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arXiv · 0705.2880

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

Sam R. Dolan
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Abstract

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 $M μ\lesssim 0.5$. For a fast rotating hole ($a = 0.99$) we find a maximum growth rate of $τ^{-1} \approx 1.5 \times 10^{-7} (GM/c^3)^{-1}$, at $M μ\approx 0.42$. The physical implications are discussed.

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Sam R. Dolan. 2007-06-05. Instability of the massive Klein-Gordon field on the Kerr spacetime. https://doi.org/10.1103/physrevd.76.084001

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