Holographic perfect fluidity, Cotton energy-momentum duality and transport properties

TL;DR

The paper studies 2+1D holographic theories in which the boundary fluid can reach perfect thermodynamic equilibrium, by identifying perfect-Cotton geometries where the Cotton–York tensor matches a perfect-fluid form. It shows that such boundary data yield exact bulk Einstein spaces with stationary horizons and no naked singularities, and that the resulting holographic fluids possess infinitely many vanishing non-dissipative transport coefficients. A key idea is a Cotton/energy–momentum duality that constrains boundary vorticity and ties to a mass/nut bulk duality, with implications for black-hole uniqueness and rigidity in AdS. While homogeneous (monopole) geometries constrain transport minimally, axisymmetric (dipolar) geometries reveal concrete holographic constraints, and the work suggests broader avenues for classifying perfect geometries and leveraging holographic RG flow to understand horizon physics.

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.