Closed conformal Killing–Yano tensor and Kerr–NUT–de Sitter space–time uniqueness

Houri, Tsuyoshi; Oota, Takeshi; Yasui, Yukinori

doi:10.1016/j.physletb.2007.09.034

Cited by 71 publications

(86 citation statements)

References 18 publications

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“…ξ is called primary Killing vector for these metrics. Riemannian metrics that admit a principal conformal Killing-Yano tensor with independent, non-constant eigenvalues have been classified (Houri et al, 2007;, and are exactly given by the canonical spacetimes above.…”

Section: Black Holes In Higher Dimensionsmentioning

confidence: 99%

Hidden symmetries of dynamics in classical and quantum physics

Cariglia

2014

Rev. Mod. Phys.

164

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This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description of physical systems as varied as non-relativistic, relativistic, with or without gravity, classical or quantum, and are related to the existence of conserved quantities of the dynamics and integrability. In recent years their study has grown intensively, due to the discovery of non-trivial examples that apply to different types of theories and different numbers of dimensions. Applications encompass the study of integrable systems such as spinning tops, the Calogero model, systems described by the Lax equation, the physics of higher dimensional black holes, the Dirac equation, supergravity with and without fluxes, providing a tool to probe the dynamics of non-linear systems.

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Section: Black Holes In Higher Dimensionsmentioning

confidence: 99%

Hidden symmetries of dynamics in classical and quantum physics

Cariglia

2014

Rev. Mod. Phys.

164

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“…It is known that the wave equation is separable in a MP spacetime and this is because of the existence of a conformal KillingYano tensor. Furthermore, it has been shown that a certain generalization of the MP solution is the most general spacetime admitting a "principal" conformal Killing-Yano tensor [155,156]. This result shows that one can exploit the existence of such a tensor to solve the Einstein equation.…”

Section: Future Directionsmentioning

confidence: 99%

NR/HEP: roadmap for the future

Cardoso

Gualtieri

Herdeiro

et al. 2012

Class. Quantum Grav.

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Abstract. Physics in curved spacetime describes a multitude of phenomena, ranging from astrophysics to high energy physics. The last few years have witnessed further progress on several fronts, including the accurate numerical evolution of the gravitational field equations, which now allows highly nonlinear phenomena to be tamed. Numerical relativity simulations, originally developed to understand strong field astrophysical processes, could prove extremely useful to understand high-energy physics processes like trans-Planckian scattering and gauge-gravity dualities. We present a concise and comprehensive overview of the state-of-the-art and important open problems in the field(s), along with guidelines for the next years. This writeup is a summary of the "NR/HEP Workshop" held in Madeira, Portugal from August 31st to September 3rd 2011.arXiv:1201.5118v1 [hep-th]

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“…This result under special assumptions was first proved in [11]. A general proof was given in [12,13].…”

Section: B Remarkable Properties Of Pckytmentioning

confidence: 83%

Black Holes, Hidden Symmetry and Complete Integrability: Brief Review

Frolov

2014

General Relativity, Cosmology and Astrophysics

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This paper contains a brief review of the remarkable properties of higher dimensional rotating black holes with the spherical topology of the horizon. We demonstrate that these properties are connected with and generated by a special geometrical object, the Principal Conformal KillingYano tensor (PCKYT). The most general solution, describing such black holes, Kerr-NUT-ADS metric, admits this structure. Moreover a solution of the Einstein Equations with (or without) a cosmological constant which possesses PCKYT is the Kerr-NUT-ADS metric. This object (PCKYT) is responsible for such remarkable properties of higher dimensional rotating black holes as: (i) complete integrability of geodesic equations and (ii) complete separation of variables of the important field equations.

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Closed conformal Killing–Yano tensor and Kerr–NUT–de Sitter space–time uniqueness

Cited by 71 publications

References 18 publications

Hidden symmetries of dynamics in classical and quantum physics

Hidden symmetries of dynamics in classical and quantum physics

NR/HEP: roadmap for the future

Black Holes, Hidden Symmetry and Complete Integrability: Brief Review

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