Quasinormal modes and continuum response of de Sitter black holes via complex scaling method
Shoya Ogawa, Okuto Morikawa, Takuya Hirose
TLDR
This paper applies complex scaling to analyze quasinormal modes and continuum response in de Sitter black holes, offering a unified spectral framework.
Key contributions
- Applies complex scaling to perturbations in four-dimensional Schwarzschild-de Sitter spacetimes.
- Unifies quasinormal modes and the rotated continuum into a common non-Hermitian spectral framework.
- Investigates how a nonzero cosmological constant modifies pole and continuum sectors for various fields.
- Demonstrates applicability to higher-dimensional dS black holes and string-inspired coupled-channel systems.
Why it matters
This work provides a novel spectral framework for understanding black hole physics, particularly for de Sitter spacetimes. It unifies the treatment of quasinormal modes and continuum response, which is crucial for analyzing gravitational wave signals and spacetime stability. This method could extend to more complex string-inspired systems.
Original 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.
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