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

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.