Exact solutions for extreme black hole magnetospheres

Lupsasca, Alexandru; Rodríguez, María Jesús Aira

doi:10.1007/jhep07(2015)090

Cited by 34 publications

(65 citation statements)

References 24 publications

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“…Examining this limit using the approach of this paper could provide important feedback when comparing the analytical results with numerical simulations. The Stream equation for the near horizon geometry of ex-tremal Kerr magnetosphere, the so-called NHEK geometry, has received considerable attention in the literature [26][27][28][29] and it would be interesting to study the solutions found in the NHEK geometry using our small θ expansion. In fact, FFE exact solutions in the NHEK limit can be very important as starting points for a perturbative expansion around extremality in the same spirit as FFE exact solutions in a Schwarzschild background, such as the split-monopole, have been used as starting point for an expansion in small α, i.e.…”

Section: Discussionmentioning

confidence: 99%

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Force-free electrodynamics near rotation axis of a Kerr black hole

Grignani

Harmark²,

Orselli

2020

Class. Quantum Grav.

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Despite their potential importance for understanding astrophysical jets, physically realistic exact solutions for magnetospheres around Kerr black holes have not been found, even in the force-free approximation. Instead approximate analytical solutions such as the Blandford-Znajek (split-)monopole, as well as numerical solutions, have been constructed. In this paper we consider a new approach to the analysis and construction of such magnetospheres. We consider force-free electrodynamics close to the rotation axis of a magnetosphere surrounding a Kerr black hole assuming axisymmetry. This is the region where the force-free approximation should work the best, and where the jets are located. We perform a systematic study of the asymptotic region with (split-)monopole, paraboloidal and vertical asymptotic behaviors. Imposing asymptotics similar to a (split-)monopole, we find that demanding regularity at the rotation axis and the event horizon restricts solutions of the stream equation so much that it is not possible for a solution to be continuously connected to the static (split-)monopole around the Schwarzschild black hole in the limit where the rotation goes to zero. This provides independent evidence to the issues discovered with the asymptotics of the Blandford-Znajek (split-)monopole in Ref.[1] from which it follows that its perturbative construction is inconsistent.

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Section: Discussionmentioning

confidence: 99%

“…To obey (27) we should thus ensure that c n,j = 0 for j = −2n, ..., −1 and that c n,0 is finite for r → ∞. The sufficient conditions for monopole-type asymptotics (19) are therefore c n,−2 = 0 , c n,−1 = 0 , d dr c n,0 = 0 for n ≥ 1 .…”

Section: A Angular Expansionmentioning

confidence: 99%

Force-free electrodynamics near rotation axis of a Kerr black hole

Grignani

Harmark²,

Orselli

2020

Class. Quantum Grav.

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“…2014; Zhang et al. 2014; Lupsasca and Rodriguez 2015; Compère and Oliveri 2016; Gralla et al. 2016b).…”

Section: Scattering From Near-extremal Black Holesmentioning

confidence: 99%

The Kerr/CFT correspondence and its extensions

Compère

2017

Living Rev Relativ

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We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory. Firstly, we review properties of extremal black holes with in particular the construction of an asymptotic Virasoro symmetry in the near-horizon limit. The entropy of extremal spinning or charged black holes is shown to match with a chiral half of Cardy’s formula. Secondly, we show how a thermal 2-dimensional conformal field theory (CFT) is relevant to reproduce the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review the hidden conformal symmetries of asymptotically-flat black holes away from extremality and present how the non-extremal entropy can be matched with Cardy’s formula. We follow an effective field theory approach and consider the Kerr–Newman black hole and its generalizations in various supergravity theories. The interpretation of these results by deformed dual conformal field theories is discussed and contrasted with properties of standard 2-dimensional CFTs. We conclude with a list of open problems.

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“…for the electromagnetic fields (11) and (12) as they are approached. The condition can be obtained directly from the stream equation (15).…”

Section: The Stream Equationmentioning

confidence: 99%

“…On the other hand, in past years, exact solutions on extremely fast rotating black holes were obtained by focusing on the near-horizon region [10,11,12,13,14]. But, a smooth connection between these near-and far-region solutions is lacking.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

2017

Phys. Rev. D

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In this work, expanded solutions of force-free magnetospheres on general Kerr black holes are derived through a radial distance expansion method. From the regular conditions both at the horizon and at spatial infinity, two previously known asymptotical solutions (one of them is actually an exact solution) are identified as the only solutions that satisfy the same conditions at the two boundaries. Taking them as initial conditions at the boundaries, expanded solutions up to the first few orders are derived by solving the stream equation order by order. It is shown that our extension of the exact solution can (partially) cure the problems of the solution: it leads to magnetic domination and a mostly timelike current for restricted parameters.

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Exact solutions for extreme black hole magnetospheres

Cited by 34 publications

References 24 publications

Force-free electrodynamics near rotation axis of a Kerr black hole

Force-free electrodynamics near rotation axis of a Kerr black hole

The Kerr/CFT correspondence and its extensions

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

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