Papers › Instability of the massive Klein-Gordon field on the Kerr spacetime
Instability of the massive Klein-Gordon field on the Kerr spacetime
Sam R. Dolan
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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 M μ≲0.5. 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 M μ≈0.42. The physical implications are discussed.
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