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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
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