Stationary strings and branes in the higher-dimensional Kerr-NUT-(A)dS spacetimes

We demonstrate complete integrability of the Nambu-Goto equations for a stationary string in the general Kerr-NUT-(A)dS spacetime describing the higher-dimensional rotating black hole. The stationary string in D dimensions is generated by a 1-parameter family of Killing trajectories and the problem of finding a string configuration reduces to a problem of finding a geodesic line in an effective (D-1)-dimensional space. Resulting integrability of this geodesic problem is connected with the existence of hidden symmetries which are inherited from the black hole background. In a spacetime with p mutually commuting Killing vectors it is possible to introduce a concept of a $\xi$-brane, that is a p-brane with the worldvolume generated by these fields and a 1-dimensional curve. We discuss integrability of such $\xi$-branes in the Kerr-NUT-(A)dS spacetime.Comment: 8 pages, no figure

Separability of Hamilton-Jacobi and Klein-Gordon Equations in General Kerr-NUT-AdS Spacetimes

We demonstrate the separability of the Hamilton-Jacobi and scalar field equations in general higher dimensional Kerr-NUT-AdS spacetimes. No restriction on the parameters characterizing these metrics is imposed.Comment: 4 pages, no figure

Hidden Symmetry of Higher Dimensional Kerr-NUT-AdS Spacetimes

It is well known that 4-dimensional Kerr-NUT-AdS spacetime possesses the hidden symmetry associated with the Killing-Yano tensor. This tensor is "universal" in the sense that there exist coordinates where it does not depend on any of the free parameters of the metric. Recently the general higher dimensional Kerr-NUT-AdS solutions of the Einstein equations were obtained. We demonstrate that all these metrics with arbitrary rotation and NUT parameters admit a universal Killing-Yano tensor. We give an explicit presentation of the Killing-Yano and Killing tensors and briefly discuss their properties.Comment: 4 pages, some discussion and references are adde

Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions

From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k=[(D+1)/2] Killing-Yano tensors, of rank D-2j for all j=0,...,k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245).Comment: 7 page