Analytical Study of a Kerr-Sen Black Hole and a Charged Massive Scalar Field.

It was reported that Kerr-Newman and Kerr-Sen black holes are unstable to perturbations of charged massive scalar field. In this paper we study analytically the complex frequencies which characterize massive charged scalar fields in a near-extremal Kerr-Sen black hole. For near-extremal Kerr-Sen black holes and for charged massive scalar fields in the eikonal large-mass $\mathcal{M}\gg \mu$ regime, where $\mathcal{M}$ is the mass of the black hole and $\mu$ is the mass of the charged scalar field, we have obtained a simple expression for the dimensionless ratio $\omega_I /\left(\omega_R - \omega_c\right)$, where $\omega_I$ and $\omega_R$ are, respectively, the imaginary and real parts of the frequency of the modes and $\omega_c$ is the critical frequency for the onset of superradiance. We have also found our expression is consistent with the result of Hod \cite{Hod:2016bas} for the case of near-extremal Kerr-Newman black hole, and the result of Zouros and Eardly \cite{Zouros:1979iw} for the case neutral scalar fields in the background of near-extremal Kerr black hole.