Gravitational wave echoes from black holes in massive gravity

Gravitational waves are rapidly becoming a very reliable tool for testing alternative theories of gravity. In particular, features in the gravitational wave emission during the black hole ringdown phase provide a direct probe of the spacetime outside the black hole. In this article, we consider the Schwarzschild-de Sitter black hole solution in ghost-free massive gravity. These black holes generically have scalar hair. We found that a simple coupling between gravitational perturbations and this scalar hair can change the quasinormal ringing of the black hole and, in particular, produce echoes in the emitted gravitational waves. This finding suggests a possible method for testing massive gravity using gravitational wave observations.