Blandford--Znajek monopole expansion revisited: novel non-analytic contributions to the power emission

TL;DR

This paper extends the perturbative analysis of the Blandford-Znajek monopole solution to higher orders, revealing non-analytic contributions to energy extraction and improving agreement with simulations.

Contribution

It introduces higher-order perturbative expansions with novel logarithmic terms and a new numerical method for better accuracy across the light surface.

Findings

Extended the split-monopole solution to sixth order in spin.

Computed perturbative contributions to energy extraction at seventh and eighth order.

Developed a faster, more accurate numerical procedure for solving FFE equations.

Abstract

The Blandford and Znajek (BZ) split-monopole serves as an important theoretical example of the mechanism that can drive the electromagnetic extraction of energy from Kerr black holes. It is constructed as a perturbative low spin solution of Force Free Electrodynamics (FFE). Recently, Armas $et~al.$ put this construction on a firmer footing by clearing up issues with apparent divergent asymptotics. This was accomplished by resolving the behavior around the outer light surface, a critical surface of the FFE equations. Building on this, we revisit the BZ perturbative expansion, and extend the perturbative approach to higher orders in the spin parameter of the Kerr black hole. We employ matched-asymptotic-expansions and semi-analytic techniques to extend the split-monopole solution to the sixth-order in perturbation theory. The expansion necessarily includes novel logarithmic contributions in the spin parameter. We show that these higher order terms result in non-analytic contributions to the power and angular momentum output. In particular, we compute for the first time the perturbative contributions to the energy extraction at seventh- and eighth-order in the spin parameter. The resulting formula for the energy extraction improves the agreement with numerical simulations at finite spin. Moreover, we present a novel numerical procedure for resolving the FFE equations across the outer light surface, resulting in significantly faster convergence and greater accuracy, and extend this to higher orders as well. Finally, we include a general discussion of light surfaces as critical surfaces of the FFE equations.