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  Strong cosmic censorship for surface-symmetric cosmological spacetimes with collisionless matter

Dafermos, M., & Rendall, A. D. (2016). Strong cosmic censorship for surface-symmetric cosmological spacetimes with collisionless matter. Communications on Pure and Applied Mathematics, 69(5), 815-908. doi:10.1002/cpa.21628.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5FB0-C Version Permalink: http://hdl.handle.net/21.11116/0000-0001-6235-5
Genre: Journal Article

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 Creators:
Dafermos, Mihalis, Author
Rendall, Alan D.1, Author              
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24012              

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 Abstract: This paper addresses strong cosmic censorship for spacetimes with self-gravitating collisionless matter, evolving from surface-symmetric compact initial data. The global dynamics exhibit qualitatively different features according to the sign of the curvature $k$ of the symmetric surfaces and the cosmological constant $\Lambda$. With a suitable formulation, the question of strong cosmic censorship is settled in the affirmative if $\Lambda=0$ or $k\le0$, $\Lambda>0$. In the case $\Lambda>0$, $k=1$, we give a detailed geometric characterization of possible "boundary" components of spacetime; the remaining obstruction to showing strong cosmic censorship in this case has to do with the possible formation of extremal Schwarzschild-de Sitter-type black holes. In the special case that the initial symmetric surfaces are all expanding, strong cosmic censorship is shown in the past for all $k,\Lambda$. Finally, our results also lead to a geometric characterization of the future boundary of black hole interiors for the collapse of asymptotically flat data: in particular, in the case of small perturbations of Schwarzschild data, it is shown that these solutions do not exhibit Cauchy horizons emanating from $i^+$ with strictly positive limiting area radius.

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 Dates: 2010-11-032016
 Publication Status: Published in print
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 Identifiers: eDoc: 301404
DOI: 10.1002/cpa.21628
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Title: Communications on Pure and Applied Mathematics
Source Genre: Journal
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Publ. Info: New York, NY : John Wiley & Sons
Pages: - Volume / Issue: 69 (5) Sequence Number: - Start / End Page: 815 - 908 Identifier: ISSN: 0010-3640
CoNE: http://pubman.mpdl.mpg.de/cone/journals/resource/954925392315