Uniqueness of the Kerr Black Hole

Robinson, David

doi:10.1103/physrevlett.34.905

Cited by 876 publications

(710 citation statements)

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“…In four dimensions, the Carter-Robinson uniqueness theorem [3,5] on the Kerr rotating black hole rests on using the Papapetrou form (1.1) of the metric. We expect therefore similar arguments to be applicable in higher dimensions, although they of course cannot prove any kind of strict uniqueness for five-dimensional rotating black holes due to the existence of rotating black rings.…”

Section: Discussionmentioning

confidence: 99%

“…We have therefore proven that for any given function z 1 (y 1 , y 2 ) with ( ∂z 1 ∂y 1 , ∂z 1 ∂y 2 ) = (0, 0) we can find a function z 2 (y 1 , y 2 ) such that 5) and so that (z 1 , z 2 ) is a coordinate system on the two-dimensional manifold.…”

Section: Diagonalizing a Two-dimensional Metricmentioning

confidence: 99%

“…5 Therefore, if we define ∇ to be the gradiant 5 It is important to remark that γ is not an actual physical variable for the solution (2.10), but rather an auxilirary coordinate that is useful for understanding the structure of Eqs. (2.12).…”

Section: Compact Notation For the Equations For G Ij (R Z)mentioning

confidence: 99%

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Stationary and axisymmetric solutions of higher-dimensional general relativity

Harmark¹

2004

Phys. Rev. D

226

473

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We study stationary and axisymmetric solutions of General Relativity, i.e. pure gravity, in four or higher dimensions. D-dimensional stationary and axisymmetric solutions are defined as having D − 2 commuting Killing vector fields. We derive a canonical form of the metric for such solutions that effectively reduces the Einstein equations to a differential equation on an axisymmetric D − 2 by D − 2 matrix field living in three-dimensional flat space (apart from a subclass of solutions that instead reduce to a set of equations on a D−2 by D−2 matrix field living in two-dimensional flat space). This generalizes the Papapetrou form of the metric for stationary and axisymmetric solutions in four dimensions, and furthermore generalizes the work on Weyl solutions in four and higher dimensions. We analyze then the sources for the solutions, which are in the form of thin rods along a line in the three-dimensional flat space that the matrix field can be seen to live in. As examples of stationary and axisymmetric solutions, we study the five-dimensional rotating black hole and the rotating black ring, write the metrics in the canonical form and analyze the structure of the rods for each solution.

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Section: Discussionmentioning

confidence: 99%

Section: Diagonalizing a Two-dimensional Metricmentioning

confidence: 99%

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Stationary and axisymmetric solutions of higher-dimensional general relativity

Harmark¹

2004

Phys. Rev. D

226

473

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“…Thus, only asymptotically the Kerr geometry is relevant for a rotating body. On the other hand when a rotating mass collapses to a 'black hole,' with |a| < M , Robinson [88] showed that the unique stationary solution to the vacuum field equations is the family of Kerr solutions. We will review the powerful Black Hole Uniqueness Theorems in the next section.…”

Section: What Is the Source Of The Kerr Field?mentioning

confidence: 99%

“…Moreover, he showed that the Kerr metric is the only one admitting zero angular momentum. Robinson [88] gave the definitive proof that the Kerr metric, with |a| < M , is the unique stationary black hole solution to the Einstein vacuum field equations.…”

Section: Black Holes Uniqueness Theoremsmentioning

confidence: 99%

Slowly rotating supercompact Schwarzschild stars

Posada¹

2017

Monthly Notices of the Royal Astronomical Society

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AcknowledgmentsI am grateful to the universe, for its harmony. The project is the study of integral and surface properties of slowly rotating homogeneous masses in the gravastar limit R → R s , where R s is the Schwarzschild radius. For this purpose we followed the perturbative method proposed by Hartle in 1967. In this model, the relativistic equations of structure for a slowly rotating star were derived at second order in the angular velocity Ω. An interesting, and educational, application of this model was investigated by Chandrasekhar and Miller. I am indebted to the Department of Physics andIn their approach, they solved numerically the structure equations of a homogeneous star (constant energy density) up to the Buchdahl bound (9/8)R s . Based on this work, our objective was to investigate the interesting region below the Buchdahl bound R s < R < (9/8)R s , which has not been studied previously in the literature.Our results were astonishing. We found that the surface properties and quadrupole mass moment approach the values corresponding to those of the Kerr metric when expanded at second order in angular momentum. This remarkable result provides a long sought solution to the problem of the source of rotation in the Kerr spacetime.iv

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Astrophysical Black Holes: A Compact Pedagogical Review

Bambi

2018

Annalen der Physik

104

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Black holes are among the most extreme objects that can be found in the Universe and an ideal laboratory for testing fundamental physics. Here, the basic properties of black holes as expected from general relativity, the main astronomical observations, and the leading astrophysical techniques to probe the strong gravity region of these objects are reviewed. The main intention is to provide a compact introductory overview on astrophysical black holes to new students entering this research field, as well as to senior researchers working in general relativity and alternative theories of gravity, who wish to quickly learn the state of the art of astronomical observations of black holes.

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Uniqueness of the Kerr Black Hole

Abstract: The family of Kerr solutions, with \al

Cited by 876 publications

References 5 publications

Stationary and axisymmetric solutions of higher-dimensional general relativity

Stationary and axisymmetric solutions of higher-dimensional general relativity

Slowly rotating supercompact Schwarzschild stars

Astrophysical Black Holes: A Compact Pedagogical Review

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