Showing papers in "General Relativity and Gravitation in 1988"

Heuristic Derivation of the Probability Distributions of Particles Emitted by a Black Hole

Abstract: A simple derivation of the probability distributions for the emission of bosons and fermions from a black hole is given. The derivation is based upon the generalized treatment of barrier penetration introduced by Damour and Ruffini. The intuitive amplitude method of Feynman is employed to establish the intimate connection between the statistics of the particles and their spectral distributions.

Cosmological models with constant deceleration parameter

Abstract: Berman presented elsewhere a law of variation for Hubble's parameter that yields constant deceleration parameter models of the universe. By analyzing Einstein, Pryce-Hoyle and Brans-Dicke cosmologies, we derive here the necessary relations in each model, considering a perfect fluid.

Cosmological Models in a {Kaluza-Klein} Theory With Variable Rest Mass

Abstract: A general class of solutions is obtained for a homogeneous, spatially isotropic five-dimensional (5D) Kaluza-Klein theory with variable rest mass. These solutions generalize in the algebraic and physical sense the previously found solutions in the literature. The 4D spacetime sections of the solutions reduce to the Minkowski metric, K=0 Robertson-Walker metric with the equation of statep=np (p=pressure,n=constant sound speed,ρ=energy density), and to the Robertson-Walker spacetime with “steady-state” metric. Some of the solutions, in different limits, show compactification of the fifth dimension. Some extensions of the model are discussed.

Optical reference geometry for stationary and static dynamics

Abstract: Attention is drawn to the advantages of representing dynamical behavior in a stationary or static background spacetime in terms of a fixed reference 3-geometry that differs from the usual one by a certain conformal rescaling factor. The resulting Riemannian metric may be appropriately described as the “optical geometry” in recognition of the fact that “line-of-sight” trajectories are faithfully represented within it as geodesic, at least in the strictly static case for which such “lines-of-sight” are unambiguously defined. (In more general stationary examples the geodesies represent what amounts to the result of a cancellation between the Coriolis-type effects that would cause a physical light path to deviate to one side or the other depending on the sense of propagation.) The application to the particular case of the Schwarzschild solution is discussed: In this example the optical 3-geometry has a throat that occurs not on the horizon (as in the directly projected 3-geometry) but at the radius of the circular null geodesic orbit.

Beam-like gravitational waves and their geodesics.

Abstract: Exact solutions for the gravitational wave produced by an impulsive, massless beam of arbitrary energy profile are constructed in any number of spacetime dimensions. Geodesics can be explicitly computed and, for homogeneous, axisymmetric, finite-size beams, they exactly focus at the location of the curvature singularity found in the infinite shell collision.

On potentials for several classes of spinor and tensor fields in curved spacetimes

Abstract: Already known results with respect to the existence of a vector potential for the Maxwell field tensor and a tensor potential for Weyl's conformal curvature tensor in four-dimensional spacetimes are generalized. It is shown that there exists a spinor potential of type (n−1,1) for any totally symmetric spinor field of rankn. From this theorem we deduce a series of corollaries, for example, that every antisymmetric tensor of second rank admits a linear representation in terms of the first derivatives of two vector fields. Further, some investigations are made on the existence of potentials for arbitrary symmetric spinors of type (n, m).

Qualitative and numerical study of Bianchi IX models.

Abstract: The continuous evolution of the Mixmaster universe toward the cosmological singularity contains features that differ substantially from its discrete counterpart. We examine here the determination and interpretation of the Liapunov exponent of the continuous orbit. It is briefly mentioned that this is not the only aspect of the Mixmaster dynamics to be affected when we switch from continuous to discrete mode of evolution.

Irrotational Bianchi V viscous fluid cosmology with heat flux

Abstract: The irrotational Bianchi V cosmological model under the influence of both shear and bulk viscosity, together with heat flux, has been studied. Exact solutions for the model are obtained with three assumptions of which the first two relate the matter density, shear scalar, and expansion scalar and the third is a barotropic equation of state, connecting the matter density and thermodynamic pressure. The properties of the solutions are studied and the temperature distribution is also given explicitly. It has been observed that along with the viscosity, heat flux further adds to the rate of entropy increase.

Homothetic transformations with fixed points in spacetime

Abstract: A study is made of homothetic motions with fixed points in spacetime. Some general properties of such spacetimes are established, and a characterization of generalized plane wave spacetimes is proved. A general discussion of homothetic motions in Einstein's theory is given.

On a family of solutions of the Einstein-Maxwell equations

Abstract: A family of axisymmetric asymptotically flat solutions of the Einstein-Maxwell field equations is presented. In a particular case we obtain a magnetostatic solution which reduces to the well-known Schwarzschild metric in the absence of a magnetic field and describes the exterior gravitational field of a massive magnetic dipole moment.

