5 research outputs found
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
-brane, that is a p-brane with the worldvolume generated by these fields
and a 1-dimensional curve. We discuss integrability of such -branes in the
Kerr-NUT-(A)dS spacetime.Comment: 8 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
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
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