigodot}}}$ black hole we find that a bound ${\mathrm{\ensuremath{\omega}}}_{\mathrm{BD}}$\ensuremath{\approxeq}2000 is achievable. The bound decreases with increasing black-hole mass. For binaries consisting of two neutron stars, the bound is less than 500 unless the stars' masses differ by more than about 0.5${\mathit{M}}_{\mathrm{\ensuremath{\bigodot}}}$. For two black holes, the behavior of the inspiralling binary is observationally indistinguishable from its behavior in general relativity. These bounds assume reasonable neutron-star equations of state and a detector signal-to-noise ratio of 10.
TL;DR: In this article, the most general dilaton gravity theory in 2 spacetime dimensions is considered and a Hamiltonian analysis is performed and the reduced phase space, which is two dimensional, is explicitly constructed in a suitable parametrization of the fields.
01 Jan 1994
TL;DR: The non-thermal particle production in contemporary starburst galaxies and in galaxy clusters is estimated from the Supernova rate, the iron content, and an evaluation of the dynamical processes which characterize these objects as mentioned in this paper.
Abstract: The nonthermal particle production in contemporary starburst galaxies and in galaxy clusters is estimated from the Supernova rate, the iron content, and an evaluation of the dynamical processes which characterize these objects. The primary energy derives from SN explosions of massive stars. The nonthermal energy is transformed by various secondary processes, like acceleration of particles by Supernova Remnants as well as diffusion and/or convection in galactic winds. If convection dominates, the energy spectrum of nonthermal particles will remain hard. At greater distances from the galaxy almost the entire enthalpy of thermal gas and Cosmic Rays will be converted into wind kinetic energy, implying a fatal adiabatic energy loss for the nonthermal component. If this wind is strong enough then it will end in a strong termination shock, producing a new generation of nonthermal particles which are subsequently released without significant adiabatic losses into the external medium. In clusters of galaxies this should only be the case for early type galaxies, in agreement with observations. Clusters should also accumulate their nonthermal component over their entire history and energize it by gravitational contraction. The pion decay γ-ray fluxes of nearby contemporary starburst galaxies is quite small. However rich clusters should be extended sources of very high energy γ-rays, detectable by the next generation of systems of air Cherenkov telescopes. Such observations will provide an independent empirical method to investigate these objects and their cosmological history.
TL;DR: In this paper, the interior structure of a locally conformal invariant fourth-order theory of gravity in the presence of a static, spherically symmetric gravitational source is determined exactly and without any approximation at all by a simple fourth order Poisson equation which thus describes both the strong and weak field limits of the theory in this static case.
Abstract: We study the interior structure of a locally conformal invariant fourth order theory of gravity in the presence of a static, spherically symmetric gravitational source. We find, quite remarkably, that the associated dynamics is determined exactly and without any approximation at all by a simple fourth order Poisson equation which thus describes both the strong and weak field limits of the theory in this static case. We present the solutions to this fourth order equation and find that we are able to recover all of the standard Newton-Euler gravitational phenomenology in the weak gravity limit, to thus establish the observational viability of the weak field limit of the fourth order theory. Additionally, we make a critical analysis of the second order Poisson equation, and find that the currently available experimental evidence for its validity is not as clearcut and definitive as is commonly believed, with there not apparently being any conclusive observational support for it at all either on the very largest distance scales far outside of fundamental sources, or on the very smallest ones within their interiors. Our study enables us to deduce that even though the familiar second order Poisson gravitational equation may be sufficient to yield Newton's Law of Gravity it is not in fact necessary.
TL;DR: In this article, Nother's symmetries in point-like Friedman-Robertson-Walker (FRW) Lagrangians derived for general non-minimally coupled gravitational theories were obtained.
