Kerr–NUT–de Sitter curvature in all dimensions

Hamamoto, Naoki; Houri, Tsuyoshi; Oota, Takeshi; Yasui, Yukinori

doi:10.1088/1751-8113/40/7/f01

Cited by 66 publications

(136 citation statements)

References 14 publications

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“…Therefore, from now on we refer to the off-shell spacetime (4.1), without imposing (4.3), as to the canonical metric. The canonical metric is of the special algebraic type D [102] of the higher-dimensional algebraic classification [178], [46], [45]. Let us finally remark that formulas (4.1)- (4.3) are applicable also in D = 3 where one recovers the 2-parametric BTZ black hole [13].…”

Section: Overview Of the Kerr-nut-(a)ds Metricsmentioning

confidence: 99%

“…In particular, it was proved that, similar to the 4D case, the most general Einstein space admitting the PCKY tensor is the Kerr-NUT-(A)dS spacetime. Meanwhile, it was shown that the Kerr-NUT-(A)dS spacetime is of the algebraic type D of higher-dimensional algebraic classification [102] and that it allows a generalized Kerr-Schild form [38]. By relaxing some of the requirements imposed on the PCKY tensor more general spacetimes were recently discovered [109], [108].…”

Section: Hidden Symmetries In Higher Dimensionsmentioning

confidence: 99%

“…, n − 1, stand for latitude coordinates. 1 The parameter c n is proportional to the cosmological constant [102] 4) and the remaining constants c k , c > 0, and b µ are related to rotation parameters, mass, and NUT parameters. One of these constants may be eliminated due to the scaling symmetry.…”

Section: Overview Of the Kerr-nut-(a)ds Metricsmentioning

confidence: 99%

“…In fact, this canonical basis has an additional nice property that many of the Ricci coefficients of rotation vanish [102], [151]; it is a principal canonical basis (see also Chapter 7). Having a PCKY tensor and its canonical basis, we may employ the machinery of Chapter 3.…”

Section: Principal Conformal Killing-yano Tensormentioning

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: Overview Of the Kerr-nut-(a)ds Metricsmentioning

confidence: 99%

Section: Hidden Symmetries In Higher Dimensionsmentioning

confidence: 99%

Section: Overview Of the Kerr-nut-(a)ds Metricsmentioning

confidence: 99%

Section: Principal Conformal Killing-yano Tensormentioning

confidence: 99%

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Hidden Symmetries of Higher-Dimensional Rotating Black Holes

2007

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“…The parameter c n is proportional to the cosmological constant, and the remaining constants c k , c and b µ are related to the rotation parameters, the mass and the NUT parameters. Hamamoto, Houri, Oota and Yasui [14] derived explicit formulas for the curvature and demonstrated that in all dimensions this metric obeys the Einstein equations…”

Section: Higher-dimensional Black-hole Spacetimesmentioning

confidence: 99%

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

et al. 2007

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In [1] we announced the complete integrability of geodesic motion in the general higherdimensional rotating black-hole spacetimes. In the present paper we prove all the necessary steps leading to this conclusion. In particular, we demonstrate the independence of the constants of motion and the fact that they Poisson commute. The relation to a different set of constants of motion constructed in [2] is also briefly discussed.

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Aligned fields double copy to Kerr-NUT-(A)dS

Chawla

Keeler

2023

J. High Energ. Phys.

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We find Abelian gauge fields that double copy to a large class of black hole spacetimes with spherical horizon topology known as the Kerr-NUT-(A)dS family. Using a multi-Kerr-Schild prescription, we extend the previously-known double copy structure for arbitrarily rotating general dimension black holes, to include NUT charges and an arbitrary cosmological constant. In all cases, these single copy gauge fields are ‘aligned fields’, because their nonzero components align with the principal tensor which generates the Killing structure of the spacetime. In five dimensions, we additionally derive the same single-copy field strengths via the Weyl double copy procedure.

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Kerr–NUT–de Sitter curvature in all dimensions

Cited by 66 publications

References 14 publications

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

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

Aligned fields double copy to Kerr-NUT-(A)dS

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