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. JaureguiEmail author


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.


Black Hole Fundamental Form Normal Bundle Minkowski Spacetime Curvature Vector 
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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

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

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