Membrane Paradigm and Holographic DC Conductivity for Nonlinear Electrodynamics
Abstract
Membrane paradigm is a powerful tool to study properties of black hole horizons. We first explore the properties of the nonlinear electromagnetic membrane of black holes. For a general nonlinear electrodynamics field, we show that the conductivities of the horizon usually have off-diagonal components and depend on the normal electric and magnetic fields on the horizon. Via the holographic duality, we find a model-independent expression for the holographic DC conductivities of the conserved current dual to a probe nonlinear electrodynamics field in a neutral and static black brane background. It shows that these DC conductivities only depend on the geometric and electromagnetic quantities evaluated at the horizon. We can also express the DC conductivities in terms of the temperature, charge density and magnetic field in the boundary theory, as well as the values of the couplings in the nonlinear electrodynamics at the horizon.
Keywords
Cite
@article{arxiv.1711.03298,
title = {Membrane Paradigm and Holographic DC Conductivity for Nonlinear Electrodynamics},
author = {Xiaobo Guo and Peng Wang and Haitang Yang},
journal= {arXiv preprint arXiv:1711.03298},
year = {2018}
}
Comments
added references, a new figure, and some context, correct a sign error, and rewrote some parts