Time flat surfaces and the monotonicity of the spacetime Hawking mass
Abstract
We identify a condition on spacelike 2-surfaces in a spacetime that is relevant to understanding the concept of mass in general relativity. We prove a formula for the variation of the spacetime Hawking mass under a uniformly area expanding flow and show that it is nonnegative for these so-called "time flat surfaces." Such flows generalize inverse mean curvature flow, which was used by Huisken and Ilmanen to prove the Riemannian Penrose inequality for one black hole. A flow of time flat surfaces may have connections to the problem in general relativity of bounding the mass of a spacetime from below by the quasi-local mass of a spacelike 2-surface contained therein.
Keywords
Cite
@article{arxiv.1310.8638,
title = {Time flat surfaces and the monotonicity of the spacetime Hawking mass},
author = {Hubert L. Bray and Jeffrey L. Jauregui},
journal= {arXiv preprint arXiv:1310.8638},
year = {2016}
}
Comments
23 pages; sign error fixed from previous version, statement of Theorem 1.1 changed accordingly