Quasinormal modes and continuum response of de Sitter black holes via complex scaling method

TL;DR

This paper employs the complex scaling method to analyze quasinormal modes and continuum responses of Schwarzschild--de Sitter black holes, revealing how a cosmological constant affects spectral properties.

Contribution

It introduces a spectral framework using complex scaling for black-hole perturbations, unifying quasinormal modes and continuum analysis in de Sitter spacetimes.

Findings

Complex scaling converts boundary-value problems into spectral problems.

The continuum level density characterizes the continuum response beyond quasinormal modes.

Higher-dimensional dS black holes can be analyzed within this framework.

Abstract

We apply the complex scaling method to black-hole perturbations in four-dimensional Schwarzschild--de~Sitter (dS) spacetimes. The method converts the outgoing-wave boundary-value problem into a non-Hermitian spectral problem and enables quasinormal-mode poles and the rotated continuum to be treated in a common framework. We focus in particular on the continuum level density, which characterizes the continuum response beyond isolated quasinormal-mode frequencies. Using Regge--Wheeler-type perturbation equations for scalar, electromagnetic, and gravitational fields, we investigate how a nonzero cosmological constant modifies the pole and continuum sectors. We also discuss a possible extension to string-inspired coupled-channel systems, and illustrate that higher-dimensional dS black holes can be treated within the same framework, at least in tensor- and vector-type sectors. Our results indicate that complex scaling offers a useful spectral framework for analyzing both quasinormal modes and continuum response in black-hole physics.