Connections and symmetries in spacetime.

Abstract: The extent to which a symmetric, metric connection on spacetime determines the metric is given, and some applications to affine collineations are discussed.

Solutions to Einstein's field equations with Kantowski-Sachs symmetry and string dust source

Abstract: Einstein's field equations are solved with a two-parameter family of classical strings as the source for the gravitational field. The solutions have Kantowski-Sachs symmetry. The singularities of the solutions and the kinematical properties of the string world sheets are discussed.

Self-similar spherical gravitational collapse and the cosmic censorship hypothesis

Abstract: We show that a self-similar general relativistic spherical collapse of a perfect fluid with an adiabatic equation of statep=(γ−1)ϱ and low enough γ values, results in a naked singularity. The singularity is tangent to an event horizon which surrounds a massive singularity and the redshift along a null geodesic from the singularity to an external observer is infinite. We believe that this is the most serious counter example to cosmic censorship obtained so far.

Dragging of inertial frames by the rotating Earth: Proposal and feasibility for a ground-based detection

Abstract: We are proposing a ground-based experiment to detect the Lense-Thirring drag due to the rotating earth by an off-line comparison between an astrometric measurement of the Earth rotation and an inertial measurement of the angular velocity of the laboratory. It is shown that the former, by means of routine observations of Very Long Baseline Interferometry, has already reached the accuracy needed to perform a 3 % experiment on a time span of ∼1 yr. We propose to perform the latter by a dynamical detector of local rotation of novel conception, the Gyromagnetic Electron Gyroscope. Its principle of operation is briefly discussed together with its response to rotationlike gravitational fields.

Volume matching in Tolman models.

Abstract: Since the equations of general relativity are nonlinear, it is not strictly correct to obtain average values by integrating over spatial volumes. Yet this is really what is done in the attempt to fit our rather lumpy universe to a standard cosmological model of uniform density. Consequently, the fitting problem, raised last year by Ellis and Stoeger [1], asks how accurate the average values derived from observational cosmology can be, even without measurement uncertainties. Do they really describe the best-fit Robertson-Walker model to our universe? One of the alternatives to averaging they suggested was that of volume matching. We try to provide a first estimate of the error due to averaging by fitting a Robertson-Walker model to an inhomogeneous Tolman model using realistic density profiles. Comparing the results from volume matching and from averaging, we find that errors are of the order of 10% or more.

Classification of null-Stäckel electrovac metrics with cosmological constant

Abstract: The complete classification of the null Stackel electrovac spacetimes is realized. For these spacetimes it is possible to integrate the geodetic equations by the complete separation of variables in the Hamilton-Jacobi equation.

A vortex-line model for a system of cosmic strings in equilibrium

Abstract: We show that the field equations of a scalar-gauge theory in general relativity can admit vortex-type solutions describingN parallel vortex lines that we interpret asN infinite straight cosmic strings remaining in equilibrium.

General and unified solution for perfect fluid homogeneous and isotropie cosmological models

Abstract: The general and unified solution for spatially homogeneous and isotropic cosmologies containing a perfect fluid [equation of statep=(γ−1)ρ] is determined in terms of hypergeometric functions. A set of four infinitely denumerable sequences of solutions consistent with the energy conditions are shown to exist in terms of elementary functions. A generation mechanism yields the construction of all the solutions in each sequence. Using the conformal form of the metric and putting the field equations in the form of that describing the classical motion of a particle subject to a linear force, the general solution is then determined in parametric form. Closed models are analogous to harmonic oscillators, and their lifetimes are determined as an explicit function ofγ, both for conformal and cosmological times.

Volume functions in general relativity

Abstract: It is shown that on every spacetime there is a finite Borel measure such that open sets have positive measure and the topological boundary of the chronological past/future of every point has measure zero. Using this measure volume, functions are defined. It is shown that they are semicontinuous, and the set of points at which they are discontinuous is a union of nullgeodesics. The following causality conditions are characterized in terms of their properties: chronological, distinguishing, strongly causal, causally continuous, globally hyperbolic.

Gravitation, torsion, and electromagnetism

Abstract: A term bilinear in the derivative of the torsion is added to the Lagrangian of general relativity to produce torsion that propagates. Using standard variational techniques, field equations are derived with the torsion being interpreted as the electromagnetic potential and the antisymmetric part of the Ricci tensor as the electromagnetic field tensor. The equation of motion is derived from the field equations, and the results are compared to the Einstein-Maxwell formulation.

