A New Look at the Plebański–demiański Family of Solutions

Griffiths, J. B.; Podolský, Jiř̌í

doi:10.1142/s0218271806007742

Cited by 247 publications

(327 citation statements)

References 44 publications

(110 reference statements)

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“…(A.16). M stands for mass, and parameters a and N are connected with rotation and NUT parameter [97]. Let us remark here that the canonical metric (A.13) is the most general metric element admitting the (non-degenerate) PCKY tensor [65], [221].…”

Section: A12 'Derivation' Of the 4d Kerr-nut-(a)ds Metricmentioning

confidence: 99%

“…also [60]). Recently, Griffiths and Podolský [95], [97], [96], [201], [98], put this metric into a new form which enables a better physical interpretation of parameters and simplifies a procedure how to derive all special cases. Among subclasses of this solution let us mention the sixparameter family of metrics without acceleration derived and studied already by Carter [28], [27] and later by Plebański [199].…”

Section: A21 Plebański-demiański Metricmentioning

confidence: 99%

“…Following [97] one can easily perform the transformations of coordinates and parameters to obtain the complete family of type D spacetimes and the corresponding particular forms of CKY tensors. In the next two sections we consider two special cases.…”

Section: A21 Plebański-demiański Metricmentioning

confidence: 99%

“…Following [97], let us introduce two new continuous parameters α (the acceleration) and ω (the 'twist') by the rescaling 55) and relabel the other parameters as…”

Section: A22 Generalized Black Holesmentioning

confidence: 99%

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Hidden Symmetries of Higher-Dimensional Rotating Black Holes

2007

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In this thesis we study higher-dimensional rotating black holes. Such black holes are widely discussed in string theory and brane-world models at present.We demonstrate that even the most general known Kerr-NUT-(A)dS spacetime, describing the general rotating higher-dimensional asymptotically (anti) de Sitter black hole with NUT parameters, is in many aspects similar to its fourdimensional counterpart. Namely, we show that it admits a fundamental hidden symmetry associated with the principal conformal Killing-Yano tensor. Such a tensor generates towers of hidden and explicit symmetries. The tower of Killing tensors is responsible for the existence of irreducible, quadratic in momenta, conserved integrals of geodesic motion. These integrals, together with the integrals corresponding to the tower of explicit symmetries, make geodesic equations in the Kerr-NUT-(A)dS spacetime completely integrable. We further demonstrate that in this spacetime the Hamilton-Jacobi, Klein-Gordon, and stationary string equations allow complete separation of variables and the problem of finding parallel-propagated frames reduces to the set of the first order ordinary differential equations. Moreover, we show that the Kerr-NUT-(A)dS spacetime is the most general Einstein space which possesses all these properties. We also explicitly derive the most general (off-shell) canonical metric admitting the principal conformal Killing-Yano tensor and demonstrate that such a metric is necessarily of the special algebraic type D of the higher-dimensional algebraic classification. The results presented in this thesis describe the new and complete picture of the relationship of hidden symmetries and rotating black holes in higher dimensions. PrefaceWhen in 1963 Kerr discovered an astrophysically relevant but relatively complicated metric describing the gravitational field of a rotating black hole, it seemed that no analytical predictions were possible even for the simplest particle geodesic motion. However, a 'miracle' happened, and it turned out that not only the geodesic motion can be analytically solved, but also the equations describing various perturbations of this background can be 'drastically' simplified. This opened a way for studying astrophysical processes, such as the plasma accretion around black holes, the radiation produced by infalling matter, the origin of jets, the production and propagation of waves produced in the vicinity of black holes, and it even led to estimates of the gravitational wave production in star collisions and galaxy merges. It also facilitated the study of more theoretical problems, such as the problem of stability of the Kerr solution, the calculation of the quasinormal modes, or the study of the Hawking radiation. A hidden symmetry responsible for this miracle can be mathematically described by a simple antisymmetric object, called the Killing-Yano tensor.Recently, higher-dimensional rotating black hole spacetimes have become of high interest due to various developments in gravity and high energy physic...

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Section: A12 'Derivation' Of the 4d Kerr-nut-(a)ds Metricmentioning

confidence: 99%

Section: A21 Plebański-demiański Metricmentioning

confidence: 99%

Section: A21 Plebański-demiański Metricmentioning

confidence: 99%

“…Following [97], let us introduce two new continuous parameters α (the acceleration) and ω (the 'twist') by the rescaling 55) and relabel the other parameters as…”

Section: A22 Generalized Black Holesmentioning

confidence: 99%

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Hidden Symmetries of Higher-Dimensional Rotating Black Holes

2007

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“…[11]), none of these has so far (to our knowledge) found application to the astrophysics of compact objects. In the limit a → 0 our metric (1) reduces to de Sitter's 1917 metric.…”

Section: The Metricmentioning

confidence: 99%

A Vortex Model for Rotating Compact Objects

Chapline¹,

Marecki²

2014

Acta Phys. Pol. B

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In this paper a rotating stationary solution of the vacuum Einstein equations with a cosmological constant is exhibited which reduces to de Sitter's interior cosmological solution when the angular momentum goes to zero. This solution is locally isomorphic to de Sitter space, but as one approaches the axis of rotation it has a novel feature: a conical event horizon. This suggests that in reality rotating compact objects have a vortex structure similar to that conjectured for rotating superfluid droplets. In the limit of slow rotation the vortex core would be nearly cylindrical and the space-time inside the core would be Gödel-like. The exterior space-time will resemble the Kerr solution for equatorial latitudes, but significant deviations from Kerr are expected for polar latitudes.

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Charged Accelerating BTZ Black Holes

Panah

2023

Fortschritte der Physik

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In this paper, general uncharged accelerating BTZ black hole solutions are extracted and studied some of their properties. The analysis shows that spacetime's asymptotic behavior depends on four parameters: the cosmological constant, mass, acceleration, and topological constant. Then, the temperature of these black holes are studied and it is found that the temperature is always positive for AdS spacetime. Next, the study is extended for extracting charged accelerating BTZ black hole solutions in the presence of a nonlinear electrodynamics field known as conformally invariant Maxwell. The findings indicate a coupling between the electrical charge and other quantities of the accelerating BTZ black holes. The asymptotic behavior of charged accelerating BTZ black holes depends on five parameters: the cosmological constant, the electrical charge, mass, the acceleration parameter, and the topological constant. Then, the effects of charge, acceleration parameters, and the topological constant on the root of these black holes are studied. Finally, the temperature of these black holes in AdS spacetime is investigated. For these black holes, the temperature depends on the electrical charge, accelerating parameter, and the cosmological constant. The analysis indicates that the temperature of charged accelerating BTZ AdS black holes is always positive.

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A New Look at the Plebański–demiański Family of Solutions

Cited by 247 publications

References 44 publications

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

A Vortex Model for Rotating Compact Objects

Charged Accelerating BTZ Black Holes

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