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arXiv · 1310.8638

Time flat surfaces and the monotonicity of the spacetime Hawking mass

Hubert L. Bray·Jeffrey L. Jauregui
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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.

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BibTeXRIS

Hubert L. Bray, Jeffrey L. Jauregui. 2013-12-18. Time flat surfaces and the monotonicity of the spacetime Hawking mass. https://doi.org/10.1007/s00220-014-2162-2

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