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Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass

Publication ,  Journal Article
Bray, HL; Jauregui, JL
Published in: Communications in Mathematical Physics
April 1, 2015

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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Published In

Communications in Mathematical Physics

DOI

EISSN

1432-0916

ISSN

0010-3616

Publication Date

April 1, 2015

Volume

335

Issue

1

Start / End Page

285 / 307

Related Subject Headings

  • Mathematical Physics
  • 0206 Quantum Physics
  • 0105 Mathematical Physics
  • 0101 Pure Mathematics
 

Citation

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Bray, H. L., & Jauregui, J. L. (2015). Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass. Communications in Mathematical Physics, 335(1), 285–307. https://doi.org/10.1007/s00220-014-2162-2
Bray, H. L., and J. L. Jauregui. “Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass.” Communications in Mathematical Physics 335, no. 1 (April 1, 2015): 285–307. https://doi.org/10.1007/s00220-014-2162-2.
Bray HL, Jauregui JL. Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass. Communications in Mathematical Physics. 2015 Apr 1;335(1):285–307.
Bray, H. L., and J. L. Jauregui. “Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass.” Communications in Mathematical Physics, vol. 335, no. 1, Apr. 2015, pp. 285–307. Scopus, doi:10.1007/s00220-014-2162-2.
Bray HL, Jauregui JL. Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass. Communications in Mathematical Physics. 2015 Apr 1;335(1):285–307.
Journal cover image

Published In

Communications in Mathematical Physics

DOI

EISSN

1432-0916

ISSN

0010-3616

Publication Date

April 1, 2015

Volume

335

Issue

1

Start / End Page

285 / 307

Related Subject Headings

  • Mathematical Physics
  • 0206 Quantum Physics
  • 0105 Mathematical Physics
  • 0101 Pure Mathematics