Hydrodynamics dual to Einstein-Gauss-Bonnet gravity: all-order gradient resummation

Abstract

Relativistic hydrodynamics dual to Einstein-Gauss-Bonnet gravity in asymptotic ${\text{AdS}}_5$ space is under study. To linear order in the amplitude of the fluid velocity and temperature, we derive the fluid's stress-energy tensor via an all-order resummation of the derivative terms. Each order is accompanied by new transport coefficients, which all together could be compactly absorbed into two functions of momenta, referred to as viscosity functions. Via inverse Fourier transform, these viscosities appear as memory functions in the constitutive relation between components of the stress-energy tensor.

Comments: v1: 23 pages, 8 multi-figures, one appendix; v2: title changed, we improved numerical calculations and found the Gauss-Bonnet corrected memory functions still have no support at negative times, and we removed wrong statement about causality violation in previous version; v3: minor revision, to appear in JHEP