Abstract: Adopting the method described in previous papers, we search for Nother's symmetries in point-like Friedman--Robertson--Walker (FRW) Lagrangians derived for general non-minimally coupled gravitational theories. We obtain exact solutions for flat models capable of producing inflation and recovering the Einstein regime at the present time (i.e. the scalar field and the coupling become constants directly related to the Newton constant ).
TL;DR: In this paper, a symmetric energy-momentum tensor for the gravitational Einstein-Hilbert action is derived and discussed in detail using Noether's theorem and a generalized Belinfante symmetrization procedure in 3+1 dimensions.
Abstract: We discuss general properties of the conservation law associated with a local symmetry. Using Noether's theorem and a generalized Belinfante symmetrization procedure in 3+1 dimensions, a symmetric energy-momentum (pseudo) tensor for the gravitational Einstein-Hilbert action is derived and discussed in detail. In 2+1 dimensions, expressions are obtained for energy and angular momentum arising in the ISO(2,1) gauge-theoretical formulation of Einstein gravity. In addition, an expression for energy in a gauge-theoretical formulation of the string-inspired (1+1)-dimensional gravity is derived and compared with the ADM definition of energy.
TL;DR: The possibility of constraining theories of gravity in which the connection is a fundamental variable is discussed by searching for observational consequences of the torsion degrees of freedom by studying constraints on the two-dimensional parameter space characterizing the theory.
Abstract: We discuss the possibility of constraining theories of gravity in which the connection is a fundamental variable by searching for observational consequences of the torsion degrees of freedom. In a wide class of models, the only modes of the torsion tensor which interact with matter are either a massive scalar or a massive spin-1 boson. Focusing on the scalar version, we study constraints on the two-dimensional parameter space characterizing the theory. For reasonable choices of these parameters the torsion decays quickly into matter fields, and no long-range fields are generated which could be discovered by ground-based or astrophysical experiments.
TL;DR: In this paper, exact solutions for k = 0 Friedmann cosmological models with perfect fluid satisfying the equation of states p=(γ-1)ρ, where γ is constant and 0≤γ≤2, in scalar-tensor gravity theories were investigated.
Abstract: A method is investigated which enables exact solutions to be found for k=0 Friedmann cosmological models with a perfect fluid satisfying the equation of states p=(γ-1)ρ, where γ is constant and 0≤γ≤2, in scalar-tensor gravity theories with an arbitrary form for the gravitational coupling function ω(φ), which defines the theory. A number of explicit solutions are investigated for p=0 universes and inflationary universes, including those for theories in which ω(φ) has a power-law dependence on the scalar field φ. When p=-ρ new varieties of inflation arise in which a(t)∝tnexp(H0tm).
TL;DR: In this article, the energy-momentum complex as well as the superpotential associated with M\o ller's theory are derived and two different solutions, giving rise to the same metric, are obtained.
Abstract: M\o ller's Tetrad Theory of Gravitation is examined with regard to the energy-momentum complex. The energy-momentum complex as well as the superpotential associated with M\o ller's theory are derived. M\o ller's field equations are solved in the case of spherical symmetry. Two different solutions, giving rise to the same metric, are obtained. The energy associated with one solution is found to be twice the energy associated with the other. Some suggestions to get out of this inconsistency are discussed at the end of the paper.
TL;DR: In this paper, the authors study the mass discrepancy in clusters of galaxies and show that the bending of light by a weakly gravitating system, like a galaxy or a cluster of galaxies, cannot exceed the bending predicted by general relativity for the mass of visible and unseen matter.
