Black hole magnetospheres in the Born-Infeld theory

TL;DR

This paper investigates the effects of Born-Infeld nonlinear electrodynamics on black hole magnetospheres, deriving modified conditions and solutions, and analyzing how quantum effects influence energy extraction processes.

Contribution

It introduces a perturbative solution for black hole magnetospheres in Born-Infeld theory, revealing dependence on the BI parameter and black hole size, and explores quantum effects on energy extraction.

Findings

Horizon resistivity in BI theory varies and is not constant.

Derived a modified Znajek regularity condition for BI theory.

Quantum effects reduce the energy extraction rate, maximizing in Maxwell theory.

Abstract

We study the force-free electrodynamics on rotating black holes in the Born-Infeld (BI) effective theory. The stream equation describing a steady and axisymmetric magnetosphere is derived. From its near-horizon behavior, we obtain the modified Znajek regularity condition, with which we find that the horizon resistivity in the BI theory is generally not a constant. As expected, the outer boundary condition far away from the hole remains unchanged. In terms of the conditions at both boundaries, we derive the perturbative solution of split monopole in the slow rotation limit. It is interesting to realise that the correction to the solution relies not only on the parameter in the BI theory, but also on the radius (or the mass) of the hole. We also show that the quantum effects can undermine the energy extraction process of the magnetosphere in the non-linear theory and the extraction rate gets the maximum in the Maxwell theory.