49 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
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
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
Ultrarelativistic boost of the black ring
We investigate the ultrarelativistic boost of the five-dimensional
Emparan-Reall non-rotating black ring. Following the classical method of
Aichelburg and Sexl, we determine the gravitational field generated by a black
ring moving ``with the speed of light'' in an arbitrary direction. In
particular, we study in detail two different boosts along axes orthogonal and
parallel to the plane of the ring circle, respectively. In both cases, after
the limit one obtains a five-dimensional impulsive pp-wave propagating in
Minkowski spacetime. The curvature singularity of the original static spacetime
becomes a singular source within the wave front, in the shape of a ring or a
rod according to the direction of the boost. In the case of an orthogonal
boost, the wave front contains also a remnant of the original disk-shaped
membrane as a component of the Ricci tensor (which is everywhere else
vanishing). We also analyze the asymptotic properties of the boosted black ring
at large spatial distances from the singularity, and its behaviour near the
sources. In the limit when the singularity shrinks to a point, one recovers the
well known five-dimensional analogue of the Aichelburg-Sexl ``monopole''
solution.Comment: 10 pages, 2 figures, REVTeX 4. v2: added boost in an arbitrary
direction, one new figure, one new reference. To appear in Phys. Rev.