The absence of the Kerr black hole in the Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper demonstrates that the Kerr black hole solution cannot exist within the modified Hořava-Lifshitz gravity framework for specific parameter choices, highlighting fundamental differences from General Relativity.

Contribution

It proves the non-existence of the Kerr metric as a solution in a particular version of Hořava-Lifshitz gravity, clarifying the theory's limitations.

Findings

Kerr metric does not satisfy the modified HL gravity equations

No fully rotating black hole solution exists in this HL gravity case

Highlights differences between HL gravity and General Relativity

Abstract

We show that the Kerr metric does not exist as a fully rotating black hole solution to the modified Ho\v{r}ava-Lifshitz (HL) gravity with $\Lambda_W=0$ and $\lambda=1$ case. We perform it by showing that the Kerr metric does not satisfy full equations derived from the modified HL gravity.