Transport Coefficients for Holographic Hydrodynamics at Finite Energy Scale

TL;DR

This paper explores the relationship between black hole thermodynamics and holographic transport coefficients, verifying formulae for conductivity and diffusion in specific black hole models and expressing Green functions in thermodynamic terms.

Contribution

It provides a detailed verification of transport coefficient formulae for charged black holes and relates Green functions to thermodynamic quantities in holographic hydrodynamics.

Findings

Verified DC conductivity and diffusion coefficient formulas for charged black holes

Expressed shear mode Green functions in terms of thermodynamic quantities

Confirmed consistency of transport coefficients with black hole thermodynamics

Abstract

We investigate the relations between black hole thermodynamics and holographic transport coefficients in this paper. The formulae for DC conductivity and diffusion coefficient are verified for electrically single-charged black holes. We examine the correctness of the proposed expressions by taking charged dilatonic and single-charged STU black holes as two concrete examples, and compute the flows of conductivity and diffusion coefficient by solving the linear order perturbation equations. We then check the consistence by evaluating the Brown-York tensor at a finite radial position. Finally, we find that the retarded Green functions for the shear modes can be expressed easily in terms of black hole thermodynamic quantities and transport coefficients.