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.
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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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Communicated by G.W. Gibbons
Supported in part by the NSF, under contract no. DMS 0407732 with the University of Miami.
Supported in part by a Feodor-Lynen Fellowship of the Humboldt Foundation.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Andersson, L., Metzger, J. The Area of Horizons and the Trapped Region. Commun. Math. Phys. 290, 941–972 (2009). https://doi.org/10.1007/s00220-008-0723-y
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DOI: https://doi.org/10.1007/s00220-008-0723-y