90 research outputs found
Electromagnetic Field in Higher-Dimensional Black-Hole Spacetimes
A special test electromagnetic field in the spacetime of the
higher-dimensional generally rotating NUT-(A)dS black hole is found. It is
adjusted to the hidden symmetries of the background represented by the
principal Killing-Yano tensor. Such electromagnetic field generalizes the field
of charged black hole in four dimensions. In higher dimensions, however, the
gravitational back reaction of such a field cannot be consistently solved.Comment: 8 pages, no figures; presented at the Black hole VI conference in
White Point, Canada, May 12-16 2007, and at the GRG18 conference in Sydney,
Australia, July 8-13 200
Gravitational and electromagnetic fields near an anti-de Sitter-like infinity
We analyze asymptotic structure of general gravitational and electromagnetic
fields near an anti-de Sitter-like conformal infinity. Dependence of the
radiative component of the fields on a null direction along which the infinity
is approached is obtained. The directional pattern of outgoing and ingoing
radiation, which supplements standard peeling property, is determined by the
algebraic (Petrov) type of the fields and also by orientation of principal null
directions with respect to the timelike infinity. The dependence on the
orientation is a new feature if compared to spacelike infinity.Comment: 4 pages, 2 figure
Asymptotic structure of radiation in higher dimensions
We characterize a general gravitational field near conformal infinity (null,
spacelike, or timelike) in spacetimes of any dimension. This is based on an
explicit evaluation of the dependence of the radiative component of the Weyl
tensor on the null direction from which infinity is approached. The behaviour
similar to peeling property is recovered, and it is shown that the directional
structure of radiation has a universal character that is determined by the
algebraic type of the spacetime. This is a natural generalization of analogous
results obtained previously in the four-dimensional case.Comment: 14 pages, no figures (two references added
Generalized Kerr-NUT-de Sitter metrics in all dimensions
We classify all spacetimes with a closed rank-2 conformal Killing-Yano
tensor. They give a generalization of Kerr-NUT-de Sitter spacetimes. The
Einstein condition is explicitly solved and written as an indefinite integral.
It is characterized by a polynomial in the integrand. We briefly discuss the
smoothness conditions of the Einstein metrics over compact Riemannian
manifolds.Comment: 12 pages, LaTeX; v2: Einstein conditions for general type included,
with slight modification of text, typos corrected; v3: references added,
typos corrected, the version published in Physics Letters
Dirac Equation in Kerr-NUT-(A)dS Spacetimes: Intrinsic Characterization of Separability in All Dimensions
We intrinsically characterize separability of the Dirac equation in
Kerr-NUT-(A)dS spacetimes in all dimensions. Namely, we explicitly demonstrate
that in such spacetimes there exists a complete set of first-order mutually
commuting operators, one of which is the Dirac operator, that allows for common
eigenfunctions which can be found in a separated form and correspond precisely
to the general solution of the Dirac equation found by Oota and Yasui
[arXiv:0711.0078]. Since all the operators in the set can be generated from the
principal conformal Killing-Yano tensor, this establishes the (up to now)
missing link among the existence of hidden symmetry, presence of a complete set
of commuting operators, and separability of the Dirac equation in these
spacetimes.Comment: 11 pages, no figure
Closed conformal Killing-Yano tensor and Kerr-NUT-de Sitter spacetime uniqueness
We study spacetimes with a closed conformal Killing-Yano tensor. It is shown
that the D-dimensional Kerr-NUT-de Sitter spacetime constructed by Chen-Lu-Pope
is the only spacetime admitting a rank-2 closed conformal Killing-Yano tensor
with a certain symmetry.Comment: 7 pages, LaTe
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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