Rotating black holes in de Rham-Gabadadze-Tolley massive gravity: Analytic calculation procedure

In this paper, we explore the solutions of rotating black holes within the framework of de Rham-Gabadadze-Tolley (dRGT) massive gravity. We provide a detailed, step-by-step analytical derivation of these solutions. Our solutions are characterized by several parameters: mass $M$ , electric charge $Q_{*}$, angular momentum $a$, and a graviton mass $m$. This graviton mass term incorporates both a cosmological constant $\Lambda$ and a St\"uckelberg charge $S_{*}$ into the black hole parameters. These solutions may serve as potential candidates for astrophysical black holes.