Note on a reformulation of the strong cosmic censor conjceture based on computability

TL;DR

This paper proposes a new formulation of the strong cosmic censorship conjecture, linking it to computability theory by considering Malament--Hogarth space-times and their computational capabilities.

Contribution

It introduces a reformulation of the strong cosmic censorship conjecture based on Malament--Hogarth space-times and their relation to non-Turing computations.

Findings

A Malament--Hogarth space-time can perform non-Turing computations.

The reformulated conjecture links cosmic censorship to computability theory.

Malament--Hogarth space-times may check the consistency of ZFC set theory.

Abstract

In this letter we provide a reformulation of the strong cosmic censor conjecture taking into account recent results on Malament--Hogarth space-times. We claim that the strong version of the cosmic censor conjecture can be formulated by postulating that a physically relevant space-time is either globally hyperbolic or possesses the Malament--Hogarth property. But it is known that a Malament--Hogarth space-time in principle is capable for performing non-Turing computations such as checking consistency of ZFC set theory. In this way we get an intimate conjectured link between the cosmic censorship scenario and computability theory.