Closed Tolman models of the universe

Mathematics

Scientific paper

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Astronomical Models, Gravitational Collapse, Singularity (Mathematics), Universe, Boundary Value Problems, Shell Theory, Theorem Proving

Scientific paper

It is shown that most versions of the spherically inhomogeneous dust
models of Tolman (1934) contain a co-moving surface layer in addition to
shell-crossing singularities. Singularities occurring in parabolic,
elliptical and hyperbolic Tolman models are considered. Conditions are
described in which a closed Tolman model must collapse everywhere.

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