Black holes in massive gravity

Abstract

We review the black hole (BH) solutions of the ghost-free massive gravity theory and its bimetric extension, and outline the main results on the stability of these solutions against small perturbations. Massive (bi)-gravity accommodates exact BH solutions, analogous to those of general relativity (GR). In addition to these solutions, hairy BHs—solutions with no correspondent in GR—have been found numerically, whose existence is a natural consequence of the absence of Birkhoff’s theorem in these theories. The existence of extra propagating degrees of freedom, makes the stability properties of these BHs richer and more complex than those of GR. In particular, the bi-Schwarzschild BH exhibits an unstable spherically symmetric mode, while the bi-Kerr geometry is also generically unstable, both against the spherical mode and against superradiant instabilities. If astrophysical BHs are described by these solutions, the superradiant instability of the Kerr solution imposes stringent bounds on the graviton mass.