  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.
