Smoothness of compact horizons

TL;DR

This paper proves that compact Cauchy horizons in smooth spacetimes satisfying the null energy condition are themselves smooth, and applies this to Lorentzian cobordisms, extending Tipler's result without requiring smoothness.

Contribution

It establishes the smoothness of compact Cauchy horizons under null energy conditions and generalizes Tipler's theorem by removing the smoothness assumption.

Findings

Compact Cauchy horizons are smooth under null energy condition.

Extended Tipler's result to non-smooth cases.

Implications for Lorentzian cobordisms.

Abstract

We prove that compact Cauchy horizons in a smooth spacetime satisfying the null energy condition are smooth. As an application, we consider the problem of determining when a cobordism admits Lorentzian metrics with certain properties. In particular, we prove a result originally due to Tipler without the smoothness hypothesis necessary in the original proof.