Massive spin-2 fields on black hole spacetimes: Instability of the Schwarzschild and Kerr solutions and bounds on the graviton mass

Richard Brito, Vitor Cardoso, Paolo Pani

Published 2013-04-24, updated 2013-07-11Version 3

Massive bosonic fields of arbitrary spin are predicted by general extensions of the Standard Model. It has been recently shown that there exists a family of bimetric theories of gravity - including massive gravity - which are free of Boulware-Deser ghosts at the nonlinear level. This opens up the possibility to describe consistently the dynamics of massive spin-2 particles in a gravitational field. Within this context, we develop the study of massive spin-2 fluctuations - including massive gravitons - around Schwarzschild and slowly-rotating Kerr black holes. Our work has two important outcomes. First, we show that the Schwarzschild geometry is linearly unstable for small tensor masses, against a spherically symmetric mode. Second, we provide solid evidence that the Kerr geometry is also generically unstable, both against the spherical mode and against long-lived superradiant modes. In the absence of nonlinear effects, the observation of spinning black holes bounds the graviton mass to be smaller than 5x10^{-23} eV.