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arXiv · 1908.02185

On the initial geometry of a vacuum cosmological spacetime

John Lott
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Abstract

In the first part of this paper we consider expanding vacuum cosmological spacetimes with a free $T^N$-action. Among them, we give evidence that Gowdy spacetimes have AVTD (asymptotically velocity term dominated) behavior for their initial geometry, in any dimension. We then give sufficient conditions to reach a similar conclusion about a $T^2$-invariant four dimensional nonGowdy spacetime. In the second part of the paper we consider vacuum cosmological spacetimes with crushing singularities. We introduce a monotonic quantity to characterize Kasner spacetimes. Assuming scale-invariant curvature bounds and local volume bounds, we give results about causal pasts.

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John Lott. 2019-08-06. On the initial geometry of a vacuum cosmological spacetime. https://doi.org/10.1088/1361-6382%2Fab77eb

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