Klein-Gordon equation and rotating black holes

Abstract

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