We study a three-dimensional holographic conformal field theory 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 setup, which are solutions to the Einstein-Maxwell equations with a negative cosmological constant in four dimensions, we calculate, to a fully nonlinear level, the conductivity of the conformal field theory in this background. Interestingly, we find that the conductivity depends nontrivially on the potential difference. The bulk solutions are flowing geometries containing black hole horizons which are non-Killing and have nonzero 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.

中文翻译：

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全息电池

我们研究了包含两个黑洞视界的时空中背景电场影响下的三维全息共形场论。电背景是固定的，使得两个边界黑洞之间存在电势差，从而感应出守恒电流。通过构造该设置的全息对偶，这是在四个维度上具有负宇宙学常数的爱因斯坦-麦克斯韦方程的解，我们在完全非线性的水平上计算了在此背景下共形场论的电导率。有趣的是，我们发现电导率很大程度上取决于电位差。体解是包含黑洞视界的流动几何形状，其非杀伤性且具有非零膨胀。我们发现了一个新奇的特性，即未来视界的过去边界位于主体深处，并表明在边界黑洞的温差发生小扰动后，该特性仍然存在。