On "No-go theorem for slowly rotating black holes in Ho\v{r}ava-Lifshitz gravity"

TL;DR

This paper refutes a previous claim by demonstrating that slowly rotating black hole solutions do exist in the IR limit of non-projectable Hořava-Lifshitz gravity, correcting the understanding of black hole solutions in this theory.

Contribution

It provides a counterexample to the claim that such black holes do not exist, establishing their existence in the IR limit of the non-projectable HL theory.

Findings

Slowly rotating black holes exist in the IR limit of non-projectable HL gravity.

Previous claims of their non-existence are incorrect.

The paper clarifies the solution space of black holes in HL gravity.

Abstract

Slowly rotating black holes in the non-projectable Ho\v{r}ava-Lifshitz (HL) theory were studied recently in Phys. Rev. Lett. {\bf 109}, 181101 (2012), and claimed that they do not exist. In this Comment, we show that this is incorrect, and such solutions indeed exist in the IR limit of the non-projectable HL theory.