Hydrodynamics of R-charged black holes

TL;DR

This paper studies the hydrodynamic properties of R-charged black holes in the context of N=4 supersymmetric Yang-Mills plasma, focusing on transport coefficients like shear viscosity and thermal conductivity at finite R-charge density.

Contribution

It provides explicit calculations of shear viscosity and thermal conductivity for R-charged black holes, revealing the universality of the viscosity to entropy ratio and analyzing critical behavior near stability limits.

Findings

Shear viscosity to entropy density ratio is 1/4π, independent of chemical potentials.

Thermal conductivity is computed for single charge black holes.

Transport coefficients exhibit critical behavior near thermodynamic stability boundary.

Abstract

We consider hydrodynamics of N=4 supersymmetric SU(N_c) Yang-Mills plasma at a nonzero density of R-charge. In the regime of large N_c and large 't Hooft coupling the gravity dual description involves an asymptotically Anti- de Sitter five-dimensional charged black hole solution of Behrnd, Cvetic and Sabra. We compute the shear viscosity as a function of chemical potentials conjugated to the three U(1) \subset SO(6)_R charges. The ratio of the shear viscosity to entropy density is independent of the chemical potentials and is equal to 1/4\pi. For a single charge black hole we also compute the thermal conductivity, and investigate the critical behavior of the transport coefficients near the boundary of thermodynamic stability.