Consistent Blandford-Znajek expansion

Armas, Jay; Cai, Yangyang; Compère, Geoffrey; Garfinkle, David; Gralla, Samuel E.

doi:10.1088/1475-7516/2020/04/009

Cited by 18 publications

(83 citation statements)

References 26 publications

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“…The numerical procedure amounts to solve a system of second order ordinary differential equations with a spectral collocation scheme. Contrary to [20], no minimization procedure is required. The same technique is subsequently employed to solve numerically for ψ at order α 4 and α 4 log |α| in the r-region.…”

Section: Introduction and Summary Of The Resultsmentioning

confidence: 99%

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

Camilloni¹,

Dias²,

Grignani³

et al. 2022

Preprint

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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 matchedasymptotic-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.

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Section: Introduction and Summary Of The Resultsmentioning

confidence: 99%

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

Camilloni¹,

Dias²,

Grignani³

et al. 2022

Preprint

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show abstract

“…Thus, one can possibly have a different solution patch on the other side of the light surface, with matching boundary conditions that do not generate a singular behavior of Ω on the axis. To analyze this further, one needs to use a matched asymptotic expansion technique [29].…”

Section: Discussionmentioning

confidence: 99%

Force-free magnetosphere attractors for near-horizon extreme and near-extreme limits of Kerr black hole

Camilloni,

Grignani,

Harmark

et al. 2020

Preprint

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We propose a new approach to find magnetically-dominated force-free magnetospheres around highly spinning black holes, relevant for models of astrophysical jets. Employing the near-horizon extreme Kerr (NHEK) limit of the Kerr black hole, any stationary, axisymmetric and regular forcefree magnetosphere reduces to the same attractor solution in the NHEK limit with null electromagnetic field strength. We use this attractor solution as the universal starting point for perturbing away from the NHEK region in the extreme Kerr spacetime. We demonstrate that by going to second order in perturbation theory, it is possible to find magnetically dominated magnetospheres around the extreme Kerr black hole. Furthermore, we consider the near-horizon near-extreme Kerr (near-NHEK) limit that provides access to a different regime of highly spinning black holes. Also in this case we find a novel force-free attractor, which can be used as the universal starting point for a perturbative construction of force-free magnetospheres. Finally, we discuss the relation between the NHEK and near-NHEK attractors.

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“…( 12) has a unique solution in a starlike neighborhood, up to a constant factor if and only if d 2 ln u = 0, and this further implies eq. (11).…”

Section: The Geometry Of the Non-null Force-free Fieldmentioning

confidence: 99%

“…A theoretical understanding of FFE was also pioneered by Uchida ([7], [8]) and Komissarov ([3]), just to name a few. Near horizon and extreme Kerr magnetospheres have been studied systematically by [9], [10], [11], [12] and [13].…”

Section: Introductionmentioning

confidence: 99%

The null and force-free electromagnetic field

Menon¹

2020

Class. Quantum Grav.

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In this paper, we present a covariant formalism that connects solutions to force-free electrodynamics in the non-null case and foliations of spacetime. In doing so, we are also able to derive an expression of the general non-null current density vector. Just as in the null case, solutions in the non-null case can give rise to a dual solution, however, as is shown below, this can happen only when the solution describes a vacuum field. All theorems are illustrated with previously known solutions.

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Consistent Blandford-Znajek expansion

Cited by 18 publications

References 26 publications

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

Force-free magnetosphere attractors for near-horizon extreme and near-extreme limits of Kerr black hole

The null and force-free electromagnetic field

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