Spacelike spherically symmetric CMC foliation in the extended Schwarzschild spacetime

TL;DR

This paper characterizes smooth spacelike spherically symmetric constant mean curvature hypersurfaces in Schwarzschild spacetime, proving a foliation property and verifying a related conjecture, advancing understanding of spacetime slicing in general relativity.

Contribution

It provides a detailed characterization of SS-CMC hypersurfaces and confirms a conjecture about their foliation properties in Schwarzschild spacetime.

Findings

Proved special SS-CMC foliation property

Verified part of Malec and d3 Murchadha's conjecture

Enhanced understanding of spacetime slicings in Schwarzschild geometry

Abstract

We first summarize the characterization of smooth spacelike spherically symmetric constant mean curvature (SS-CMC) hypersurfaces in the Schwarzschild spacetime and Kruskal extension. Then use the characterization to prove special SS-CMC foliation property, and verify part of the conjecture by Malec and \'{O} Murchadha in their 2003 paper.