On the global geometry of the Stephani universe

Details On the global geometry of the Stephani universe On the global geometry of the Stephani universe

Jul 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983gregr..15..673k&link_type=abstract

General Relativity and Gravitation (ISSN 0001-7701), vol. 15, July 1983, p. 673-689. Research supported by the Alexander von Hum

Mathematics

29

Cosmology, Hyperspaces, Relativity, Space-Time Functions, Big Bang Cosmology, Curvature, Gravitation Theory, Ideal Fluids, Manifolds (Mathematics), Singularity (Mathematics)

Scientific paper

A preliminary investigation of global properties of the Stephani solution of the Einstein field equations is presented. This solution generalizes those of Friedman-Robertson-Walker (FRW) in such a way that the spatial curvature index k (a constant in the FRW models) is a function of the time coordinate. The de Sitter solution, which is also a special case of the Stephani solution, is analyzed in the Stephani coordinates to gain insight into the global structure of the manifold and its foliation. The general metric is found to have several properties in common with this example. It has singularities which can be avoided either by matching the solution to an (as yet unknown) empty-space solution or confining the curvature index to be positive at all times.

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