On the existence of the Blandford-Znajek monopole for a slowly rotating Kerr black hole

TL;DR

This paper critically examines the proposed Blandford-Znajek monopole solution around slowly rotating Kerr black holes, finding that it is inconsistent with physical boundary conditions and questioning its existence.

Contribution

It provides a detailed perturbative analysis showing the Blandford-Znajek monopole cannot satisfy realistic boundary conditions, challenging prior assumptions about energy extraction from black holes.

Findings

The Blandford-Znajek monopole is not consistent with physical boundary conditions.

The analysis uses matched asymptotic expansions for the perturbative regime.

The existence of the monopole in the slow rotation limit is questioned.

Abstract

The Blandford-Znajek monopole is a conjectured solution of force-free electrodynamics in the vicinity of a slowly rotating Kerr black hole, supposedly defined as a perturbation in small angular momentum. It is used to argue for the extraction of energy from rotating black holes by the Blandford-Znajek process. We set up a careful analysis of the perturbative definition of the Blandford-Znajek monopole, showing in particular that the regime in which it is defined allows to use the technique of matched asymptotic expansions. Our conclusion is that the Blandford-Znajek monopole, as it is defined, is not consistent with demanding physically reasonable boundary conditions far away from the event horizon. This puts into question the existence of the Blandford-Znajek monopole, at least in the limit of slow rotation of the Kerr black hole.