Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Bray, HL; Jauregui, JL

Published Date

  • April 1, 2015

Published In

Volume / Issue

  • 335 / 1

Start / End Page

  • 285 - 307

Electronic International Standard Serial Number (EISSN)

  • 1432-0916

International Standard Serial Number (ISSN)

  • 0010-3616

Digital Object Identifier (DOI)

  • 10.1007/s00220-014-2162-2

Citation Source

  • Scopus