A universal inequality between the angular momentum and horizon area for axisymmetric and stationary black holes with surrounding matter

Hennig, Jörg; Ansorg, Marcus; Cederbaum, Carla

doi:10.1088/0264-9381/25/16/162002

Cited by 49 publications

(99 citation statements)

References 4 publications

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“…In this context, an alternative (but related) bound on the angular momentum can be formulated in terms of a horizon area-angular momentum inequality A ≥ 8π|J|. This inequality was conjectured for the non-vacuum axisymmetric stationary case (actually, including the charged case) with matter surrounding the horizon in [8] and then proved in [9][10][11], whereas its validity in the vacuum axisymmetric dynamical case was conjectured and discussed in [12], partial results were given in [13,14] and a complete proof in [15]. Equality holds in the extremal case.…”

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confidence: 99%

Black hole area–angular-momentum inequality in nonvacuum spacetimes

2011

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Black hole area–angular-momentum inequality in nonvacuum spacetimes

2011

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“…These studies considered axisymmetric and stationary BHs surrounded by matter [1,2]. In some cases, Maxwell fields were also included [3].…”

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Superextremal spinning black holes via accretion

2011

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A Kerr black hole with mass M and angular momentum J satisfies the extremality inequality |J| ≤ M 2 . In the presence of matter and/or gravitational radiation, this bound needs to be reformulated in terms of local measurements of the mass and the angular momentum directly associated with the black hole. The isolated and dynamical horizon framework provides such quasi-local characterization of black hole mass and angular momentum. With this framework, it is possible in axisymmetry to reformulate the extremality limit as |J| ≤ 2 M 2 H , with MH the irreducible mass of the black hole computed from its apparent horizon area and J obtained using a rotational Killing vector field on the apparent horizon. The |J| ≤ 2 M 2 H condition is also equivalent to requiring a non-negative black hole surface gravity. We present numerical experiments of an accreting black hole that temporarily violates this extremality inequality. The initial configuration consists of a single, rotating black hole surrounded by a thick, shell cloud of negative energy density. For these numerical experiments, we introduce a new matter-without-matter evolution method.

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“…J(H t ) = J. Moreover, at every time slice {t} the universal inequality 8π J ≤ A(H t ) holds [16], [8], [14] and we also expect the validity of the Penrose inequality A(H t ) ≤ 8πM 2 , where M is the ADM-mass which is also conserved. Thus, in this scenario we have J(H t ) = J, 8π J ≤ A(H t ) and we expect to have A(H t ) ≤ 8πM 2 .…”

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confidence: 78%

“…Secondly, we found that rotation stabilizes the shape of stable horizons to such an extent that rotating holes of a given area and angular momentum have their entire shapes controlled (and not just their global measures like R or L). This is manifest from the pointwise bounds (14) σ…”

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confidence: 99%

Shape of rotating black holes

Clement

Reiris

2013

Phys. Rev. D

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We give a thorough description of the shape of rotating axisymmetric stable black-hole (apparent) horizons applicable in dynamical or stationary regimes. It is found that rotation manifests in the widening of their central regions (rotational thickening), limits their global shapes to the extent that stable holes of a given area A and angular momentum J ≠ 0 form a precompact family (rotational stabilization) and enforces their whole geometry to be close to the extreme-Kerr horizon geometry at almost maximal rotational speed (enforced shaping). The results, which are based on the stability inequality, depend only on A and J. In particular they are entirely independent of the surrounding geometry of the space-time and of the presence of matter satisfying the strong energy condition. A complete set of relations between A, J, the length L of the meridians and the length R of the greatest axisymmetric circle, is given. We also provide concrete estimations for the distance between the geometry of horizons and that of the extreme Kerr, in terms only of A and J. Besides its own interest, the work has applications to the Hoop conjecture as formulated by Gibbons in terms of the Birkhoff invariant, to the Bekenstein-Hod entropy bounds and to the study of the compactness of classes of stationary black-hole space-times.

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A universal inequality between the angular momentum and horizon area for axisymmetric and stationary black holes with surrounding matter

Cited by 49 publications

References 4 publications

Black hole area–angular-momentum inequality in nonvacuum spacetimes

Black hole area–angular-momentum inequality in nonvacuum spacetimes

Superextremal spinning black holes via accretion

Shape of rotating black holes

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