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Black holes, hidden symmetries, and complete integrability. (arXiv:1705.05482v1 [gr-qc])

来源于:arXiv
The study of higher-dimensional black holes is a subject which has recently attracted a vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of higher-dimensional black holes with the spherical horizon topology are very similar to the properties of the well known four-dimensional Kerr metric. This remarkable result stems from the existence of a single object called the principal tensor. In our review we discuss explicit and hidden symmetries of higher-dimensional black holes. We start with the overview of the Liouville theory of completely integrable systems and introduce Killing and Killing-Yano objects representing explicit and hidden symmetries. We demonstrate that the principal tensor can be used as a 'seed object' which generates all these symmetries. It determines the form of the black hole geometry, as well as guarantees its remarkable properties, such as special algebraic type of the spacetime, complete integrability of geodesic mot 查看全文>>