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Anti-de Sitter black holes, perfect fluids, and holography

We consider asymptotically anti-de Sitter black holes in $d$-spacetime dimensions in the thermodynamically stable regime. We show that the Bekenstein-Hawking entropy and its leading order corrections due to thermal fluctuations can be reproduced by a weakly interacting fluid of bosons and fermions (`dual gas') in $Δ=α(d-2)+1$ spacetime dimensions, where the energy-momentum dispersion relation for the constituents of the fluid is assumed to be $ε= κp^α$. We examine implications of this result for entropy bounds and the holographic hypothesis.