Second order hydrodynamics for a special class of gravity duals

TL;DR

This paper computes second order hydrodynamic dispersion relations for certain gravity duals, including Schwarzschild AdS and Dp-Branes, and explores implications for transport coefficients within Israel-Stewart theory.

Contribution

It extends hydrodynamic analysis to third order for a specific class of gravity duals, linking sound and shear modes.

Findings

Derived second order dispersion relations for sound modes.

Compared sound and shear mode results to identify third order contributions.

Provided insights into second and third order transport coefficients.

Abstract

The sound mode hydrodynamic dispersion relation is computed up to order $q^3$ for a class of gravitational duals which includes both Schwarzschild $AdS$ and Dp-Brane metrics. The implications for second order transport coefficients are examined within the context of Israel-Stewart theory. These sound mode results are compared with previously known results for the shear mode. This comparison allows one to determine the third order hydrodynamic contributions to the shear mode for the class of metrics considered here.