Cosmological spacetimes not covered by a constant mean curvature slicing

TL;DR

This paper demonstrates that certain solutions to Einstein-dust equations with a constant mean curvature surface do not necessarily admit a foliation by such surfaces, revealing limitations in the applicability of CMC slicing.

Contribution

It provides a counterexample showing that not all maximal globally hyperbolic solutions with a CMC surface can be foliated by CMC surfaces, challenging previous assumptions.

Findings

Existence of solutions with a CMC surface but no CMC foliation

Counterexample to the universality of CMC foliations in Einstein-dust spacetimes

Implications for the understanding of spacetime slicing in general relativity

Abstract

We show that there exist maximal globally hyperbolic solutions of the Einstein-dust equations which admit a constant mean curvature Cauchy surface, but are not covered by a constant mean curvature foliation.