Quasinormal modes for the SdS black hole: An analytical approximation scheme

Abstract

Quasinormal modes for scalar field perturbations of a Schwarzschild--de Sitter (SdS) black hole are investigated. An analytical approximation is proposed for the problem. The quasinormal modes are evaluated for this approximate model in the limit when the black hole mass is much smaller than the radius of curvature of the spacetime. The model mirrors some striking features observed in numerical studies of time behavior of scalar perturbations of the SdS black hole. In particular, it shows the presence of two sets of modes relevant at two different time scales, proportional to the surface gravities of the black hole and cosmological horizons, respectively. These quasinormal modes are not complete---another feature observed in the numerical studies. Refinements of this model to yield more accurate quantitative agreement with numerical results are discussed. Further investigations of this model are outlined, which would provide valuable insight into time behavior of perturbations in the SdS spacetime.