Spatially homothetic cosmological models.
Abstract
Spatially homothetic cosmological models are defined as spacetime manifolds acted on by a 3parameter group of transformations transitive over spacelike hypersurfaces, whose effect is to multiply the metric by a constant conformal factor. Previous work on these models is reviewed briefly and the algebraic classification scheme of Eardley is described. Explicit forms of the metric and group generators are given for each class in terms of a conformally synchronous coordinate system using an invariant orthogonal basis of 1forms. It is shown that certain subclasses are necessarily incomplete in the sense that a singularity of the conformally synchronous system must develop within a finite time.
 Publication:

General Relativity and Gravitation
 Pub Date:
 August 1978
 DOI:
 10.1007/BF00760139
 Bibcode:
 1978GReGr...9..673L
 Keywords:

 Astronomical Models;
 Cosmology;
 Relativity;
 SpaceTime Functions;
 Transformations (Mathematics);
 Manifolds (Mathematics);
 Mathematical Models;
 Astrophysics;
 Cosmological Models