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

TL;DR

This paper derives an all-order resummed hydrodynamic stress-energy tensor dual to Einstein-Gauss-Bonnet gravity in AdS5, revealing viscosity functions as memory functions that encode complex transport phenomena.

Contribution

It introduces a novel all-order gradient resummation method for relativistic hydrodynamics dual to Einstein-Gauss-Bonnet gravity, capturing infinite derivative effects.

Findings

Viscosity functions depend on momenta and act as memory functions.

All-order resummation encodes complex transport phenomena.

Provides a compact representation of transport coefficients.

Abstract

Relativistic hydrodynamics dual to Einstein-Gauss-Bonnet gravity in asymptotic $\textrm{AdS}_5$ 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.