Hidden symmetries and higher-dimensional rotating black holes


Kubiznak, D. (2011). Hidden symmetries and higher-dimensional rotating black holes. Perimeter Institute. https://pirsa.org/11020139


Kubiznak, David. Hidden symmetries and higher-dimensional rotating black holes. Perimeter Institute, Feb. 23, 2011, https://pirsa.org/11020139


          @misc{ pirsa_11020139,
            doi = {10.48660/11020139},
            url = {https://pirsa.org/11020139},
            author = {Kubiznak, David},
            keywords = {Quantum Fields and Strings, Cosmology},
            language = {en},
            title = {Hidden symmetries and higher-dimensional rotating black holes},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {feb},
            note = {PIRSA:11020139 see, \url{https://pirsa.org}}

David Kubiznak Perimeter Institute for Theoretical Physics


The 4D rotating black hole described by the Kerr geometry possesses many of what was called by Chandrasekhar "miraculous" properties. Most of them are related to the existence of a fundamental hidden symmetry of a principal conformal Killing-Yano (PCKY) tensor. In my talk I shall demonstrate that hidden symmetry of the PCKY tensor plays exceptional role also in higher dimensions. Namely, I shall present the most general spacetime admitting the PCKY tensor and show that is possesses the following properties: 1) It is of the algebraic type D and admits the Kerr-Schild form 2) It allows a separation of variables for the Hamilton-Jacobi, Klein-Gordon, Dirac, and stationary string equations. 3) When the Einstein equations with the cosmological constant are imposed the metric describes the most general known (spherical) Kerr-NUT-AdS black hole spacetime. I will also discuss the generalization of Killing-Yano symmetries for spacetimes with natural "torsion 3-form", such as the black hole of D=5 minimal supergravity, or the Kerr-Sen solution of heterotic string theory, and comment on connection to special Riemannian manifolds admiting Killing spinors.