On rotating black holes in equilibrium in general relativity

Weinstein, Gilbert

doi:10.1002/cpa.3160430705

Cited by 94 publications

(188 citation statements)

References 9 publications

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“…We mentioned already that the transcription of the system (16)- (17) to the Ernst equation promises no progress in the exclusion of U-minima. In analogy to work by Weinstein [27] one may think of an application of harmonic mappings to these equations. However, direct application of the formalism of [27] does not seem to be successful because results about extrema of the potential X = ρ 2 e −2U , appearing there, say nothing about U-minima.…”

Section: The Question Of Minima Of the Potential U In The Exterior Vamentioning

confidence: 99%

Do rotating dust stars exist in general relativity?

Pfister

2010

Class. Quantum Grav.

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If rotating dust stars would exist in general relativity, they would represent examples of an improbable complete balance between the attractive quasi-Newtonian force (gravitoelectricity) and the repulsive gravitomagnetism. However, nonexistence proofs are available hitherto only for some dust "stars" extending to infinity, and for isolated dust stars of a very restricted class. By analyzing the lines of constant generalized Newtonian potential U in the interior and exterior of a large class of (hypothetical) stationary and axisymmetrically rotating dust stars in general relativity, we find that the existence of such stars can be disproved as soon as minima of the potential U in the exterior vacuum region can be excluded. We present some ideas how this minimum-problem could be attacked, and we summarize the present knowledge about Newtonian and Einsteinian rotating dust systems.

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Section: The Question Of Minima Of the Potential U In The Exterior Vamentioning

confidence: 99%

Do rotating dust stars exist in general relativity?

Pfister

2010

Class. Quantum Grav.

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“…Then, there exist two complex constants l and c such that H = −6/(c − χ) and F 2 = −l(c − χ) 4 . If, in addition, c = 1 and l is real and positive, then (M, g) is locally isometric to the Kerr spacetime.…”

Section: The Killing Form and The Weyl Tensor Are Related Bymentioning

confidence: 99%

Uniqueness properties of the Kerr metric

Mars

2000

Class. Quantum Grav.

129

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We obtain a geometrical condition on vacuum, stationary, asymptotically flat spacetimes which is necessary and sufficient for the spacetime to be locally isometric to Kerr. Namely, we prove a theorem stating that an asymptotically flat, stationary, vacuum spacetime such that the so-called Killing form is an eigenvector of the self-dual Weyl tensor must be locally isometric to Kerr. Asymptotic flatness is a fundamental hypothesis of the theorem, as we demonstrate by writing down the family of metrics obtained when this requirement is dropped. This result indicates why the Kerr metric plays such an important role in general relativity. It may also be of interest in order to extend the uniqueness theorems of black holes to the non-connected and to the non-analytic case.

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“…An alternative approach, in which the main parameters are angular momenta rather than angular velocities, exists [7,8]. To show this let us introduce the Ernst potentials…”

Section: Boundary Conditionsmentioning

confidence: 99%

Equilibrium configuration of black holes and the inverse scattering method

Varzugin

1997

Theor Math Phys

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The inverse scattering method is applied to the investigation of the equilibrium configuration of black holes. A study of the boundary problem corresponding to this configuration shows that any axially symmetric, stationary solution of the Einstein equations with disconnected event horizon must belong to the class of Belinskii-Zakharov solutions. Relationships between the angular momenta and angular velocities of black holes are derived.

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On rotating black holes in equilibrium in general relativity

Cited by 94 publications

References 9 publications

Do rotating dust stars exist in general relativity?

Do rotating dust stars exist in general relativity?

Uniqueness properties of the Kerr metric

Equilibrium configuration of black holes and the inverse scattering method

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