Showing papers on "Gravitation published in 1993"

Theory and Experiment in Gravitational Physics

Abstract: New technological advances have made it feasible to conduct measurements with precision levels which are suitable for experimental tests of the theory of general relativity. This book has been designed to fill a new need for a complete treatment of techniques for analyzing gravitation theory and experience. The Einstein equivalence principle and the foundations of gravitation theory are considered, taking into account the Dicke framework, basic criteria for the viability of a gravitation theory, experimental tests of the Einstein equivalence principle, Schiff's conjecture, and a model theory devised by Lightman and Lee (1973). Gravitation as a geometric phenomenon is considered along with the parametrized post-Newtonian formalism, the classical tests, tests of the strong equivalence principle, gravitational radiation as a tool for testing relativistic gravity, the binary pulsar, and cosmological tests.

Nonperturbative strong field effects in tensor - scalar theories of gravitation

Abstract: It is shown that a wide class of tensor-scalar theories can pass the present weak-field gravitational tests and exhibit nonperturbative strong-field deviations away from general relativity in systems involving neutron stars. This is achieved without requiring either large dimensionless parameters, fine tuning, or the presence of negative-energy modes. This gives greater significance to tests of the strong gravitational field regime, notably binary pulsar experiments.

Tensor-scalar cosmological models and their relaxation toward general relativity

Abstract: Cosmological models within general tensor-multiscalar theories of gravity are studied. By isolating an autonomous evolution equation for the scalar fields, one shows that the expansion of the Universe during the matter-dominated era tends to drive the scalar fields toward a minimum of the function $a(\ensuremath{\phi})$ describing their coupling to matter, i.e., toward a state where the tensor-scalar theory becomes indistinguishable from general relativity. The two main parameters determining the efficiency of this natural attractor mechanism toward general relativity are the redshift at the beginning of the matter era (or equivalently the present cosmological matter density) and the curvature of the coupling function $a(\ensuremath{\phi})$. Quantitative estimates for the present level of deviation from general relativity, as measured by the post-Newtonian parameters $\ensuremath{\gamma}\ensuremath{-}1$, $\ensuremath{\beta}\ensuremath{-}1$, and $\frac{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{G}}{G}$, are derived, which give greater significance to future improvements of solar-system gravitational tests. Another prediction of many tensor-scalar scenarios (whose consequences, particularly for the formation of structure in the Universe, remain to be studied in detail) is the existence of strong oscillations of the effective Newtonian coupling strength during the first few Hubble time scales of the matter era.

General relativity as a cosmological attractor of tensor-scalar theories.

Abstract: Tensor-scalar theories of gravity are shown to generically contain an attractor mechanism toward general relativity, with the redshift at the beginning of the matter-dominated era providing the measure for the present level of deviation from general relativity. Quantitative estimates for the post-Newtonian parameters \ensuremath{\gamma}-1, \ensuremath{\beta}-1, and G\ifmmode \dot{}\else \.{}\fi{}/G are given, which give greater significance to future improvements of solar-system gravitational tests.

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

Gravitational action for spacetimes with nonsmooth boundaries.

Abstract: In this paper, I examine the gravitational action for spacetimes with nonsmooth boundaries. By two independent techniques, I derive the contribution to the gravitational action of spacelike and timelike two-surfaces on the boundary at which the unit normal changes discontinuously. I discuss the relationship between constraints imposed at such two-surfaces and their contribution to the gravitational action. I derive the form of the action and the juncture conditions appropriate to cases in which a spacetime includes a singular matter distribution whose world history corresponds to a timelike two-dimensional surface.

Cosmological theory without singularities

Abstract: A theory of gravitation is constructed in which all homogeneous and isotropic solutions are nonsingular, and in which all curvature invariants are bounded All solutions for which curvature invariants approach their limiting values approach de Sitter space The action for this theory is obtained by a higher-derivative modification of Einstein's theory We expect that our model can easily be generalized to solve the singularity problem also for anisotropic cosmologies

