Sound Modes in Holographic Hydrodynamics for Charged AdS Black Hole

Understand

In the previous paper we studied the transport coefficients of Quark-Gluon Plasma in finite temperature and finite density in vector and tensor modes.

• In this paper, we extend it to the scalar modes.
• We work out the decoupling problem and hydrodynamic analysis for the sound mode in charged AdS black hole and calculate the sound velocity, the charge susceptibility and the electrical conductivity.
• We find that Einstein relation among the conductivity, the diffusion constant and the susceptibility holds exactly.