124 research outputs found
Charged particle in higher dimensional weakly charged rotating black hole spacetime
We study charged particle motion in weakly charged higher dimensional black
holes. To describe the electromagnetic field we use a test field approximation
and use the higher dimensional Kerr-NUT-(A)dS metric as a background geometry.
It is shown that for a special configuration of the electromagnetic field the
equations of motion of charged particles are completely integrable. The vector
potential of such a field is proportional to one of the Killing vectors (called
primary Killing vector) from the `Killing tower' of symmetry generating objects
which exists in the background geometry. A free constant in the definition of
the adopted electromagnetic potential is proportional to the electric charge of
the higher dimensional black hole. The full set of independent conserved
quantities in involution is found. It is demonstrated, that Hamilton-Jacobi
equations are separable, as well as the corresponding Klein-Gordon equation and
its symmetry operators.Comment: 9 pages, no figure
Weakly charged generalized Kerr-NUT-(A)dS spacetimes
We find an explicit solution of the source free Maxwell equations in a
generalized Kerr-NUT-(A)dS spacetime in all dimensions. This solution is
obtained as a linear combination of the closed conformal Killing-Yano tensor
, which is present in such a spacetime, and a derivative of the primary
Killing vector, associated with . For the vanishing cosmological
constant the obtained solution reduces to the Wald's electromagnetic field
generated from the primary Killing vector.Comment: 4 pages, no figures v2: added reference
Electron in higher-dimensional weakly charged rotating black hole spacetimes
We demonstrate separability of the Dirac equation in weakly charged rotating
black hole spacetimes in all dimensions. The electromagnetic field of the black
hole is described by a test field approximation, with vector potential
proportional to the primary Killing vector field. It is shown that the
demonstrated separability can be intrinsically characterized by the existence
of a complete set of mutually commuting first order symmetry operators
generated from the principal Killing-Yano tensor. The presented results
generalize the results on integrability of charged particle motion and
separability of charged scalar field studied in [1].Comment: 12 pages, no figure
Geometry of Lax pairs: particle motion and Killing-Yano tensors
A geometric formulation of the Lax pair equation on a curved manifold is
studied using phase space formalism. The corresponding (covariantly conserved)
Lax tensor is defined and the method of generation of constants of motion from
it is discussed. It is shown that when the Hamilton equations of motion are
used, the conservation of the Lax tensor translates directly to the well known
Lax pair equation, with one matrix identified with components of the Lax tensor
and the other matrix constructed from the (metric) connection. A generalization
to Clifford objects is also discussed. Nontrivial examples of Lax tensors for
geodesic and charged particle motion are found in spacetimes admitting hidden
symmetry of Killing--Yano tensors.Comment: 13 pages, 1 figur
Hidden Symmetries of Higher Dimensional Black Holes and Uniqueness of the Kerr-NUT-(A)dS spacetime
We prove that the most general solution of the Einstein equations with the
cosmological constant which admits a principal conformal Killing-Yano tensor is
the Kerr-NUT-(A)dS metric. Even when the Einstein equations are not imposed,
any spacetime admitting such hidden symmetry can be written in a canonical form
which guarantees the following properties: it is of the Petrov type D, it
allows the separation of variables for the Hamilton-Jacobi, Klein-Gordon, and
Dirac equations, the geodesic motion in such a spacetime is completely
integrable. These results naturally generalize the results obtained earlier in
four dimensions.Comment: 5 pages, no figure
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