The University of Southampton
University of Southampton Institutional Repository

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

Blandford--Znajek monopole expansion revisited: novel non-analytic contributions to the power emission
Blandford--Znajek monopole expansion revisited: novel non-analytic contributions to the power emission
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.
GR black holes, Magnetohydrodynamics, astrophysical black holes
1475-7516
Camilloni, Filippo
05dab656-2dc6-4885-b54e-731643dd3bc2
Dias, Oscar J. C.
f01a8d9b-9597-4c32-9226-53a6e5500a54
Grignani, Gianluca
2f781e76-406a-4d33-8b88-e04d214d8477
Harmark, Troels
623989f5-4fc3-49f3-94f0-87b413b0d9d8
Oliveri, Roberto
c1e470ae-28e0-4b9e-90f0-0ac25e162e75
Orselli, Marta
26ddbcf2-3629-4598-8b20-562053ae6042
Placidi, Andrea
ee26a883-d76d-4fed-8c20-15802c6cf000
Santos, Jorge E.
88cca86d-9e1e-40a7-acba-f7986bd7f84b
Camilloni, Filippo
05dab656-2dc6-4885-b54e-731643dd3bc2
Dias, Oscar J. C.
f01a8d9b-9597-4c32-9226-53a6e5500a54
Grignani, Gianluca
2f781e76-406a-4d33-8b88-e04d214d8477
Harmark, Troels
623989f5-4fc3-49f3-94f0-87b413b0d9d8
Oliveri, Roberto
c1e470ae-28e0-4b9e-90f0-0ac25e162e75
Orselli, Marta
26ddbcf2-3629-4598-8b20-562053ae6042
Placidi, Andrea
ee26a883-d76d-4fed-8c20-15802c6cf000
Santos, Jorge E.
88cca86d-9e1e-40a7-acba-f7986bd7f84b

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]. (doi:10.1088/1475-7516/2022/07/032).

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.
Request a copy

More information

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 iD orcid.org/0000-0003-4855-4750

Catalogue record

Date deposited: 18 Aug 2022 17:12
Last modified: 19 Aug 2022 01:44

Export record

Altmetrics

Contributors

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

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×