Rotating black holes in de Rham-Gabadadze-Tolley massive gravity: Newman-Janis Algorithm

TL;DR

This paper discovers rotating black hole solutions in dRGT massive gravity, demonstrating the applicability of the Newman-Janis algorithm and providing an analytic hairy black hole solution that generalizes non-rotating cases.

Contribution

It introduces a method to derive rotating black holes in dRGT massive gravity using the Newman-Janis algorithm, including an explicit hairy black hole solution.

Findings

Rotating black hole solutions in dRGT massive gravity are obtained.

The Newman-Janis algorithm is validated in the context of massive gravity.

An explicit analytic hairy black hole solution is presented.

Abstract

We report the discovery of rotating black hole solutions within the framework of de Rham-Gabadadze-Tolley (dRGT) massive gravity. We demonstrate that any nonunitary gauge with the Minkowski reference metric are equal to a unitary gauge with some curved reference metric. Based on this Lemma, we revisit the process of deriving black hole solutions in dRGT theory. We explain how to obtain a static, spherically symmetric solution and then transform it into the corresponding rotating black hole using the Newman-Janis algorithm. For the first time, we provide an analytic expression for a hairy black hole that can reduce to the non-rotating case. Additionally, we confirm that the Newman-Janis algorithm is applicable in the context of massive gravity.