Constants of geodesic motion in higher-dimensional black-hole spacetimes

Krtouš, Pavel; Kubizňák, David; Page, Don N.; Vasudevan, Muraari

doi:10.1103/physrevd.76.084034

Cited by 68 publications

(78 citation statements)

References 21 publications

(36 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The thesis is based on the following published papers in peer reviewed journals: [77], [153], [193], [85], [148], [149], [155], [154], [78], [52], [151].…”

mentioning

confidence: 99%

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

2007

Self Cite

View full text Add to dashboard Cite

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...

show abstract

“…The thesis is based on the following published papers in peer reviewed journals: [77], [153], [193], [85], [148], [149], [155], [154], [78], [52], [151].…”

mentioning

confidence: 99%

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

2007

Self Cite

View full text Add to dashboard Cite

show abstract

“…(For odd D, ε = 1, one of these rank-2 Killing tensors is the tensor product of a Killing vector with itself and so is not independent or irreducible, leaving only D = 2k − ε independent rank-2 and rank-1 Killing tensors.) We also show the relations of the constants of motion arising from all these Killing tensors with those given in [21,22], as well as with the constants of motion arising from the recent separation of the Hamilton-Jacobi and Klein-Gordon equations [23].…”

Section: Jhep02(2007)004mentioning

confidence: 99%

“…It is shown in [22] that the observables C j Poisson commute between each other. The relation (3.18), which shows that the c j 's are polynomial combinations of the C j 's and w with constant coefficients, thus proves that also the observables c j are in involution,…”

Section: Jhep02(2007)004mentioning

confidence: 99%

“…With the recent interest in higher-dimensional spacetimes, it has become of interest to extend these old four-dimensional studies to higher dimensions D. For example, it has been found that the rotating black hole metrics [13 -18] in higher dimensions have a KillingYano tensor of rank D − 2 [19,20] (which we shall call a principal Killing-Yano tensor) that was used (along with the Killing vectors) to show [21,22] that geodesic motion in the general D-dimensional Kerr-NUT-AdS rotating black hole spacetime [18] is completely integrable, with D independent constants of motion in involution.…”

Section: Introductionmentioning

confidence: 99%

“…For convenience, we use square brackets to denote the integer part of what is inside and define n ≡ [D/2], k ≡ [(D + 1)/2], and ε ≡ k − n (0 for even D and 1 for odd D), so D = 2n + ε = 2k − ε = k + n. Then the Kerr-NUT-AdS spacetimes have k Killing vectors (giving constants of motion linear in the velocity) and n independent Killing tensors of higher rank (including the metric) [21,22] (giving other independent constants of motion in involution that are higher-order polynomials in the velocity).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions

Krtouš¹,

Kubizňák²,

Page³

et al. 2007

J. High Energy Phys.

Self Cite

122

250

View full text Add to dashboard Cite

From the metric and one Killing-Yano tensor of rank D − 2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D +1)/2] Killing-Yano tensors, of rank D − 2j for all 0 ≤ j ≤ k − 1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245).

show abstract

Excitations of the Myers-Perry black holes

Lunin

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

We demonstrate separability of the dynamical equations for all p-form fluxes in the Myers-Perry-(A)dS geometry, extending the earlier results for electromagnetic field. In the physically important cases of p = (1, 2, 3, 4), we explicitly write the ODEs governing the dynamics of separable solutions. email: olunin@albany.edu 1 See also [22] for a general discussion of the GLPP black holes and their properties. 2 While the analysis of spherical harmonics for all p-form fields is rather straightforward [23], study of gravitational waves is quite challenging even in the backgrounds of static black holes. We refer to [24] for the detailed discussion.3 Various extensions of this work, including incorporation of massive vector fields, have been reported in [26,27].4 To our knowledge, in the past, the dynamics of p-forms in black holes geometries has been studied only in static backgrounds [23].

show abstract

Constants of geodesic motion in higher-dimensional black-hole spacetimes

Cited by 68 publications

References 21 publications

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions

Excitations of the Myers-Perry black holes

Contact Info

Product

Resources

About