Perturbative Analysis of a Stationary Magnetosphere in an Extreme Black Hole Spacetime : On the Meissner-like Effect of an Extreme Black Hole

TL;DR

This paper investigates how electric currents influence the Meissner-like effect in extreme black hole magnetospheres, revealing that currents can introduce higher multipole magnetic flux components at the horizon.

Contribution

It provides a perturbative analysis of force-free electromagnetic fields around extreme black holes, showing currents can alter the magnetic flux structure at the horizon.

Findings

Electric currents can superpose higher multipole components on the monopole flux.

The perturbative solution is constructed under the assumption of slow rotation.

Higher multipole flux components can penetrate the event horizon in the presence of currents.

Abstract

It is known that the Meissner-like effect is seen in a magnetosphere without an electric current in black hole spacetime: no non-monopole component of magnetic flux penetrates the event horizon if the black hole is extreme. In this paper, in order to see how an electric current affects the Meissner-like effect, we study a force-free electromagnetic system in a static and spherically symmetric extreme black hole spacetime. By assuming that the rotational angular velocity of the magnetic field is very small, we construct a perturbative solution for the Grad-Shafranov equation, which is the basic equation to determine a stationary, axisymmetric electromagnetic field with a force-free electric current. Our perturbation analysis reveals that, if an electric current exists, higher multipole components may be superposed upon the monopole component on the event horizon, even if the black hole is extreme.