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Communications in Mathematical Physics

, Volume 335, Issue 1, pp 285–307 | Cite as

Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass

  • Hubert L. Bray
  • Jeffrey L. Jauregui
Article

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

Black Hole Fundamental Form Normal Bundle Minkowski Spacetime Curvature Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of MathematicsDuke UniversityDurhamUSA
  2. 2.Department of MathematicsUnion CollegeSchenectadyUSA

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