Quasinormal modes of Plebański-Demiański black hole in the near-Nariai regime

We investigate the massless scalar perturbations of the Plebański-Demiański black hole considering the general case that admits all nonzero parameters. This case, which is the most generic black hole spacetime in general relativity, is characterized by mass, spin, acceleration, electric and magnetic charges, Newman-Unti-Tamburino 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 Pöschl-Teller potential in the near-Nariai limit in which 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.