Showing papers on "Gravitation published in 1995"

Gravitation and Inertia

Abstract: PrefaceChart of Main Topics1A First Tour12Einstein Geometrodynamics133Tests of Einstein Geometrodynamics874Cosmology, Standard Models, and Homogeneous Rotating Models1855The Initial-Value Problem in Einstein Geometrodynamics2696The Gravitomagnetic Field and Its Measurement3157Some Highlights of the Past and a Summary of Geometrodynamics and Inertia384Mathematical Appendix403Symbols and Notations437Author Index445Subject Index of Mathematical Appendix455Subject Index461Fundamental and Astronomical Constants and Units493

Natural wormholes as gravitational lenses.

Abstract: Once quantum mechanical effects are included, the hypotheses underlying the positive mass theorem of classical general relativity fail. As an example of the peculiarities attendant upon this observation, a wormhole mouth embedded in a region of high mass density might accrete mass, giving the other mouth a net [ital negative] mass of unusual gravitational properties. The lensing of such a gravitationally negative anomalous compact halo object (GNACHO) will enhance background stars with a time profile that is observable and qualitatively different from that recently observed for massive compact halo objects (MACHO's) of positive mass. While the analysis is discussed in terms of wormholes, the observational test proposed is more generally a search for compact negative mass objects of any origin. We recommend that MACHO search data be analyzed for GNACHO's.

Quasilocal Thermodynamics of Dilaton Gravity coupled to Gauge Fields

Abstract: We consider an Einstein-Hilbert-dilaton action for gravity coupled to various types of Abelian and non-Abelian gauge fields in a spatially finite system. These include Yang-Mills fields and Abelian gauge fields with three-form and four-form field strengths. We obtain various quasilocal quantities associated with these fields, including their energy and angular momentum, and develop methods for calculating conserved charges when a solution possesses sufficient symmetry. For stationary black holes, we find an expression for the entropy from the microcanonical form of the action. We also find a form of the first law of black hole thermodynamics for black holes with the gauge fields of the type considered here.

Spacetime quantum mechanics and the quantum mechanics of spacetime

Abstract: These are the author's lectures at the 1992 Les Houches Summer School, "Gravitation and Quantizations". They develop a generalized sum-over-histories quantum mechanics for quantum cosmology that does not require either a preferred notion of time or a definition of measurement. The "post-Everett" quantum mechanics of closed systems is reviewed. Generalized quantum theories are defined by three elements (1) the set of fine-grained histories of the closed system which are its most refined possible description, (2) the allowed coarse grainings which are partitions of the fine-grained histories into classes, and (3) a decoherence functional which measures interference between coarse grained histories. Probabilities are assigned to sets of alternative coarse-grained histories that decohere as a consequence of the closed system's dynamics and initial condition. Generalized sum-over histories quantum theories are constructed for non-relativistic quantum mechanics, abelian gauge theories, a single relativistic world line, and for general relativity. For relativity the fine-grained histories are four-metrics and matter fields. Coarse grainings are four-dimensional diffeomorphism invariant partitions of these. The decoherence function is expressed in sum-over-histories form. The quantum mechanics of spacetime is thus expressed in fully spacetime form. The coarse-grainings are most general notion of alternative for quantum theory expressible in spacetime terms. Hamiltonian quantum mechanics of matter fields with its notion of unitarily evolving state on a spacelike surface is recovered as an approximation to this generalized quantum mechanics appropriate for those initial conditions and coarse-grainings such that spacetime geometry

Wormholes in the Brans-Dicke theory of gravitation.

Abstract: It is shown that the static spherically symmetric solutions to the Brans-Dicke theory of gravitation give rise either to a naked singularity if the post Newtonian parameter γ 1.

Lagrangian dynamics in non-flat universes and non-linear gravitational evolution

Abstract: We present a new formalism which allows to derive the general Lagrangian dynamical equations for the motion of gravitating particles in a non--flat Friedmann universe with arbitrary density parameter $\Omega$ and no cosmological constant. We treat the set of particles as a Newtonian collisionless fluid. The non--linear dynamical evolution of the fluid element trajectories is then described up to the third--order expansion in Lagrangian coordinates. This work generalizes recent investigations carried out by Bouchet \etal (1992) and Buchert (1994).

Exact supersymmetric massive and massless white holes.

Abstract: We study special points in the moduli space of vacua at which supersymmetric electric solutions of the heterotic string theory become massless. We concentrate on configurations for which supersymmetric non-renormalization theorem is valid. Those are ten-dimensional supersymmetric string waves and generalized fundamental strings with $SO(8)$ holonomy group. >From these we find the four dimensional spherically symmetric configurations which saturate the BPS bound, in particular near the points of the vanishing ADM mass. The non-trivial massless supersymmetric states in this class exist only in the presence of non-Abelian vector fields. We also find a new class of supersymmetric massive solutions, closely related to the massless ones. A distinctive property of all these objects, either massless or massive, is the existence of gravitational repulsion. They reflect all particles with nonvanishing mass and/or angular momentum, and therefore they can be called white holes, in contrast to black holes which tend to absorb particles of all kinds. If such objects can exist, we will have the first realization of the universal gravitational force which repels all particles with the strength proportional to their mass and therefore can be associated with antigravity.

