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Large rotating AdS black holes from fluid mechanics. (English) Zbl 1245.83022
Summary: We use the AdS/CFT correspondence to argue that large rotating black holes in global $$AdS_{D}$$ spaces are dual to stationary solutions of the relativistic Navier-Stokes equations on $$S^{D - 2}$$. 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 fluid dynamical description applies to large non-extremal black holes as well as a class of large non-supersymmetric extremal black holes, but is never valid for supersymmetric black holes. Our results yield predictions for the thermodynamics of all large black holes in all theories of gravity on AdS spaces, for example, string theory on $$AdS_{5} \times S^{5}$$ and M theory on $$AdS_{4} \times S^{7}$$ and $$AdS_{7} \times S^{4}$$.

##### MSC:
 83C57 Black holes