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arXiv · 2407.21524

Vacuum cosmological spacetimes without CMC Cauchy surfaces

Eric Ling·Argam Ohanyan
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Abstract

In this article, we extend a construction of [6] to obtain a large class of vacuum cosmological spacetimes that do not contain any CMC Cauchy surfaces. The allowed spatial topologies for these examples are of the form $M \# M$, where $M$ is any closed, oriented, irreducible $3$-manifold which is not spherical. This complements the recent results of [19], where, instead of initial data methods, global spacetime gluing arguments were used. The study of such examples is sure to yield insight into Bartnik's cosmological splitting conjecture [1].

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Eric Ling, Argam Ohanyan. 2024-07-31. Vacuum cosmological spacetimes without CMC Cauchy surfaces. https://arxiv.org/abs/2407.21524

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