57 research outputs found
Isotropic cosmological singularities 3: The Cauchy problem for the inhomogeneous conformal Einstein-Vlasov equations
We consider the conformal Einstein equations for massless collisionless gas
cosmologies which admit an isotropic singularity. It is shown that the Cauchy
problem for these equations is well-posed with data consisting of the limiting
particle distribution function at the singularity.Comment: LaTeX, 29 pages, no figure
Isotropic cosmological singularities 2: The Einstein-Vlasov system
We consider the conformal Einstein equations for massless collisionless gas
cosmologies which admit an isotropic singularity. After developing the general
theory, we restrict to spatially-homogeneous cosmologies. We show that the
Cauchy problem for these equations is well-posed with data consisting of the
limiting particle distribution function at the singularity.Comment: LaTeX, 37 pages, no figures, submitted to Ann. Phy
A class of plane symmetric perfect-fluid cosmologies with a Kasner-like singularity
We prove the existence of a class of plane symmetric perfect-fluid
cosmologies with a (-1/3, 2/3, 2/3) Kasner-like singularity. These solutions of
the Einstein equations depend on two smooth functions of one space coordinate.
They are constructed by solving a symmetric hyperbolic system of Fuchsian
equations.Comment: LaTeX, 15 pages, no figures, to appear in CQG, correction to
existence proo
A point mass in an isotropic universe: III. The region
McVittie's solution of Einstein's field equations, representing a point mass
embedded into an isotropic universe, possesses a scalar curvature singularity
at proper radius . The singularity is space-like and precedes, in the
expanding case, all other events in the space-time. It is shown here that this
singularity is gravitationally weak, and the possible structure of the region
is investigated. A characterization of this solution which does not
involve asymptotics is given.Comment: Revtex, 11pp. To appear in Class.Quant.Grav. Paper II appeared as
Class. Quant. Grav. 16 (1999) 122
Isotropic cosmological singularities 1: Polytropic perfect fluid spacetimes
We consider the conformal Einstein equations for polytropic perfect fluid
cosmologies which admit an isotropic singularity. For the polytropic index
gamma strictly greater than 1 and less than or equal to 2 it is shown that the
Cauchy problem for these equations is well-posed, that is to say that solutions
exist, are unique and depend smoothly on the data, with data consisting of
simply the 3-metric of the singularity. The analogous result for gamma=1 (dust)
is obtained when Bianchi type symmetry is assumed.Comment: LaTeX, 43 pages, no figures, submitted to Ann. Phy
Measures of gravitational entropy I. Self-similar spacetimes
We examine the possibility that the gravitational contribution to the entropy
of a system can be identified with some measure of the Weyl curvature. In this
paper we consider homothetically self-similar spacetimes. These are believed to
play an important role in describing the asymptotic properties of more general
models. By exploiting their symmetry properties we are able to impose
significant restrictions on measures of the Weyl curvature which could reflect
the gravitational entropy of a system. In particular, we are able to show, by
way of a more general relation, that the most widely used "dimensionless"
scalar is \textit{not} a candidate for this measure along homothetic
trajectories.Comment: revtex, minor clarifications, to appear in Physical Review
Fuchsian analysis of singularities in Gowdy spacetimes beyond analyticity
Fuchsian equations provide a way of constructing large classes of spacetimes
whose singularities can be described in detail. In some of the applications of
this technique only the analytic case could be handled up to now. This paper
develops a method of removing the undesirable hypothesis of analyticity. This
is applied to the specific case of the Gowdy spacetimes in order to show that
analogues of the results known in the analytic case hold in the smooth case. As
far as possible the likely strengths and weaknesses of the method as applied to
more general problems are displayed.Comment: 14 page
Fuchsian methods and spacetime singularities
Fuchsian methods and their applications to the study of the structure of
spacetime singularities are surveyed. The existence question for spacetimes
with compact Cauchy horizons is discussed. After some basic facts concerning
Fuchsian equations have been recalled, various ways in which these equations
have been applied in general relativity are described. Possible future
applications are indicated
- …