Membrane Paradigm and Holographic DC Conductivity for Nonlinear Electrodynamics

TL;DR

This paper investigates the properties of nonlinear electromagnetic fields at black hole horizons using the membrane paradigm and derives holographic DC conductivities that depend on horizon data, applicable to boundary theories.

Contribution

It provides a model-independent formula for holographic DC conductivities in nonlinear electrodynamics, linking horizon properties to boundary theory parameters.

Findings

Horizon conductivities have off-diagonal components influenced by electric and magnetic fields.

DC conductivities depend only on horizon quantities like temperature, charge density, and couplings.

The results are model-independent and applicable to a broad class of nonlinear electrodynamics theories.

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.