Hydrodynamics of strongly coupled non-conformal fluids from gauge/gravity duality.

Abstract

The subject of relativistic hydrodynamics is explored using the tools of gauge/gravity duality. A brief literature review of AdS/CFT and gauge/gravity duality is presented first. This is followed by a pedagogical introduction to the use of these methods in determining hydrodynamic dispersion relations, w(q), of perturbations in a strongly coupled fluid. Shear and sound mode perturbations are examined in a special class of gravity duals: those where the matter supporting the metric is scalar in nature. Analytical solutions (to order q4 and q3 respectively) for the shear and sound mode dispersion relations are presented for a subset of these backgrounds. The work presented here is based on previous publications by the same author [1], [2], and [3], though some previously unpublished results are also included. In particular, the subleading term in the shear mode dispersion relation is analyzed using the AdS/CFT correspondence without any reference to the black hole membrane paradigm.