Sonic velocity in holographic fluids and its applications

Gravity/fluid correspondence acts as an important tool in investigating 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 in clarifying the superficial similarity between the 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 a more general boundary condition. In this more genaral case, although two parameters in the first order stress tensor of holographic fluid cannot be fixed, one can still extract the information about the transport coefficients by considering the sonic velocity seriously.