The vacuum conservation theorem

TL;DR

This paper proves a version of the vacuum conservation theorem that requires only the dominant energy condition and no time function, with implications for the stability of compact Cauchy horizons.

Contribution

It introduces a more general vacuum conservation theorem without assuming a time function, enhancing understanding of energy conditions in general relativity.

Findings

Proves a version of the vacuum conservation theorem under weaker assumptions.

Shows the importance of a stronger stable version for compact Cauchy horizons.

Highlights the role of the dominant energy condition in conservation laws.

Abstract

A version of the vacuum conservation theorem is proved which does not assume the existence of a time function nor demands stronger properties than the dominant energy condition. However, it is shown that a stronger stable version plays a role in the study of compact Cauchy horizons.