Holographic Hydrodynamics with a Chemical Potential

TL;DR

This paper explores the effects of a chemical potential on holographic hydrodynamics by analyzing charged AdS black holes with higher-derivative corrections, revealing enhanced violations of the shear viscosity bound and insights into electrical conductivity.

Contribution

It introduces a perturbative construction of charged AdS black holes with four-derivative interactions and examines their hydrodynamic properties in the dual CFT, including viscosity and conductivity.

Findings

Shear viscosity to entropy density ratio is affected by chemical potential.

Violation of the KSS bound is more pronounced with chemical potential.

Electrical conductivity behavior is analyzed in the presence of higher-derivative terms.

Abstract

We consider five-dimensional gravity coupled to a negative cosmological constant and a single U(1) gauge field, including a general set of four-derivative interactions. In this framework, we construct charged planar AdS black hole solutions perturbatively and consider the thermal and hydrodynamic properties of the plasma in the dual CFT. In particular, we calculate the ratio of shear viscosity to entropy density and argue that the violation of the KSS bound is enhanced in the presence of a chemical potential. We also compute the electrical conductivity and comment on various conjectured bounds related to this coefficient.