Sonic velocity in holographic fluids and its applications

TL;DR

This paper explores how sonic velocity in holographic fluids at finite cutoff surfaces influences the understanding of bulk viscosity and transport coefficients, using gravity/fluid correspondence with various boundary conditions.

Contribution

It introduces the role of sonic velocity in clarifying the relationship between bulk viscosity and pressure perturbations in holographic fluids with different boundary conditions.

Findings

Sonic velocity is critical for understanding bulk viscosity.

Boundary conditions affect the parameters in the stress tensor.

Transport coefficients can be extracted considering sonic velocity.

Abstract

Gravity/fluid correspondence becomes an important tool to investigate the strongly correlated fluids. We carefully investigate the holographic fluids at the finite cutoff surface by considering different boundary conditions in the scenario of gravity/fluid correspondence. We find that the sonic velocity of the boundary fluids at the finite cutoff surface is critical to clarify the superficial similarity between bulk viscosity and perturbation of the pressure for the holographic fluid, where we set a special boundary condition at the finite cutoff surface to explicitly express this superficial similarity. Moreover, we further take the sonic velocity into account to investigate a case with more general boundary condition. In this more general case, two parameters in the first order stress tensor of holographic fluid cannot be fixed, one can still extract the information of transport coefficients by considering the sonic velocity seriously.