Solutions of the sourceless Einstein's equation with weak and strong cosmological constants are discussed by using Inonu-Wigner contractions of the de Sitter groups and spaces. The more usual case corresponds to a weak cosmological-constant limit, in which the de Sitter groups are contracted to the Poincare group, and the de Sitter spaces are reduced to the Minkowski space. In the strong cosmological-constant limit, however, the de Sitter groups are contracted to another group which has the same abstract Lie algebra of the Poincare group. The de Sitter spaces are reduced to a 4-dimensional cone-space with vanishing Riemann and Ricci curvature tensors, but with an infinite scalar curvature. In such a space, the special conformal transformations act transitively, and the equivalence between inertial frames is that given by special relativity.
19th Texas Symposium on Relativistic Astrophysics and Cosmology
- Pub Date:
- December 1998
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory
- RevTeX, 7 pages, no figures, contribution to "Topics in Theoretical Physics II: Festschrift for A. H. Zimerman"