Fluid-gravity duality and hydrodynamics of black holes
Since the work of Bekenstein, Hawking and others in the early 1970s, it was known that the laws of black hole mechanics are closely related if not identical to the laws of thermodynamics. A natural question to ask, then, is whether this analogy or the correspondence extends beyond the equilibrium state. The affirmative answer, given by various authors during the 1980s and 90s, became known as the "black hole membrane paradigm". It was shown that black hole horizons can be viewed as being endowed with fluid-like properties such as viscosity, thermal conductivity and so on, whose values remained mysterious. The development of holography 15-20 years ago clarified many of these issues and has led to the quantitative correspondence between Navier-Stokes and Einstein equations. It became possible to study the long-standing problems such as thermalization and turbulence by re-casting them in the dual gravity language. We review those developments focusing, in particular, on the issue of the "unreasonable effectiveness" of hydrodynamic description in strongly interacting quantum systems.