Hydrodynamics from charged black branes

TL;DR

This paper extends the fluid-gravity correspondence to charged black branes, deriving dual metrics, energy-momentum tensors, and charge currents up to second order, including effects of Chern-Simons interactions.

Contribution

It provides the first second-order charged black brane solutions with explicit dual hydrodynamic quantities, resolving previous thermodynamics-hydrodynamics discrepancies.

Findings

Derived second-order charged black brane metrics and currents.

Identified a new term in charge current due to Chern-Simons interaction.

Confirmed covariance under boundary Weyl-transformations.

Abstract

We extend the recent work on fluid-gravity correspondence to charged black-branes by determining the metric duals to arbitrary charged fluid configuration up to second order in the boundary derivative expansion. We also derive the energy-momentum tensor and the charge current for these configurations up to second order in the boundary derivative expansion. We find a new term in the charge current when there is a bulk Chern-Simons interaction thus resolving an earlier discrepancy between thermodynamics of charged rotating black holes and boundary hydrodynamics. We have also confirmed that all our expressions are covariant under boundary Weyl-transformations as expected.