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Hidden Symmetries and Separation of Variables in Higher-Dimensional Black Holes: Exploring Einstein's Gravity

This paper explores hidden symmetries and separation of variables in higher-dimensional black holes, focusing on the General Kerr-NUT-AdS metrics, Plebanski solution, and integrability of geodesic motion. The study also delves into Killing-Yano tensors and the separability of Hamilton-Jacobi and Klein-Gordon equations in Kerr-NUT-AdS spacetimes. Further questions are raised regarding massless fields of higher spin and decoupling separation of variables.

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Hidden Symmetries and Separation of Variables in Higher-Dimensional Black Holes: Exploring Einstein's Gravity

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  1. Hidden Symmetries and Separation of Variables in Higher Dimensional Black Holes Valeri P. Frolov University of Alberta “Einstein’s Gravity in Higher Dimensions” Jerusalem, 18-22 February, 2007

  2. "General Kerr-NUT-AdS metrics in all dimensions“, W. Chen, H. Lü and C. N. Pope, Class. Quant. Grav. 23 , 5323 (2006).

  3. Orthonormal form: ( )

  4. where: “Higher dimensional” Plebanski solution: J. F. Plebanski, Ann. Phys. 90, 196 (1975).

  5. Alberta Separatists

  6. V. F., D.Kubiznak,"Hidden symmetries of higher-dimensional rotating black holes". Phys.Rev.Lett.98:011101,2007; gr-qc/0605058 D. Kubiznak, V. F.,"Hidden Symmetry of Higher Dimensional Kerr-NUT-AdS Spacetimes". Class.Quant.Grav.24:F1-F6,2007; gr-qc/0610144

  7. D. N. Page, D. Kubiznak, M. Vasudevan, P. Krtous,"Complete integrability of geodesic motion in general Kerr-NUT-AdS spacetimes". Phys.Rev.Lett.2007; hep-th/0611083 P. Krtous, D. Kubiznak, D. N. Page, V. F.,"Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions". JHEP 0702:004,2007; hep-th/0612029

  8. Klein-Gordon equation multiplicative separation "Separability of Hamilton-Jacobi and Klein-Gordon Equations in General Kerr-NUT-AdS Spacetimes". V. F., P. Krtous , D. Kubiznak , JHEP 0702:005,2007; hep-th/0611245

  9. Further Questions: Massless fields of higher spin: Decoupling Separation of Variables

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