Rotating (A)dS black holes in bigravity

Abstract

In this paper we explore the advantage of using the Kerr-Schild Ansatz in the search for analytic configurations to bigravity. It turns out that it plays a crucial role by providing means to straightforwardly calculate the square root matrix encoding the interaction terms between both gravities. In this spirit, we rederive the Babichev-Fabbri family of asymptotically flat rotating black holes with the aid of an emerging circularity theorem. Taking into account that the interaction terms contain by default two cosmological constants, we repeat our approach starting from the more natural seeds for the Kerr-Schild Ansatz in this context: the (A)dS spacetimes. As a result, we show that a couple of Kerr--(A)dS black holes constitute an exact solution to ghost-free bigravity. Similar to the asymptotically flat case, these black holes share the same angular momentum and (A)dS radius, but their masses are not constrained to be equal.