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

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Rendall,  Alan D.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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(Preprint), 787KB

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Citation

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.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-5FB0-C
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.