Spectral Problems for Quasinormal Modes of Black Holes
Yasuyuki Hatsuda, Masashi Kimura
TL;DR
This paper reviews spectral problems in black hole perturbation theory, demonstrating how quantum mechanics techniques like WKB and Borel summation can be applied to analyze quasinormal modes.
Contribution
It introduces the application of quantum mechanics methods to spectral problems in black hole physics, with practical analytical and numerical approaches.
Findings
Application of WKB and semiclassical methods to black hole spectra
Use of Borel summation and Padé approximants for spectral analysis
Illustrative examples demonstrating technique versatility
Abstract
This is an unconventional review article on spectral problems in black hole perturbation theory. Our purpose is to explain how to apply various known techniques in quantum mechanics to such spectral problems. The article includes analytical/numerical treatments, semiclassical perturbation theory, the (uniform) WKB method and useful mathematical tools: Borel summations, Pad\'e approximants, etc. The article is not comprehensive, but rather looks into a few examples from various points of view. The techniques in this article are widely applicable to many other examples.
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