Quasinormal modes of Pleba\'nski-Demia\'nski black hole in the near-Nariai regime

Abstract

We investigates the massless scalar perturbations of the Pleba\'nski-Demia\'nski black hole considering the general case that admits all nonzero parameters. This case is the most generic black hole spacetime in general relativity, characterized by mass, spin, acceleration, electric and magnetic charges, NUT parameter, and cosmological constant. Employing conformal transformations, we can separate the massless scalar field equation and reduce the effective potential in the radial perturbation equation into the P\"oschl--Teller potential in the near-Nariai limit where the event and cosmo-acceleration horizons are close. This allows us to obtain an exact analytical solution of the quasinormal frequency, implying that the decay rate of the field is quantized depending only on the surface gravity of the black hole.