Holographic perfect fluidity, Cotton energy-momentum duality and transport properties
arXiv:1309.2310 · doi:10.1007/JHEP04(2014)136
Abstract
We investigate background metrics for 2+1-dimensional holographic theories where the equilibrium solution behaves as a perfect fluid, and admits thus a thermodynamic description. We introduce stationary perfect-Cotton geometries, where the Cotton--York tensor takes the form of the energy--momentum tensor of a perfect fluid, i.e. they are of Petrov type D_t. Fluids in equilibrium in such boundary geometries have non-trivial vorticity. The corresponding bulk can be exactly reconstructed to obtain 3+1-dimensional stationary black-hole solutions with no naked singularities for appropriate values of the black-hole mass. It follows that an infinite number of transport coefficients vanish for holographic fluids. Our results imply an intimate relationship between black-hole uniqueness and holographic perfect equilibrium. They also point towards a Cotton/energy--momentum tensor duality constraining the fluid vorticity, as an intriguing boundary manifestation of the bulk mass/nut duality.
V3: 1+39 pages, JHEP version
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