Abstract: We study gravitational lensing by clusters of galaxies in the context of the generic class of unconventional gravity theories which describe gravity in terms of a metric and one or more scalar fields (called here scalar-tensor theories). We conclude that, if the scalar fields have positive energy, then whatever their dynamics, the bending of light by a weakly gravitating system, like a galaxy or a cluster of galaxies, cannot exceed the bending predicted by general relativity for the mass of visible and hitherto undetected matter (but excluding the scalar field's energy). Thus using general relativity to interpret gravitational lensing observations can only underestimate the mass present in stars, gas, and dark matter. The same conclusion obtains within general relativity if a nonnegligible part of the mass in clusters is in the form of coherent scalar fields, i.e., Higgs fields. The popular observational claim that clusters of galaxies deflect light much more strongly than would be expected from the observable matter contained by them, if it survives, cannot be interpreted in terms of some scalar-tensor unconventional gravity theory with no dark matter. And if the observations eventually show that the matter distribution inferred via general relativity from the lensing is very much like that determined from the dynamics of test objects, then scalar-tensor unconventional gravity will be irrelevant for understanding the mass discrepancy in clusters. However, even a single system in which the dynamical mass determined from virial methods significantly exceeds the lensing mass as determined by general relativity would be very problematic for the dark matter picture but would be entirely consistent with unconventional scalar-tensor gravity theory.
TL;DR: Some approaches to 2D gravity which have been developed in the last few years are reviewed in this paper, which are physical (Liouville) gravity, topological theories and matrix models.
Abstract: Some approaches to 2D gravity which have been developed in the last few years are reviewed. They are physical (Liouville) gravity, topological theories and matrix models. Special attention is paid to matrix models and their interrelations with different approaches. Almost all technical details are omitted, but examples are presented.
Book•
01 Jan 1994
TL;DR: The Uncertainty Principle as mentioned in this paper is a fundamental principle of quantum physics and is the basis of the uncertainty principle in quantum physics, as well as the theory of gravitation and the Cavendish experiment.
Abstract: Introduction by Paul Davies Atoms In Motion Introduction Matter Is Made From Atoms Atomic Processes Chemical Reactions Basic Physics Introduction Physics Before Quantum Physics Nuclei and Particles The Relation Of Physics To Other Sciences Introduction Chemistry Biology Astronomy Geology Psychology How Did It Get That Way? Conservation Of Energy What Is Energy? Gravitational Potential Energy Kinetic Energy Other Forms of Energy The Theory Of Gravitation Planetary Motions Keplers Laws Development of Dynamics Newtons Law of Gravitation Universal Gravitation Cavendishs Experiment What Is Gravity? Gravity and Relativity Quantum Behavior Atomic Mechanics An Experiment with Bullets An Experiment with Waves An Experiment with Electrons The Interface of Electron Waves Watching the Electrons First Principles of Quantum Mechanics The Uncertainty Principle.
TL;DR: In this paper, a new theory of gravitational shocking based on time-dependent perturbation theory was proposed, which predicts significant shock heating by slowly varying perturbations previously thought to be negligible according to the adiabatic criterion.
Abstract: A new theory of gravitational shocking based on time-dependent perturbation theory shows that the changes in energy and angular momentum due to a slowly varying disturbance are not exponentially small for stellar dynamical systems in general. It predicts significant shock heating by slowly varying perturbations previously thought to be negligible according to the adiabatic criterion. The theory extends the scenarios traditionally computed only with the impulse approximation and is applicable to a wide class of disturbances. The approach is applied specifically to the problem of disk shocking of star clusters.
TL;DR: In this paper, a general analysis of electromagnetic as well as gravitational birefringence is presented for the propagation of photons in the Reissner-Nordstrom spacetime characterising a charged black hole.
TL;DR: In this article, a new theory of gravitational shocking based on time-dependent perturbation theory was proposed, which predicts significant shock heating by slowly varying perturbations previously thought to be negligible according to the adiabatic criterion.
Abstract: A new theory of gravitational shocking based on time-dependent perturbation theory shows that the changes in energy and angular momentum due to a slowly varying disturbance are not exponentially small for stellar dynamical systems in general. It predicts significant shock heating by slowly varying perturbations previously thought to be negligible according to the adiabatic criterion. The theory extends the scenarios traditionally computed only with the impulse approximation and is applicable to a wide class of disturbances. The approach is applied specifically to the problem of disk shocking of star clusters.
