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.
Highlights
Black holes are among the most intriguing concepts of general relativity
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
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
Summary
Black holes are among the most intriguing concepts of general relativity. The event horizon of a black hole is a puzzling and fascinating object, in that natural descriptions of physics often have trouble accommodating the horizon. The authors of [12] studied the electromagnetic membrane properties of the horizon and considered a charged particle dropping onto the horizon in the framework of Maxwell-Chern-Simons theory. The aim of the paper is to study the NLED electromagnetic membrane properties and find a modelindependent expression for the holographic DC conductivities of the dual conserved current in the boundary theory. V, the DC conductivities of the dual conserved current are calculated in the framework of gauge/gravity duality We show that these DC conductivities usually depend on both the geometry and values of the couplings in NLED at the black hole horizon as well as the probe charge density and magnetic field in the boundary theory. We use the convention that the Minkowski metric has the signature of the metric ð− þ þþÞ in this paper
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