The Klein-Gordon equation for a scalar field of mass $\mu$ is analyzed in the geometry of a rotating black hole. It is shown that in the limit $\mu M\ll 1$, 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 $\tau ={\left(\frac{a}{M}\right)}^{-1\mathrm{}}24{\left(\mu M\right)}^{-8\mathrm{}}{\mu }^{-1\mathrm{}}$.

• Received 7 July 1980

DOI:https://doi.org/10.1103/PhysRevD.22.2323