TL;DR: In this article, the authors reduced the problem of topologically massive gravity with cosmological constant to a special-relativistic dynamical problem, and applied it to the construction of exact sourceless, horizonless solutions asymptotic to the BTZ extreme black holes.
Abstract: The solution of topologically massive gravity with cosmological constant is reduced, for spacetimes with two commuting Killing vectors, to a special-relativistic dynamical problem. This approach is applied to the construction of a class of exact sourceless, horizonless solutions asymptotic to the BTZ extreme black holes.
TL;DR: The total energy of the system is non-negative, vanishing if and only if space-time is Minkowskian, and the expression provides a formula for energy per-unit length of gravitational waves with a spacelike symmetry in 3+1 dimensions.
Abstract: A Hamiltonian framework for (2+1)-dimensional gravity coupled with matter (satisfying positive energy conditions) is considered in the asymptotically flat context. It is shown that the total energy of the system is non-negative, vanishing if and only if space-time is (globally) Minkowskian. Furthermore, contrary to one's experience with usual field theories, the Hamiltonian is bounded from above. This is a genuinely nonperturbative result. In the presence of a spacelike Killing field, (3+1)-dimensional vacuum general relativity is equivalent to (2+1)-dimensional general relativity coupled to certain matter fields. Therefore, our expression provides, in particular, a formula for energy per-unit length (along the symmetry direction) of gravitational waves with a spacelike symmetry in 3+1 dimensions. A special case is that of cylindrical waves which have two hypersurface orthogonal, spacelike Killing fields. In this case, our expression is related to the ``c energy'' in a nonpolynomial fashion. While in the weak field limit the two agree, in the strong field regime they differ significantly. By construction, our expression yields the generator of the time translation in the full theory, and therefore represents the physical energy in the gravitational field.
TL;DR: In this paper, a Lagrangian method based on the velocity gradient and gravity gradient tensors is proposed to solve the nonlinear evolution of pressureless, irrotational density fluctuations in a perturbed Robertson-Walker spacetime using a new Lagrangians method.
Abstract: We solve the nonlinear evolution of pressureless, irrotational density fluctuations in a perturbed Robertson-Walker spacetime using a new Lagrangian method based on the velocity gradient and gravity gradient tensors. Borrowing results from general relativity, we obtain a set of Newtonian ordinary differential equations for these quantities following a given mass element. Using these Lagrangian fluid equations we prove the following results: (1) The spherical tophat perturbation, having zero shear, is the slowest configuration to collapse for a given initial density and growth rate. (2) Initial density maxima are not generally the sites where collapse first occurs. (3) Initially underdense regions may undergo collapse if the shear is not too small. If the magnetic part of the Weyl tensor vanishes, the nonlinear evolution is described purely locally by our equations; this condition holds for spherical, cylindrical, and planar perturbations and may be a good approximation in other circumstances. Assuming the vanishing of the magnetic part of the Weyl tensor, we compute the exact nonlinear gravitational evolution of cold matter. We find that 56\% of initially underdense regions collapse in an Einstein-de Sitter universe for a homogeneous and isotropic random field. We also show that, given this assumption, the final stage of collapse is generically two-dimensional, leading to strongly prolate filaments rather than Zel'dovich pancakes. While this result may explain the prevalence of filamentary collapses in N-body simulations, it is not true in general, suggesting that the magnetic part of the Weyl tensor need not vanish in the Newtonian limit.
TL;DR: This work provides a general prescription for the change in action that results when different portions of the boundary of a spacetime are topologically identified and presents a definition of ``generalized additivity'' which does hold for arbitrary spacetime composition.
Abstract: The gravitational action is not always additive in the usual sense. We provide a general prescription for the change in action that results when different portions of the boundary of a spacetime are topologically identified. We discuss possible implications for the superposition law of quantum gravity. We present a definition of ``generalized additivity'' which does hold for arbitrary spacetime composition.