Thermoelectric DC conductivities and Stokes flows on black hole horizons

Understand

We consider a general class of electrically charged black holes of Einstein-Maxwell-scalar theory that are holographically dual to conformal field theories at finite charge density which break translation invariance explicitly.

• We examine the linearised perturbations about the solutions that are associated with the thermoelectric DC conductivity.
• We show that there is a decoupled sector at the black hole horizon which must solve generalised Stokes equations for a charged fluid.
• By solving these equations we can obtain the DC conductivity of the dual field theory.