Holographic thermal DC response in the hydrodynamic limit.

We consider black hole solutions of Einstein gravity that describe deformations of CFTs at finite temperature in which spatial translations have been broken explicitly. We focus on deformations that are periodic in the non-compact spatial directions, which effectively corresponds to considering the CFT on a spatial torus with a non-trivial metric. We apply a DC thermal gradient and show that in a hydrodynamic limit the linearised, local thermal currents can be determined by solving linearised, forced Navier–Stokes equations for an incompressible fluid on the torus. We also show how sub-leading corrections to the thermal current can be calculated as well as showing how the full stress tensor response that is generated by the DC source can be obtained. We also compare our results with the fluid-gravity approach.