Integrability of particle motion and scalar field propagation in Kerr-(anti-) de Sitter black hole spacetimes in all dimensions

Vasudevan, Muraari; Stevens, Kory A.

doi:10.1103/physrevd.72.124008

Cited by 37 publications

(33 citation statements)

References 28 publications

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“…Later it was shown that 5D results can be extended to an arbitrary number of dimensions, provided that rotation parameters of the MP metric can be divided into two classes, and within each of the classes these parameters are equal of one another [228]. Similar results were found in the presence of the cosmological constant and NUT parameters [163], [229], [156], [227], [225], [40], [59], [226]. It was also demonstrated that a stationary string configuration in the 5D Myers-Perry spacetime is completely integrable [79].…”

Section: Hidden Symmetries In Higher Dimensionssupporting

confidence: 70%

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: Hidden Symmetries In Higher Dimensionssupporting

confidence: 70%

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

2007

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“…Higher dimensional, asymptotically flat, Kerr black holes were first found in [2] and the asymptotically (A)dS analogues were found more recently in [3]. The five-dimensional Myers-Perry and Kerr-(A)dS black holes were shown to possess Killing tensors for arbitrary rotation parameters in [4] and [5] respectively, and in the case where the rotation parameters can take one of two different values, a Killing tensor has been found in all dimensions [6].…”

Section: Introductionmentioning

confidence: 97%

Separability of multi-charge black holes in supergravity

Davis¹

2006

Class. Quantum Grav.

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In this paper, we show that some five-dimensional rotating black hole solutions of both gauged and ungauged supergravity, with independent rotation parameters and three charges admit separable solutions to the massless Hamilton-Jacobi and Klein-Gordon equations. This allows us to write down a conformal Killing tensor for the spacetime. Conformal Killing tensors obey an equation involving a co-vector field. We find this co-vector field in three specific examples, and also give a general formula for it.

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“…Secondly, this equation can be reduced to ODEs governing the radial and angular behaviour by separation of variables. It is known that this separability property of the Kerr metric does extend to some of the higher-dimensional MP metrics [17,18,19], and MP metrics with a cosmological constant [20]. This makes the study of scalar field perturbations in such backgrounds tractable.…”

Section: Introductionmentioning

confidence: 98%

Gravitational perturbations of higher dimensional rotating black holes: Tensor perturbations

2006

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Assessing the stability of higher-dimensional rotating black holes requires a study of linearized gravitational perturbations around such backgrounds. We study perturbations of Myers-Perry black holes with equal angular momenta in an odd number of dimensions (greater than five), allowing for a cosmological constant. We find a class of perturbations for which the equations of motion reduce to a single radial equation. In the asymptotically flat case we find no evidence of any instability. In the asymptotically anti-de Sitter case, we demonstrate the existence of a superradiant instability that sets in precisely when the angular velocity of the black hole exceeds the speed of light from the point of view of the conformal boundary. We suggest that the endpoint of the instability may be a stationary, nonaxisymmetric black hole.

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Integrability of particle motion and scalar field propagation in Kerr-(anti-) de Sitter black hole spacetimes in all dimensions

Cited by 37 publications

References 28 publications

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Separability of multi-charge black holes in supergravity

Gravitational perturbations of higher dimensional rotating black holes: Tensor perturbations

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