Quasinormal modes of black holes: from astrophysics to string theory

TL;DR

This paper surveys the theory and computation of quasinormal modes across astrophysical and string-theory motivated black holes. It surveys master equations, separation techniques, and a spectrum of semi-analytical and numerical methods (Mashhoon, WKB, Frobenius/Leaver, time-domain, and monodromy), highlighting stability analyses and late-time tails. The AdS/CFT interpretation links QNMs to poles of retarded Green's functions, elucidating hydrodynamic behavior in strongly coupled plasmas and holographic superconductors, while discussions of higher-dimensional instabilities and area quantization connect perturbations to quantum gravity ideas. The work emphasizes practical computation, stability criteria, and potential observational implications for gravitational-wave astronomy and holographic condensed matter analogs.

Abstract

Perturbations of black holes, initially considered in the context of possible observations of astrophysical effects, have been studied for the past ten 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 (QNMs), 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, AdS/CFT interpretation of quasinormal modes, and holographic superconductors. We also touch on state-of-the-art observational possibilities for detecting quasinormal modes of black holes.

Figures (16)

• Figure 1: The three regions separated by the two turning points $Q(x)=0$.
• Figure 2: The integration grid. Each cell of the grid represents an integration step. The thick points illustrate the choice of ($S$, $W$, $E$, and $N$) for the particular step of the integration. The initial data are specified on the left and bottom sides of the rhombus.
• Figure 3: An example of a time-domain profile for the Schwarzschild black hole gravitational perturbations ($l=2$ vector type, in the point $r=11r_+$).
• Figure 4: Potential for electromagnetic perturbations near the Schwarzschild black hole ($r_+=1$, $\ell=2$) and the same potential interpolated numerically near its maximum. Despite the behavior of the two potentials being different in the full region of $r$, except for a small region near the black hole, low-lying quasinormal modes for both potentials are close.
• Figure 5: The first 60 quasinormal modes for the gravitational perturbations of the Schwarzschild black hole; the numerical values of 1000 lower quasinormal modes are available from http://qnms.way.to.