Slowly rotating black holes in Horava-Lifshitz gravity

TL;DR

This paper revises previous conclusions about the existence of slowly rotating black holes in Horava-Lifshitz gravity, clarifying the relationship with Einstein-aether theory and presenting new solutions with potential universal horizons.

Contribution

It corrects earlier claims by identifying a subtlety in the theory equivalence and provides new slowly rotating black hole solutions in Horava-Lifshitz gravity.

Findings

No slowly rotating black holes are solutions of both theories simultaneously.

New solutions in Horava-Lifshitz gravity with a consistent foliation structure.

Black holes likely possess universal horizons.

Abstract

In a recent paper we claimed that there there are no slowly rotating, stationary, axisymmetric black holes in the infrared limit of Horava-Lifshitz gravity, provided that they are regular everywhere apart from the central singularity. Here we point out a subtlety in the equivalence between Einstein-aether theory and the infrared limit of Horava-Lifshitz gravity which was missed in our earlier derivation and drastically modifies our conclusion: our earlier calculations (which are otherwise technically correct) do not really imply that there are no slowly rotating black holes in Horava-Lifshitz gravity, but that there are no slowly rotating black holes in the latter that are also solutions of Einstein-aether theory and vice versa. That is, even though the two theories share the static, spherically symmetric solutions, there are no slowly rotating black holes that are solutions to both theories. We proceed to generate slowly rotating black hole solutions in the infrared limit of Horava-Lifshitz gravity, and we show that the configuration of the foliation-defining scalar remains the same as in spherical symmetry, thus these black holes are expected to posses a universal horizon.