Breakdown of predictability in gravitational collapse

Abstract: The principle of equivalence, which says that gravity couples to the energy-momentum tensor of matter, and the quantum-mechanical requirement that energy should be positive imply that gravity is always attractive. This leads to singularities in any reasonable theory of gravitation. A singularity is a place where the classical concepts of space and time break down as do all the known laws of physics because they are all formulated on a classical space-time background. In this paper it is claimed that this breakdown is not merely a result of our ignorance of the correct theory but that it represents a fundamental limitation to our ability to predict the future, a limitation that is analogous but additional to the limitation imposed by the normal quantum-mechanical uncertainty principle. The new limitation arises because general relativity allows the causal structure of space-time to be very different from that of Minkowski space. The interaction region can be bounded not only by an initial surface on which data are given and a final surface on which measurements are made but also a "hidden surface" about which the observer has only limited information such as the mass, angular momentum, and charge. Concerning this hidden surface one has a "principle of ignorance": The surface emits with equal probability all configurations of particles compatible with the observers limited knowledge. It is shown that the ignorance principle holds for the quantum-mechanical evaporation of black holes: The black hole creates particles in pairs, with one particle always falling into the hole and the other possibly escaping to infinity. Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state. This means there is no $S$ matrix for the process of black-hole formation and evaporation. Instead one has to introduce a new operator, called the superscattering operator, which maps density matrices describing the initial situation to density matrices describing the final situation.

Cosmological event horizons, thermodynamics, and particle creation

Abstract: It is shown that the close connection between event horizons and thermodynamics which has been found in the case of black holes can be extended to cosmological models with a repulsive cosmological constant. An observer in these models will have an event horizon whose area can be interpreted as the entropy or lack of information of the observer about the regions which he cannot see. Associated with the event horizon is a surface gravity kappa which enters a classical ''first law of event horizons'' in a manner similar to that in which temperature occurs in the first law of thermodynamics. It is shown that this similarity is more than an analogy: An observer with a particle detector will indeed observe a background of thermal radiation coming apparently from the cosmological event horizon. If the observer absorbs some of this radiation, he will gain energy and entropy at the expense of the region beyond his ken and the event horizon will shrink. The derivation of these results involves abandoning the idea that particles should be defined in an observer-independent manner. They also suggest that one has to use something like the Everett-Wheeler interpretation of quantum mechanics because the back reaction andmore » hence the spacetime metric itself appear to be observer-dependent, if one assumes, as seems reasonable, that the detection of a particle is accompanied by a change in the gravitational field.« less

Actions for Gravity, with Generalizations: A Review

Abstract: 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 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 (in the beginning of chapter 2 and 3, respectively) showing the relations between different action-formulations for Einstein gravity in (2+1)- and (3+1)-dimensions.

Modeling the Spatial Distribution of Star Formation in Interacting Disk Galaxies

Abstract: Models of star-forming interacting galaxies are combined with observational data to investigate the nature of star formation in interacting and merging disk galaxies. Detailed models of specific interacting systems are created using the observed morphology and kinematics of the system to constrain model parameters describing the interaction. The models employ an N-body code to calculate the gravitational dynamics, a discrete cloud model to govern the ISM dynamics, and a modified Schmidt law to describe star formation

Limiting configurations allowed by the energy conditions

Abstract: The energy conditions of general relativity are satisfied by all experimentally detected fields. We discuss their interpretation and application to charged spheres. It is found that they prevent the existence of naked singularities, and demand that the effective gravitational mass be everywhere non-negative. We focus on the emergence of limiting configurations-sources of the Reissner-Nordstrom field that have vanishing effective mass everywhere within the sphere. These configurations have a number of interesting features. Among them we find that, near the center, the limiting form of the equation of state isρ+3p=0. Notably this is the only equation of state consistent with the existence of zero-point electromagnetic field, and it has been considered in different contexts, in discussions of cosmic strings and in derivations of (3+1) properties of matter from (4+1) geometry. The consistency of these configurations with the Einstein-Maxwell equations is shown by means of explicit examples. These configurations can be interpreted as due to selfinteracting gravitational effects of the zero-point electromagnetic field.

Gravitational observables and local symmetries.

Abstract: Using a recent classification of local symmetries of the vacuum Einstein equations, it is shown that there can be no observables for the vacuum gravitational field (in a closed universe) built as spatial integrals of local functions of Cauchy data and their derivatives.

The Analysis of Gravitational Lens Surveys. II. Maximum Likelihood Models and Singular Potentials

Abstract: We do a maximum likelihood analysis of three optical surveys for gravitational lenses The results are consistent with lensing by normal galaxies modeled as singular isothermal spheres with standard values for observational parameters, aside from the need to add a small amount of ellipticity to produce the observed four image lenses We tested the model for variations in the number of galaxies, the velocity dispersions of galaxies, the distribution of galaxies, the relation between luminosity and velocity dispersion, the quasar apparent magnitude number counts, and the mean magnification produced by the lenses

The D to 2 limit of general relativity

Abstract: A method for taking the D to 2 limit of D-dimensional general relativity is constructed, yielding a two-dimensional theory which couples gravitation to conserved stress-energy. The authors show how this theory is related to those obtained via an alternative dimensional reduction approach.

Nonsymmetric gravity theories: Inconsistencies and a cure.

