Generalised hyperbolicity in singular space-times

TL;DR

This paper introduces a new concept of hyperbolicity based on test fields, demonstrating that certain singular space-times are globally hyperbolic in this sense, which may impact understanding of cosmic censorship.

Contribution

It proposes a novel hyperbolicity concept for singular space-times and links it to shell crossing singularities and cosmic censorship.

Findings

Curve integrable space-times are globally hyperbolic in the new sense

Shell crossing singularities may not violate cosmic censorship

Plausibility argument supports the applicability of the new hyperbolicity concept

Abstract

A new concept analogous to global hyperbolicity is introduced, based on test fields. It is shown that the space-times termed here ``curve integrable'' are globally hyperbolic in this new sense, and a plausibility argument is given suggesting that the result applies to shell crossing singularities. If the assumptions behind this last argument are valid, this provides an alternative route to the assertion that such singularities do not violate cosmic censorship.