  Within holography the DC conductivity can be obtained by solving a system of
Stokes equations for an auxiliary fluid living on the black hole horizon. We
show that these equations can be derived from a novel variational principle
involving a functional that depends on the fluid variables of interest as well
as the time reversed quantities. This leads to simple derivation of the Onsager
relations for the conductivity. We also obtain the relevant Stokes equations
for bulk theories of gravity in four dimensions including a $\vartheta F\wedge
F$ term in the Lagrangian, where $\vartheta$ is a function of dynamical scalar
fields. We discuss various realisations of the anomalous Hall conductivity that
this term induces and also solve the Stokes equations for holographic lattices
which break translations in one spatial dimension.

High Energy Physics - Theory