Abstract: Motivated by the apparent dependence of string σ models on the sum of spacetime metric and antisymmetric tensor fields, we reconsider gravity theories constructed from a nonsymmetric metric. We first show, by expanding in powers of the antisymmetric field, that all such ‘‘geometrical’’ theories homogeneous in second derivatives violate standard physical requirements: ghost freedom, absence of algebraic inconsistencies, or continuity of degree-of-freedom content. This no-go result applies in particular to the old unified theory of Einstein and its recent avatars. However, we find that the addition of nonderivative, ‘‘cosmological’’ terms formally restores consistency by giving a mass to the antisymmetric tensor field, thereby transmuting it into a fifth-force-like massive vector but with novel possible matter couplings. The resulting macroscopic models also exhibit ‘‘van der Waals’’–type gravitational effects, and may provide useful phenomenological foils to general relativity.

Linear potentials and galactic rotation curves

Abstract: We present a simple, closed-form expression for the potential of an axisymmetric disk of stars interacting through gravitational potentials of the form V(r)=−β/r+γr/2, the potential associated with fundamental sources in the conformal invariant fourth-order theory of gravity which has recently been advanced by Mannheim and Kazanas as a candidate alternative to the standard second-order Einstein theory. Using the model, we obtain a reasonable fit to some representative galactic rotation curve data without the need for any nonluminous or dark matter. Our study suggests that the observed flatness of rotation curves might only be an intermediate phenomenon rather than, an asymptotic one

Conservation laws and two-dimensional black holes in dilaton gravity.

Abstract: A very general class of Lagrangians which couple scalar fields to gravitation and matter in two spacetime dimensions is investigated. It is shown that a vector field exists along whose flow lines the stress-energy tensor is conserved, regardless of whether or not the equations of motion are satisfied or if any Killing vectors exist. Conditions necessary for the existence of Killing vectors are derived. A new set of two-dimensional (2D) black-hole solutions is obtained for one particular member within this class of Lagrangians, which couples a Liouville field to 2D gravity in a novel way. One solution of this theory bears an interesting resemblance to the 2D string-theoretic black hole, yet contains markedly different thermodynamic properties.

Classical solutions in three-dimensional Einstein-Maxwell cosmological gravity

Abstract: The three-dimensional cosmological Einstein-Maxwell equations for fields depending on only one variable are shown to have a hidden SO(2,1) group of invariance. The solution of the coupled field equations is reduced to that of the special relativistic motion of a particle in a given potential. A wide class of exact stationary rotationally symmetric solutions are derived and discussed.

The Einsteinian Gravitational Field of the Rigidly Rotating Disk of Dust

Abstract: This paper presents the gravitational field of a uniformly rotating stationary and axisymmetric disk consisting of dust particles as a rigorous global solution to the Einstein equations. The problem is formulated as a boundary value problem of the Ernst equation and solved by means of inverse methods. The solution is given in terms of linear integral equations and depends on two parameters: the angular velocity Ω and the relative redshift z from the center of the disk. The Newtonian limit z<<1 represents the MacLaurin solution of a rotating fluid in the disk limit. For z→∞ the exterior solution is given by the extreme Kerr solution. This proves a conjecture of Bardeen & Wagoner (1969, 1971)

Visual distortions near a neutron star and black hole

Abstract: The visual distortion effects visible to an observer traveling around and descending to the surface of an extremely compact star are described. Specifically, trips to a ‘‘normal’’ neutron star, a black hole, and an ultracompact neutron star with extremely high surface gravity, are described. Concepts such as multiple imaging, red‐ and blue‐shifting, conservation of surface brightness, the photon sphere, and the existence of multiple Einstein rings are discussed in terms of what the viewer would see. Computer generated, general relativistically accurate illustrations highlighting the distortion effects are presented and discussed. A short movie (VHS) depicting many of these effects is available to those interested free of charge.

Spinning strings and cosmic dislocations.

Abstract: It is shown that the 1+2 gravity spinning particle metric, when lifted to 1+3 dimensions in a boost-covariant way, gives rise to a chiral conical space-time which includes as particular cases the space-time of a spinning string and two space-times that can be associated with the chiral string with a lightlike phase and the twisted string recently discovered by Bekenstein. Some gravitational effects are briefly discussed and a possibility for a new type of anyon is mentioned

Signature dynamics in general relativity

Abstract: The authors describe classical models of gravitation interacting with scalar fields whose solutions involve degenerate metrics. Some of these solutions exhibit transitions from a Euclidean domain to a Lorentzian spacetime corresponding to a spatially flat Robertson-Walker cosmology.