The Klein-Gordon equation for a scalar field of mass μ is analyzed in the geometry of a rotating black hole. It is shown that in the limit μM1, i.e., particle Compton wavelength much larger than the size of the black hole, the scalar field is unstable with an e-folding time of τ=(a/M)^-124(μM)^-8μ^-1.
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Steven Detweiler (1980) studied this question.
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