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

Camilloni, Filippo, Dias, Oscar J. C., Grignani, Gianluca, Harmark, Troels, Oliveri, Roberto, Orselli, Marta, Placidi, Andrea and Santos, Jorge E. (2022) Blandford--Znajek monopole expansion revisited: novel non-analytic contributions to the power emission. JCAP, 2022 (7), [032].

Record type: Article

## 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.

Text
2201.11068v2 - Accepted Manuscript
Restricted to Repository staff only until 19 July 2023.
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Accepted/In Press date: 28 May 2022
e-pub ahead of print date: 19 July 2022
Additional Information: v1: 30 pages + 5 Appendices, 5 figures; v2: matches published version in JCAP
Keywords: GR black holes, Magnetohydrodynamics, astrophysical black holes

## Identifiers

Local EPrints ID: 468622
URI: http://eprints.soton.ac.uk/id/eprint/468622
ISSN: 1475-7516
PURE UUID: 4f6ab13b-31b7-4fdf-ae49-0784bb8a56a8
ORCID for Oscar J. C. Dias: orcid.org/0000-0003-4855-4750

## Catalogue record

Date deposited: 18 Aug 2022 17:12

## Contributors

Author: Filippo Camilloni
Author: Gianluca Grignani
Author: Troels Harmark
Author: Roberto Oliveri
Author: Marta Orselli
Author: Andrea Placidi
Author: Jorge E. Santos