CMC-Slicings of Kottler-Schwarzschild-de Sitter Cosmologies

TL;DR

This paper constructs and analyzes spherically symmetric constant mean curvature slicings in Kottler-Schwarzschild-de Sitter cosmologies, determining conditions for these slicings to form non-intersecting foliations.

Contribution

It introduces a new family of Cauchy hypersurface slicings in these cosmological models, establishing their uniqueness and conditions for foliation formation.

Findings

Slicings are unique up to the static Killing vector.

Conditions for slicings to form foliations are analytically and numerically determined.

The constructed slicings provide insights into the geometric structure of these spacetimes.

Abstract

There is constructed, for each member of a one-parameter family of cosmological models, which is obtained from the Kottler-Schwarzschild-de Sitter spacetime by identification under discrete isometries, a slicing by spherically symmetric Cauchy hypersurfaces of constant mean curvature. These slicings are unique up to the action of the static Killing vector. Analytical and numerical results are found as to when different leaves of these slicings do not intersect, i.e. when the slicings form foliations.