TY - JOUR

T1 - Strong Cosmic Censorship for Surface-Symmetric Cosmological Spacetimes with Collisionless Matter

AU - Dafermos, Mihalis

AU - Rendall, Alan D.

N1 - Funding Information:
Much of this research was done while A.D.R. was at the Albert Einstein Institute. M.D. thanks the Albert Einstein Institute and A.D.R. thanks the University of Cambridge for hospitality during visits. Some of this research was carried out during the program “Global Problems in Mathematical Relativity” at the Isaac Newton Institute of the University of Cambridge. The authors thank Piotr Chrúsciel for useful discussions and Jacques Smulevici for helpful comments on the manuscript. M.D. also thanks Dan Pollack and Igor Rodnianski. During the period when this research was carried out, M.D. was supported in part by National Science Foundation Grant DMS-0302748 and a Marie Curie International Re-integration Grant from the European Commission.
Funding Information:
Much of this research was done while A.D.R. was at the Albert Einstein Institute. M.D. thanks the Albert Einstein Institute and A.D.R. thanks the University of Cambridge for hospitality during visits. Some of this research was carried out during the program ?Global Problems in Mathematical Relativity? at the Isaac Newton Institute of the University of Cambridge. The authors thank Piotr Chr?sciel for useful discussions and Jacques Smulevici for helpful comments on the manuscript. M.D. also thanks Dan Pollack and Igor Rodnianski. During the period when this research was carried out, M.D. was supported in part by National Science Foundation Grant DMS-0302748 and a Marie Curie International Re-integration Grant from the European Commission.
Publisher Copyright:
© 2016 Wiley Periodicals, Inc.

PY - 2016/5/1

Y1 - 2016/5/1

N2 - 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 Λ. With a suitable formulation, the question of strong cosmic censorship is settled in the affirmative if Λ=0 or k≤0, Λ>0. In the case Λ>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,Λ. 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.

AB - 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 Λ. With a suitable formulation, the question of strong cosmic censorship is settled in the affirmative if Λ=0 or k≤0, Λ>0. In the case Λ>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,Λ. 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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U2 - 10.1002/cpa.21628

DO - 10.1002/cpa.21628

M3 - Article

AN - SCOPUS:84961204806

SN - 0010-3640

VL - 69

SP - 815

EP - 908

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

IS - 5

ER -