Holographic Batteries

TL;DR

This paper investigates the nonlinear electrical conductivity of a holographic conformal field theory with two black hole horizons under a background electric field, revealing a dependence on potential difference and novel horizon properties.

Contribution

It constructs fully nonlinear holographic dual solutions to study conductivity in a two-black-hole background, uncovering new horizon features and their stability.

Findings

Conductivity depends non-trivially on potential difference.

Bulk solutions exhibit flowing, non-Killing horizons with non-zero expansion.

The horizon property persists under small temperature perturbations.

Abstract

We study a three-dimensional holographic CFT under the influence of a background electric field on a spacetime containing two black hole horizons. The electric background is fixed such that there is potential difference between the two boundary black holes, inducing a conserved current. By constructing the holographic duals to this set-up, which are solutions to the Einstein-Maxwell equations with a negative cosmological constant in four dimensions, we calculate, to a fully non-linear level, the conductivity of the CFT in this background. Interestingly, we find that the conductivity depends non-trivially on the potential difference. The bulk solutions are flowing geometries containing black hole horizons which are non-Killing and have non-zero expansion. We find a novel property that the past boundary of the future horizon lies deep in the bulk and show this property remains present after small perturbations of the temperature difference of the boundary black holes.