Instability of the massive Klein-Gordon field on the Kerr spacetime

This is the authors' abstract. We don't add key points for this paper.

We investigate the instability of the massive scalar field in the vicinity of a rotating black hole. The instability arises from amplification caused by the classical superradiance effect. The instability affects bound states: solutions to the massive Klein-Gordon equation which tend to zero at infinity. We calculate the spectrum of bound state frequencies on the Kerr background using a continued-fraction method, adapted from studies of quasinormal modes. We demonstrate that the instability is most significant for the $l=1$, $m=1$ state, for Mμ0.5. For a fast rotating hole ($a=0.99$) we find a maximum growth rate of τ^-1≈1.5×10^-7(GM/c³)^-1, at Mμ≈0.42. The physical implications are discussed.