Constraints from inflation on scalar-tensor gravity theories.

Abstract: We show how observations of the perturbation spectra produced during inflation may be used to constrain the parameters of general scalar-tensor theories of gravity, which include both an inflaton and dilaton field. An interesting feature of these models is the possibility that the curvature perturbations on super-horizon scales may not be constant due to non-adiabatic perturbations of the two fields. Within a given model, the tilt and relative amplitude of the scalar and tensor perturbation spectra gives constraints on the parameters of the gravity theory, which may be comparable with those from primordial nucleosynthesis and post-Newtonian experiments.

Quantum Backreaction on "Classical" Variables.

Abstract: A mathematically consistent procedure for coupling quasiclassical and quantum variables through coupled Hamilton-Heisenberg equations of motion is derived from a variational principle. During evolution, the quasiclassical variables become entangled with the quantum variables with the result that the value of the quasiclassical variables depends on the quantum state. This provides a formalism to compute the backreaction of any quantum system on a quasiclassical one. In particular, it leads to a natural candidate for a theory of gravity coupled to quantized matter in which the gravitational field is not quantized.

The value of singularities

Abstract: We point out that spacetime singularities play a useful role in gravitational theories by eliminating unphysical solutions. In particular, we argue that any modification of general relativity which is completely nonsingular cannot have a stable ground state. This argument applies both to classical extensions of general relativity, and to candidate quantum theories of gravity.

The classical tests in Kaluza-Klein gravity

Abstract: The possible existence of extra dimensions to spacetime can be tested astrophysically using Kaluza-Klein theory, which is a natural extension of Einsteins's general relativity. In the simplest version of the theory, there is a standard class of five-dimensional solutions that are analogous to the four-dimensional Schwarzschild solution. However, even a small departure of the extra dimension from flatness affects the first or dominant part of the potential, making it possible to test for the existence of an extra dimension. Data from the solar system indicate that in our region of space the terms due to the fifth dimension are small (less than or equal to 0.1%) compared to those due to the usual for dimensions of spacetime. However, the parameters of Kaluza-Klein theory are not universal constants and can vary from place to place depending on local physics. Hence other astrophysical systems may serve as better laboratories for investigating the possible existence of extra dimensions.

Spinning strings as torsion line spacetime defects

Abstract: A consistent description of spinning strings with dislocations (chiral strings) as a missing part of the spacetime manifold (spacetime defect) is achieved by introducing a line of torsion along the string. Also, the definition of a spin-dislocation tensor associated with the chiral string allows its interpretation in the context of the Einstein--Cartan theory of gravitation. Some generalizations, as well as the Dirac equations, are briefly discussed. In particular, we argue that the behaviour of the fermions near the chiral string can be used to test the torsion hypothesis.

Gravity's rainbow: Limits for the applicability of the equivalence principle.

Abstract: Limits for the applicability of the equivalence principle are considered in the context of low-energy effective field theories. In particular, we find a class of higher-derivative interactions for the gravitational and electromagnetic fields which produce dispersive photon propagation. The latter is illustrated by calculating the energy-dependent contribution to the deflection of light rays.

Standard and generalized Newtonian gravities as `gauge' theories of the extended Galilei group: I. The standard theory

Abstract: Newton's standard theory of gravitation is reformulated in terms of a generally Galilei-covariant action principle as a gauge theory of the extended Galilei group. A suitable modification of Utiyama's method for gauging the projective realization of the Galilei group associated with the free mass-point, together with the connections between the consequent 11 external gauge fields and known facts about Galilean and Newtonian geometrical structures, are discussed from a unified point of view. Then the problem of the existence of an action principle for the dynamical evolution of the gauge fields is analysed. Since it is not known how to extend Utiyama's method from the case of `invariance' to the case of `quasi-invariance, modulo the equations of motion', which turns out to be the key factor in the Galilean case, an action principle is derived, starting from a suitable power expansion of the 4-metric tensor, as a contraction, for , of the ADM-De-Witt action of general relativity. The Galilean action depends on 27 fields (i.e. it contains 16 auxiliary fields besides the 11 gauge fields) and is indeed quasi-invariant, modulo the equations of motion under general Galilean coordinate transformations. The physical equivalence of this theory and Newton's theory of gravity is shown explicitly, by analysing its first- and second-class constraints. Finally, we discuss the feasibility of a symplectic reduction of the 27-fields theory to a minimal theory depending on only the 11 gauge fields, in the sense of Utiyama's method.

Eulerian perturbation theory in non-flat universes: second-order approximation

Abstract: The problem of solving perturbatively the equations describing the evolution of self-gravitating collisionless matter in an expanding universe considerably simplifies when directly formulated in terms of the gravitational and velocity potentials: the problem can be solved {\it exactly}, rather than approximately, even for cosmological models with arbitrary density parameter $\Omega$. The Eulerian approach we present here allows to calculate the higher-order moments of the initially Gaussian density and velocity fields: in particular, we compute the gravitationally induced skewness of the density and velocity-divergence fields for any value of $\Omega$, confirming the extremely weak $\Omega$-dependence of the skewness previously obtained via Lagrangian perturbation theory. Our results show that the separability assumption of higher-order Eulerian perturbative solutions is restricted to the Einstein-de Sitter case only.

