Analysis of the wave equations for the near horizon static isotropic metric

Abstract

We find that, for the near horizon static isotropic metric, all of the massless field equations of the spin $\ensuremath{\le}2$ have the same characteristic: they can be reduced to the Fuchsian-type equation with three regular singular points. Three general solutions, corresponding to different parameter values, are obtained. Two of the solutions have discrete imaginary frequencies. Based on the results above, we obtain exact formulas for the quasinormal modes of the Rindler-type spacetime. We also derive an elegant wave equation, which is the fundamental formula of the perturbation theory for general static spherically symmetric spacetime.