Energy conditions in standard static spacetimes

Abstract: Let (H, h) be a Riemannian manifold and letf∶H→(0,∞) be a smooth function. The Lorentzian warped product (a,b) f ×H, -∞⩽a

Observationally homogeneous shear-free perfect fluids

Abstract: It has been conjectured that, in general relativity, shear-free perfect fluids which obey any reasonable barotropic equation of state are necessarily either non-expanding or nonrotating. We prove that this is valid in the restricted case when the fluid's expansion and energy density are assumed to be functionally dependent. In a cosmological context, this condition of functional dependence is of interest, because it is closely related to a recently proposed criterion of observational (spatial) homogeneity, which has been enunciated in the Postulate of Uniform Thermal Histories (indeed, the two are equivalent when the fluid's expansion is nonzero). Our result on shear-free fluids may be readily specialized to the case of hypersurface-homogeneous spacetimes, and in particular to that of spatially homogeneous cosmological models. We briefly examine all subcases in which the fluid's expansion is nonzero and focus attention on the one-parameter family of solutions which are not hypersurface-homogeneous.

On the Stephani universes

Abstract: The spacetimes corresponding to a weak version of the cosmological principle are considered. It appears that, starting from very different criteria, they were already obtained by Stephani and studied by Krasinski and Barnes. The only barotropic universes of this class are the Friedmann-Robertson-Walker ones. Among the others, some admit a general thermodynamic scheme; it is shown that, as for barotropic fluids, such a scheme also imposes additional symmetries.

A new gravitational energy tensor

Abstract: The Bel-Robinson tensor is the most used gravitational energy tensor; however, it has the dimensions of energy squared. How to construct tensors with the dimensions of energy by using Lancoz tensors is shown here. The resulting tensors have a large number of arbitrary parameters, frequently have spacelike currents, and frequently do not reduce to familiar pseudo-energy tensors in the weak field limit. Two particular examples of interest are one with well-behaved currents and one which reduces to an energy pseudo-tensor in the weak field limit.

Single kerr-schild metrics: A double view

Abstract: Real-vacuum single Kerr-Schild (ISKS) metrics are discussed and new results proved. It is shown that if the Weyl tensor of such a metric has a twist-free expanding principal null direction, then it belongs to the Schwarzschild family of metrics — there are no Petrov type-II Robinson-Trautman metrics of Kerr-Schild type. If such a metric has twist then it belongs either to the Kerr family or else its Weyl tensor is of Petrov type II. The main part of the paper is concerned with complexified versions of Kerr-Schild metrics. The general real ISKS metric is written in double Kerr-Schild (IDKS) form. TheH andl potentials which generate IDKS metrics are determined for the general vacuum ISKS metric and given explicitly for the Schwarzschild and Kerr families of metrics.

Boost-rotation symmetric gravitational null cone data

Abstract: The potential role of boost-rotation symmetric vacuum spacetimes as test beds for numerical studies of gravitational radiation is discussed. For application to null cone evolution codes, these spacetimes are analyzed in terms of their data on the preferred null cone left invariant by the symmetry group. On this cone, an explicit solution of the Bondi hypersurface and evolution equations is found. This solution has a smooth vertex, a smooth interior, and, except for polar singularities, admits a well-definedℐ+.

Inhomogeneous two-fluid cosmologies

Abstract: A new class of expanding cosmological solutions is derived. The matter content of these models is a mixture of two interacting simple fluids: the first one, homogeneous and isotropic with equation of statep = (γ-1)ρ, the dynamics of which is given by the FRW equation and the second one an inhomogenous dust. The limiting case of two dusts corresponds to the Szekeres' universes of class II. A large subclass of the models evolve to a FRW phase for all physically meaningful values of the polytropic indexγ and the curvature parameterk. A gauge condition, under which the metric is invariant, is shown to exist for k≠0. In particular, it explains why the parabolic model is a peculiar solution in the class found by Szekeres.

Stationary axisymmetric perfect fluid solutions in general relativity

Abstract: A new class of exact solutions of Einstein's field equations with the energy-momentum tensor of a perfect fluid is given. The class of solutions is invariantly characterized by means of the following properties: (i) The energy-momentum tensor describes a perfect fluid. (ii) There are two commuting Killing vectors ξ andη which form an abelian groupG2 of motion. (iii) There is a timelike Killing vector parallel to the four-velocity of the fluid (rigid rotation of the fluid). (iv) The four-vector of the angular velocity of the fluid is a gradientΩi=−(1/4c)ɛirklUl (Ur:k−Uk:r)=χ′i. The last assumption is the reason that all solutions of this class can be found by solving an ordinary differential equation of the second order.

Causal boundary for stably causal spacetimes

Abstract: An explicit identification rule is defined for stably causal spacetimes on the set of the ideal points of the spacetime. In addition, the properties of the extended Alexandrov topology are examined.

Existence of solutions of the Robinson-Trautman equation and spatial infinity

Abstract: The existence of solutions of the Robinson-Trautman equation is established. If solutions exist global in time, they describe spacetimes with negative ADM mass andC ∞ scri±.