Black holes from fluid mechanics

We use the AdS/CFT correspondence in a regime where the field theory is well described by fluid mechanics to study large black holes in asymptotically locally anti de Sitter spaces. In particular, we use the fluid description to study the thermodynamics of the black holes and the existence of exotic horizon topologies in higher dimensions.;First we test this method by comparing large rotating black holes in global AdSD spaces to stationary solutions of the relativistic Navier-Stokes equations on SD-2. Reading off the equation of state of this fluid from the thermodynamics of non-rotating black holes, we proceed to construct the nonlinear spinning solutions of fluid mechanics that are dual to rotating black holes. In all known examples, the thermodynamics and the local stress tensor of our solutions are in precise agreement with the thermodynamics and boundary stress tensor of the spinning black holes. Our results yield predictions for the thermodynamics of all large black holes in all theories of gravity on AdS spaces, for example, IIB string theory on AdS5 x S 5 and M theory on AdS4 x S7 and AdS7 x S 4.;We then construct solutions to the relativistic Navier-Stokes equations that describe the long wavelength collective dynamics of the deconfined plasma phase of N = 4 Yang Mills theory compactified down to d = 3 on a Scherk-Schwarz circle. Our solutions are stationary, axially symmetric spinning balls and rings of plasma. These solutions, which are dual to (yet to be constructed) rotating black holes and black rings in Scherk-Schwarz compactified AdS 5, and have properties that are qualitatively similar to those of black holes and black rings in flat five dimensional gravity.;We also study the stability of these solutions to small fluctuations, which provides an indirect method for studying Gregory-Laflamme instabilities. We also extend the construction to higher dimensions, allowing one to study the existence of new black hole topologies and their phase diagram.