Hydrodynamics from charged black branes

Understand

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.