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

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 M0. 5. For a fast rotating hole (a=0. 99) we find a maximum growth rate of ^-11. 510^-7 (GM/c^3) ^-1, at M0. 42. The physical implications are discussed.