Quasinormal modes of black holes: From astrophysics to string theory

TLDR

Black‑hole perturbations, originally studied for astrophysical signatures, have become central to string theory, brane‑world models, and quantum gravity, with quasinormal modes providing a bridge to the hydrodynamic regime of strongly coupled finite‑temperature field theories via gauge/gravity duality. This review surveys recent progress in black‑hole perturbation theory, focusing on variable decoupling, quasinormal‑mode calculations, late‑time tails, stability analyses, AdS/CFT interpretations, and holographic superconductors, while also outlining emerging observational prospects. The authors discuss analytical and numerical techniques for decoupling perturbation equations, computing quasinormal modes, analyzing late‑time tails, assessing gravitational stability, and applying AdS/CFT correspondence to interpret these modes.

Abstract

Perturbations of black holes, initially considered in the context of possible observations of astrophysical effects, have been studied for the past 10 years in string theory, brane-world models, and quantum gravity. Through the famous gauge/gravity duality, proper oscillations of perturbed black holes, called quasinormal modes, allow for the description of the hydrodynamic regime in the dual finite temperature field theory at strong coupling, which can be used to predict the behavior of quark-gluon plasmas in the nonperturbative regime. On the other hand, the brane-world scenarios assume the existence of extra dimensions in nature, so that multidimensional black holes can be formed in a laboratory experiment. All this stimulated active research in the field of perturbations of higher-dimensional black holes and branes during recent years. In this review recent achievements on various aspects of black hole perturbations are discussed such as decoupling of variables in the perturbation equations, quasinormal modes (with special emphasis on various numerical and analytical methods of calculations), late-time tails, gravitational stability, anti--de Sitter/conformal field theory interpretation of quasinormal modes, and holographic superconductors. We also touch on state-of-the-art observational possibilities for detecting quasinormal modes of black holes.