  In this thesis we study higher-dimensional rotating black holes. Such black
holes are widely discussed in string theory and brane-world models at present.
We demonstrate that even the most general known Kerr-NUT-(A)dS spacetime,
describing the general rotating higher-dimensional asymptotically (anti) de
Sitter black hole with NUT parameters, is in many aspects similar to its
four-dimensional counterpart. Namely, we show that it admits a fundamental
hidden symmetry associated with the principal conformal Killing-Yano tensor.
Such a tensor generates towers of hidden and explicit symmetries. The tower of
Killing tensors is responsible for the existence of irreducible, quadratic in
momenta, conserved integrals of geodesic motion. These integrals, together with
the integrals corresponding to the tower of explicit symmetries, make geodesic
equations in the Kerr-NUT-(A)dS spacetime completely integrable. We further
demonstrate that in this spacetime the Hamilton-Jacobi, Klein-Gordon, and
stationary string equations allow complete separation of variables and the
problem of finding parallel-propagated frames reduces to the set of the first
order ordinary differential equations. Moreover, we show that the
Kerr-NUT-(A)dS spacetime is the most general Einstein space which possesses all
these properties. We also explicitly derive the most general (off-shell)
canonical metric admitting the principal conformal Killing-Yano tensor and
demonstrate that such a metric is necessarily of the special algebraic type D
of the higher-dimensional algebraic classification. The results presented in
this thesis describe the new and complete picture of the relationship of hidden
symmetries and rotating black holes in higher dimensions.
