Recollapse of the closed Tolman spacetimes

TL;DR

This paper proves that in certain closed, spherically symmetric Tolman spacetimes with positive energy density, there is an upper limit to the length of timelike curves, supporting the recollapse conjecture.

Contribution

It establishes an explicit upper bound on timelike curve lengths in closed Tolman spacetimes with positive energy density, advancing understanding of their global structure.

Findings

Existence of an upper bound on timelike curve lengths.

Construction of an explicit bound from initial data.

Support for the closed-universe recollapse conjecture.

Abstract

The closed-universe recollapse conjecture is studied for the spherically symmetric spacetimes. It is proven that there exists an upper bound to the lengths of timelike curves in any Tolman spacetime that possesses $S^3$ Cauchy surfaces and whose energy density is positive. Furthermore, an explicit bound is constructed from the initial data for such a spacetime.