A positive energy theorem for Einstein-aether and Ho\v{r}ava gravity

TL;DR

This paper proves an energy positivity theorem for specific solutions in Einstein-aether and Hořava gravity theories, focusing on divergence-free aether vectors on maximal spacelike surfaces, including spherically symmetric cases.

Contribution

It establishes a positive energy theorem for a class of solutions in Einstein-aether and Hořava gravity, extending previous results to new solution classes.

Findings

Energy positivity holds for divergence-free aether solutions.

The theorem applies to spherically symmetric solutions at time symmetry.

Results depend on specific coupling parameter ranges.

Abstract

Energy positivity is established for a class of solutions to Einstein-aether theory and the IR limit of Ho\v{r}ava gravity within a certain range of coupling parameters. The class consists of solutions where the aether 4-vector is divergence free on a spacelike surface to which it is orthogonal (which implies that the surface is maximal). In particular, this result holds for spherically symmetric solutions at a moment of time symmetry.