Newtonian quantum gravity

Abstract: We develop a nonlinear quantum theory of Newtonian gravity consistent with an objective interpretation of the wavefunction. Inspired by the ideas of Schrodinger, and Bell, we seek a dimensional reduction procedure to map complex wavefunctions in configuration space onto a family of observable fields in space-time. Consideration of quasi-classical conservation laws selects the reduced one-body quantities as the basis for an explicit quasi-classical coarse-graining. These we interpret as describing the objective reality of the laboratory. Thereafter, we examine what may stand in the role of the usual Copenhagen observer to localise this quantity against macroscopic dispersion. Only a tiny change is needed, via a generically attractive self-potential. A nonlinear treatment of gravitational self-energy is thus advanced. This term sets a scale for all wavepackets. The Newtonian cosmology is thus closed, without need of an external observer. Finally, the concept of quantisation is re-interpreted as a nonlinear eigenvalue problem. To illustrate, we exhibit an elementary family of gravitationally self-bound solitary waves. Contrasting this theory with its canonically quantised analogue, we find that the given interpretation is empirically distinguishable, in principle. This result encourages deeper study of nonlinear field theories as a testable alternative to canonically quantised gravity.

Evolution of distorted rotating black holes. II. Dynamics and analysis

Abstract: We have developed a numerical code to study the evolution of distorted, rotating black holes. This code is used to evolve a new family of black hole initial data sets corresponding to distorted ``Kerr'' holes with a wide range of rotation parameters, and distorted Schwarzschild black holes with odd-parity radiation. Rotating black holes with rotation parameters as high as $a/m=0.87$ are evolved and analyzed in this paper. The evolutions are generally carried out to about $t=100M$, where $M$ is the ADM mass. We have extracted both the even- and odd-parity gravitational waveforms, and find the quasinormal modes of the holes to be excited in all cases. We also track the apparent horizons of the black holes, and find them to be a useful tool for interpreting the numerical results. We are able to compute the masses of the black holes from the measurements of their apparent horizons, as well as the total energy radiated and find their sum to be in excellent agreement with the ADM mass.

Cosmic vacuum strings and domain walls in Brans–Dicke theory of gravity

Abstract: The gravitational field of cosmic vacuum strings and domain walls in the context of Brans–Dicke theory of gravity are investigated. Using the weak field approximation, the solutions which describe the space–time and the scalar field generated by these topological structures are found, the results are compared with the ones obtained in General Relativity.

Bianchi type I cosmological models with variableG and Λ: A comment

Abstract: We treat in an alternate way a problem recently considered by Beesham [1]. We find that anisotropic Bianchi I inflationary cosmologies with variable gravitational and cosmological “constants” admit de Sitter expansion at least for late times.

Conserved quasilocal quantities and general covariant theories in two dimensions.

Abstract: General matterless theories in 1+1 dimensions include dilaton gravity, Yang-Mills theory, as well as non-Einsteinian gravity with dynamical torsion and higher power gravity, and even models of spherically symmetric d=4 general relativity. Their recent identification as special cases of ``Poisson-\ensuremath{\sigma} models'' with a simple general solution in an arbitrary gauge allows a comprehensive discussion of the relation between the known absolutely conserved quantities in all those cases and Noether charges, or notions of quasilocal ``energy-momentum.'' In contrast with Noether-like quantities, quasilocal energy definitions require some sort of ``asymptotics'' to allow an interpretation as a (gauge-independent) observable. Dilaton gravitation, although a little different in detail, shares this property with the other cases. We also present a simple generalization of the absolute conservation law for the case of interactions with matter of any type. \textcopyright{} 1995 The American Physical Society.

A Machian interpretation of the cosmological constant

Abstract: A 5D Machian generalization of Einstein's theory of gravitation is described in which the cosmological constant appears as the contribution of the rest of the universe to the gravitational field of an “isolated” source. This work amounts to a Machian interpretation of the Kaluza-Klein theory. The standard cosmological models are derived in this framework, and it is shown that - in conformity with the interpretation presented here - the cosmological constant does not directly contribute to the geometric description of the universe as a whole.

Multiparticle dynamics in an expanding universe.

Abstract: Approximate equations of motion for multiparticle systems in an expanding Einstein-deSitter universe are derived from the Einstein-Maxwell field equations using the Einstein-Infeld-Hoffmann surface integral method. At the Newtonian level of approximation one finds that, in comoving coordinates, both the Newtonian gravitational and Coulomb interactions in these equations are multiplied by the inverse third power of the scale factor $R(t)$ appearing in the Einstein-deSitter field and they acquire a cosmic "drag" term. Nevertheless, both the period and luminosity size of bound two-body systems whose period is small compared to the Hubble time are found to be independent of $t$.