Expanded solutions of force-free electrodynamics on general Kerr black holes

Li, Huiquan; Wang, Jiancheng

doi:10.1103/physrevd.96.023014

Cited by 5 publications

(7 citation statements)

References 22 publications

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“…Force-free solutions are notoriously hard to come by, and we reserve the attempt at a force-free set-up for another work (see e.g. [46,47] for formal aspects of forcefree electrodynamics, and [48][49][50][51][52][53][54][55] for studies of force-free fields in BH spacetimes). However, the reader might be concerned, as we were, that force-free solutions somehow ensure an uncharged BH.…”

Section: Charged Force-free Solutionsmentioning

confidence: 99%

Black hole pulsar

2018

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In anticipation of a LIGO detection of a black hole/neutron star merger, we expand on the intriguing possibility of an electromagnetic counterpart. Black hole/Neutron star mergers could be disappointingly dark since most black holes will be large enough to swallow a neutron star whole, without tidal disruption and without the subsequent fireworks. Encouragingly, we previously found a promising source of luminosity since the black hole and the highly-magnetized neutron star establish an electronic circuit -a black hole battery. In this paper, arguing against common lore, we consider the electric charge of the black hole as an overlooked source of electromagnetic radiation. Relying on the well known Wald mechanism by which a spinning black hole immersed in an external magnetic field acquires a stable net charge, we show that a strongly-magnetized neutron star in such a binary system will give rise to a large enough charge in the black hole to allow for potentially observable effects. Although the maximum charge is stable, we show there is a continuous flux of charges contributing to the luminosity. Most interestingly, the spinning charged black hole then creates its own magnetic dipole to power a black hole pulsar. arXiv:1808.07887v3 [astro-ph.HE]

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Section: Charged Force-free Solutionsmentioning

confidence: 99%

Black hole pulsar

2018

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“…Finding a solution of the FFE equations corresponds to finding ψ, Ω and I that solves the integrability conditions (6) and (8) as well as the Stream equation (9). At the event horizon r = r + of the Kerr black hole we demand regularity of ψ and B φ .…”

Section: Force Free Electrodynamics Around Kerr Black Holementioning

confidence: 99%

“…One can now expand the Stream equation (9) in terms of the expansions (11). More specifically, we expand the field ψ in even powers of α and the fields Ω, I and B φ in odd powers in α and put this into the Stream equation (9) along with the metric (2), and subsequently expand the Stream equation in powers of α. Schematically, this gives the equations [1,5,6,12]…”

Section: Blandford-znajek Monopole From Perturbative Expansion In αmentioning

confidence: 99%

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

Grignani

Harmark²,

Orselli

2018

Phys. Rev. D

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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.

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“…As done in the Maxwell theory in the previous work [8], the conditions of the differential equation (26) at the event horizon and spatial infinity can be determined. In what follows, we examine the conditions in the BI theory.…”

Section: Boundary Behaviorsmentioning

confidence: 99%

“…It is seen that the two boundaries of any field line in the black hole magnetosphere are in two different regimes: one is in the Maxwell theory and the other is in the BI theory. As in [8], we first consider the case that the functions at the horizon and at infinity are matched to be identical:…”

Section: Matching the Boundary Conditionsmentioning

confidence: 99%

Black hole magnetospheres in the Born–Infeld theory

Wang

2020

Int. J. Mod. Phys. D

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We study the force-free electrodynamics on rotating black holes in the Born-Infeld (BI) effective theory. The stream equation describing a steady and axisymmetric magnetosphere is derived. From its near-horizon behavior, we obtain the modified Znajek regularity condition, with which we find that the horizon resistivity in the BI theory is generally not a constant. As expected, the outer boundary condition far away from the hole remains unchanged. In terms of the conditions at both boundaries, we derive the perturbative solution of split monopole in the slow rotation limit. It is interesting to realise that the correction to the solution relies not only on the parameter in the BI theory, but also on the radius (or the mass) of the hole. We also show that the quantum effects can undermine the energy extraction process of the magnetosphere in the non-linear theory and the extraction rate gets the maximum in the Maxwell theory.The force-free magnetosphere can be used to extract the rotational energy of a rotating black hole. As a kind of Penrose process, the energy is extracted through the rotation of the magnetosphere dragged by the black hole spacetime. This process has become a promising mechanism nowadays that can explain the formation of powerful jets observed in many high energy objects, like AGN, GRB and microquasars.It is known that the magnetic fields on neutron stars are very high, even exceeding the quantum electrodynamics (QED) critical value. In this case, the QED corrections should be included in the force-free magnetospheres and the Maxwell electrodynamics should be replaced by the non-linear theory. This has been discussed in magnetar magnetospheres (e.g., [2,3,4]), whose surface magnetic fields sometimes can be above 10 15 G.However, this is not the case for black hole magnetospheres. The astronomical black holes do not have their own magnetic fields. The magnetic fields on them come from accretion and are usually far weaker (e.g., 10 4 G for a black hole with mass M = 10 9 M ⊙ [5]) than the QED critical value. But, the study of the black hole magnetosphere in non-linear electrodynamics is useful for that of the QED corrected magnetosphere near a magnetar where gravity is important. The latter can be obtained in a weak field limit of the former despite a difference of the inner boundary condition.The study of black hole magnetospheres in non-linear electrodynamics is also of theoretical interest. The force-free magnetospheres on black holes are not well understood even in the Maxwell theory. We still do not know well the structure and geometry of the field lines in the force-free magnetosphere. The extension to the non-linear theory help find the analytical properties of black hole magnetospheres in a general sense.Moreover, non-linear electrodynamics include quantum corrections to the Maxwell theory. As is known, strong quantum effects also happen in black holes. Thermal particles are excited and radiated in the near-horizon regions of black holes. It is interesting to examine the force-free non-lin...

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Expanded solutions of force-free electrodynamics on general Kerr black holes

Cited by 5 publications

References 22 publications

Black hole pulsar

Black hole pulsar

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

Black hole magnetospheres in the Born–Infeld theory

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