Tuesday, May 22, 2012

1205.4550 (Gabor Etesi)

A proof of the Geroch-Horowitz-Penrose formulation of the strong cosmic
censor conjecture motivated by computability theory
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Gabor Etesi
In this paper we present a proof of a mathematical version of the strong cosmic censor conjecture attributed to Geroch-Horowitz and Penrose but formulated explicitly by Wald. The proof is based on the existence of future-inextendible causal curves in causal pasts of events on the future Cauchy horizon in a non-globally hyperbolic space-time.By examining explicit non-globally hyperbolic space-times we find that in case of several physically relevant solutions these future-inextendible curves have in fact infinite length. This way we recognize a close relationship between asymptotically flat or anti-de Sitter, physically relevant extendible space-times and the so-called Malament-Hogarth space-times which play a central role in recent investigations in the theory of "gravitational computers". This motivates us to exhibit a more sharp, more geometric formulation of the strong cosmic censor conjecture, namely "all physically relevant, asymptotically flat or anti-de Sitter but non-globally hyperbolic space-times are Malament-Hogarth ones". Our observations may indicate a natural but hidden connection between the strong cosmic censorship scenario and the Church-Turing thesis revealing an unexpected conceptual depth beneath the strong cosmic censor conjecture.
View original: http://arxiv.org/abs/1205.4550

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