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.Comment: 0+ 31 Pages; v2: 0+33 pages, typos corrected and new sections (in
appendix) added; v3:published versio