Black holes with massive graviton hair

No-hair theorems exclude the existence of nontrivial scalar and massive vector hair outside four-dimensional, static, asymptotically flat black-hole spacetimes. We show, by explicitly building nonlinear solutions, that black holes can support massive graviton hair in theories of massive gravity. These hairy solutions are, most likely, the generic end state of the recently discovered monopole instability of Schwarzschild black holes in massive graviton theories.