Spectral Problems for Quasinormal Modes of Black Holes

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, Padé 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.

This is a contribution to the special issue "Black Hole Physics and Beyond: From the Ringdown Analysis with Gravitational Waves" (Editors: Hiroyuki Nakano and Nami Uchikata) in Universe. V2: Published version. V3: Minor revision

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