Superradiant instability of D-dimensional Reissner-Nordström black hole mirror system

Abstract: We analytically study the superradiant instability of a charged massless scalar field in the background of D-dimensional Reissner-Nordstr\"{o}m (RN) black hole caused by the mirror's boundary condition. By using the asymptotic matching method to solve the Klein-Gordon equation that govern the dynamics of the scalar field, we have derived the expressions of the complex parts of the boxed quasinormal frequencies, and shown they are positive in the regime of superradiance. This indicates the charged scalar field is unstable in D-dimensional Reissner-Nordstr\"{o}m (RN) black hole surrounded by mirror. The numerical work to calculate the boxed quasinormal frequencies in this system is still required in the future.