Instability of black holes in massive gravity

Abstract: We show that linear perturbations around the simplest black hole solution of massive bi-gravity theories, the bi-Schwarzschild solution, exhibit an unstable mode featuring the Gregory-Laflamme instability of higher-dimensional black strings. The result is obtained for the massive gravity theory which is free from the Boulware-Deser ghost, as well as for its extension with two dynamical metrics. These results may indicate that static black holes in massive gravity do not exist. For graviton mass of order of Hubble scale, however, the instability timescale is of order of the Hubble time.