Area theorem and smoothness of compact Cauchy horizons

TL;DR

This paper improves the area theorem for non-differentiable horizons, showing under certain energy conditions that compact Cauchy horizons are smooth and compact, impacting theories of time machines, black holes, and cosmic censorship.

Contribution

It provides a new proof that compact Cauchy horizons are smooth and compact under the null energy condition, extending previous results to less regular horizons.

Findings

Compact Cauchy horizons are smooth and compact under null energy condition.

Compact Cauchy horizons cannot form in spacetimes with stable dominant energy condition and sources.

Implications for the formation of time machines and topology change in general relativity.

Abstract

We obtain an improved version of the area theorem for not necessarily differentiable horizons which, in conjunction with a recent result on the completeness of generators, allows us to prove that under the null energy condition every compactly generated Cauchy horizon is smooth and compact. We explore the consequences of this result for time machines, topology change, black holes and cosmic censorship. For instance, it is shown that compact Cauchy horizons cannot form in a non-empty spacetime which satisfies the stable dominant energy condition wherever there is some source content.