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Communications in Mathematical Physics

, Volume 290, Issue 3, pp 941–972 | Cite as

The Area of Horizons and the Trapped Region

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Abstract

This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally trapped surfaces is proved. The proof makes use of an existence result for marginal surfaces, in the presence of barriers, curvature estimates, together with a novel surgery construction for marginal surfaces. These results are applied to characterize the boundary of the trapped region.

Keywords

Black Hole Disjoint Union Fundamental Form Apparent Horizon Curvature Estimate 
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Notes

Acknowledgements

The authors wish to thank Walter Simon, Marc Mars, Greg Galloway, Rick Schoen and Gerhard Huisken for helpful conversations. The second author would also like to thank Michael Eichmair and Leon Simon for their comments.

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This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.Albert-Einstein-InstitutPotsdamGermany
  2. 2.Department of MathematicsUniversity of MiamiCoral GablesUSA
  3. 3.Stanford University, MathematicsStanfordUSA

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