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

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

2007-05-20

arxiv.org/abs/0705.2880v2

Phys.Rev.D76:084001,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Added references. 27 pages, 7 figures

Scientific paper

10.1103/PhysRevD.76.084001

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

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