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

TL;DR

This paper introduces an analytical approximation scheme to study scalar field quasinormal modes in Schwarzschild-de Sitter black holes, capturing key features observed in numerical simulations and providing insights into their time evolution.

Contribution

The paper presents a novel analytical approximation method for quasinormal modes in SdS black holes, highlighting two distinct mode sets and discussing refinements for better accuracy.

Findings

Identifies two sets of quasinormal modes at different time scales.

Shows the approximate model reflects features seen in numerical studies.

Discusses potential refinements for improved quantitative agreement.

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 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 behaviour 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 numerical studies. Refinements of this model to yield more accurate quantitative agreement with numerical studies are discussed. Further investigations of this model are outlined, which would provide a valuable insight into time behaviour of perturbations in the SdS spacetime.