43 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
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
Closed conformal Killing-Yano tensor and geodesic integrability
Assuming the existence of a single rank-2 closed conformal Killing-Yano
tensor with a certain symmetry we show that there exist mutually commuting
rank-2 Killing tensors and Killing vectors. We also discuss the condition of
separation of variables for the geodesic Hamilton-Jacobi equations.Comment: 17 pages, no figure, LaTe
Massive Vector Fields in Rotating Black-Hole Spacetimes: Separability and Quasinormal Modes.
We demonstrate the separability of the massive vector (Proca) field equation in general Kerr-NUT-AdS black-hole spacetimes in any number of dimensions, filling a long-standing gap in the literature. The obtained separated equations are studied in more detail for the four-dimensional Kerr geometry and the corresponding quasinormal modes are calculated. Two of the three independent polarizations of the Proca field are shown to emerge from the separation ansatz and the results are found in an excellent agreement with those of the recent numerical study where the full coupled partial differential equations were tackled without using the separability property.be equally used in those circumstances.
V. F. thanks the Natural Sciences and Engineering
Research Council of Canada (NSERC) and the Killam
Trust for their financial support. P. K. is supported by
Czech Science Foundation Grant No. 17-01625S. D. K.
acknowledges the Perimeter Institute for Theoretical
Physics and the NSERC for their support. Research at
Perimeter Institute is supported by the Government of
Canada through the Department of Innovation, Science and
Economic Development Canada and by the Province of
Ontario through the Ministry of Research, Innovation and
Science. J. E. S. is supported in part by STFC Grants
No. PHY-1504541 and No. ST/P000681/1
Parallel-propagated frame along null geodesics in higher-dimensional black hole spacetimes
In [arXiv:0803.3259] the equations describing the parallel transport of
orthonormal frames along timelike (spacelike) geodesics in a spacetime
admitting a non-degenerate principal conformal Killing-Yano 2-form h were
solved. The construction employed is based on studying the Darboux subspaces of
the 2-form F obtained as a projection of h along the geodesic trajectory. In
this paper we demonstrate that, although slightly modified, a similar
construction is possible also in the case of null geodesics. In particular, we
explicitly construct the parallel-transported frames along null geodesics in
D=4,5,6 Kerr-NUT-(A)dS spacetimes. We further discuss the parallel transport
along principal null directions in these spacetimes. Such directions coincide
with the eigenvectors of the principal conformal Killing-Yano tensor. Finally,
we show how to obtain a parallel-transported frame along null geodesics in the
background of the 4D Plebanski-Demianski metric which admits only a conformal
generalization of the Killing-Yano tensor.Comment: 17 pages, no figure
Radiation generated by accelerating and rotating charged black holes in (anti-)de Sitter space
Asymptotic behaviour of gravitational and electromagnetic fields of exact
type D solutions from the large Plebanski-Demianski family of black hole
spacetimes is analyzed. The amplitude and directional structure of radiation is
evaluated in cases when the cosmological constant is non-vanishing, so that the
conformal infinities have either de Sitter-like or anti-de Sitter-like
character. In particular, explicit relations between the parameters that
characterize the sources (that is their mass, electric and magnetic charges,
NUT parameter, rotational parameter, and acceleration) and properties of the
radiation generated by them are presented. The results further elucidate the
physical interpretation of these solutions and may help to understand radiative
characteristics of more general spacetimes than those that are asymptotically
flat.Comment: 24 pages, 18 figures. To appear in Classical and Quantum Gravit