A proof of the Geroch–Horowitz–Penrose formulation of the strong cosmic censor conjecture motivated by computability theory

Etesi, Gábor (2013) A proof of the Geroch–Horowitz–Penrose formulation of the strong cosmic censor conjecture motivated by computability theory. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 52. pp. 946-960. ISSN 0020-7748

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Abstract

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 cos- mic censorship scenario and the Church–Turing thesis revealing an unexpected conceptual depth beneath both conjectures.

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