Hidden Symmetries of Higher-Dimensional Rotating Black Holes - General Relativity and Quantum CosmologyReport as inadecuate




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Abstract: In this thesis we study higher-dimensional rotating black holes. Such blackholes are widely discussed in string theory and brane-world models at present.We demonstrate that even the most general known Kerr-NUT-AdS spacetime,describing the general rotating higher-dimensional asymptotically anti deSitter black hole with NUT parameters, is in many aspects similar to itsfour-dimensional counterpart. Namely, we show that it admits a fundamentalhidden symmetry associated with the principal conformal Killing-Yano tensor.Such a tensor generates towers of hidden and explicit symmetries. The tower ofKilling tensors is responsible for the existence of irreducible, quadratic inmomenta, conserved integrals of geodesic motion. These integrals, together withthe integrals corresponding to the tower of explicit symmetries, make geodesicequations in the Kerr-NUT-AdS spacetime completely integrable. We furtherdemonstrate that in this spacetime the Hamilton-Jacobi, Klein-Gordon, andstationary string equations allow complete separation of variables and theproblem of finding parallel-propagated frames reduces to the set of the firstorder ordinary differential equations. Moreover, we show that theKerr-NUT-AdS spacetime is the most general Einstein space which possesses allthese properties. We also explicitly derive the most general off-shellcanonical metric admitting the principal conformal Killing-Yano tensor anddemonstrate that such a metric is necessarily of the special algebraic type Dof the higher-dimensional algebraic classification. The results presented inthis thesis describe the new and complete picture of the relationship of hiddensymmetries and rotating black holes in higher dimensions.



Author: David Kubiznak

Source: https://arxiv.org/



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