Black holes in massive gravity

TL;DR

This paper reviews black hole solutions in ghost-free massive gravity and bimetric theories, highlighting their stability properties, existence of novel hairy solutions, and implications for astrophysical black holes and graviton mass constraints.

Contribution

It provides a comprehensive review of black hole solutions in massive gravity theories, including stability analysis and the discovery of new hairy black holes.

Findings

Exact black hole solutions similar to General Relativity

Existence of hairy black holes without GR counterparts

Unstable modes in bi-Schwarzschild and bi-Kerr solutions

Abstract

We review the black hole 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 black hole solutions, analogous to those of General Relativity. In addition to these solutions, hairy black holes -- solutions with no correspondent in General Relativity -- 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 black holes richer and more complex than those of General Relativity. In particular, the bi-Schwarzschild black hole 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 black holes are described by these solutions, the superradiant instability of the Kerr solution imposes stringent bounds on the graviton mass.