Embedding spherical spacelike slices in a Schwarzschild solution
General Relativity and Quantum Cosmology
2009-11-10 v1
Abstract
Given a spherical spacelike three-geometry, there exists a very simple algebraic condition which tells us whether, and in which, Schwarzschild solution this geometry can be smoothly embedded. One can use this result to show that any given Schwarzschild solution covers a significant subset of spherical superspace and these subsets form a sequence of nested domains as the Schwarzschild mass increases. This also demonstrates that spherical data offer an immediate counter example to the thick sandwich `theorem'.
Cite
@article{arxiv.gr-qc/0307050,
title = {Embedding spherical spacelike slices in a Schwarzschild solution},
author = {Niall Ó Murchadha and Krzysztof Roszkowski},
journal= {arXiv preprint arXiv:gr-qc/0307050},
year = {2009}
}