Annales Henri Poincaré

, Volume 17, Issue 6, pp 1457–1475 | Cite as

Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass II

  • Hubert L. Bray
  • Jeffrey L. Jauregui
  • Marc Mars


In this sequel paper, we give a shorter, second proof of the monotonicity of the Hawking mass for time flat surfaces under spacelike uniformly area expanding flows in spacetimes that satisfy the dominant energy condition. We also include a third proof which builds on a known formula and describe a class of sufficient conditions of divergence type for the monotonicity of the Hawking mass. These flows of surfaces may have connections to the problem in general relativity of bounding the total mass of a spacetime from below by the quasi-local mass of spacelike 2-surfaces in the spacetime.


Fundamental Form Normal Bundle Variation Formula Curvature Vector Round Sphere 
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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Hubert L. Bray
    • 1
  • Jeffrey L. Jauregui
    • 2
  • Marc Mars
    • 3
  1. 1.Dept. of MathematicsDuke UniversityDurhamUnited States
  2. 2.Department of MathematicsUnion CollegeSchenectadyUSA
  3. 3.Instituto de Física Fundamental y MatematicasUniversidad de SalamancaSalamancaSpain

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