Surface gravity of compact non-degenerate horizons under the dominant energy condition

TL;DR

This paper proves that under the dominant energy condition, compact non-degenerate horizons have constant surface gravity and are Cauchy horizons bounded by chronology-violating regions, extending previous vacuum results to non-vacuum cases.

Contribution

It generalizes existing theorems about horizon properties to include non-vacuum spacetimes under the dominant energy condition.

Findings

Non-degenerate horizons have constant surface gravity.

Such horizons are Cauchy horizons.

They are bounded by chronology-violating regions.

Abstract

We prove that under the dominant energy condition any non-degenerate smooth compact totally geodesic horizon admits a smooth tangent vector field of constant non-zero surface gravity. This result generalizes previous work by Isenberg and Moncrief, and by Bustamante and Reiris to the non-vacuum case, the vacuum case being given a largely independent proof. Moreover, we prove that any such achronal non-degenerate horizon is actually a Cauchy horizon bounded on one side by a chronology violating region.