7 research outputs found
Quasi-local rotating black holes in higher dimension: geometry
With a help of a generalized Raychaudhuri equation non-expanding null
surfaces are studied in arbitrarily dimensional case. The definition and basic
properties of non-expanding and isolated horizons known in the literature in
the 4 and 3 dimensional cases are generalized. A local description of horizon's
geometry is provided. The Zeroth Law of black hole thermodynamics is derived.
The constraints have a similar structure to that of the 4 dimensional spacetime
case. The geometry of a vacuum isolated horizon is determined by the induced
metric and the rotation 1-form potential, local generalizations of the area and
the angular momentum typically used in the stationary black hole solutions
case.Comment: 32 pages, RevTex
Mechanics of multidimensional isolated horizons
Recently a multidimensional generalization of Isolated Horizon framework has
been proposed by Lewandowski and Pawlowski (gr-qc/0410146). Therein the
geometric description was easily generalized to higher dimensions and the
structure of the constraints induced by the Einstein equations was analyzed. In
particular, the geometric version of the zeroth law of the black hole
thermodynamics was proved. In this work we show how the IH mechanics can be
formulated in a dimension--independent fashion and derive the first law of BH
thermodynamics for arbitrary dimensional IH. We also propose a definition of
energy for non--rotating horizons.Comment: 25 pages, 4 figures (eps), last sections revised, acknowledgements
and a section about the gauge invariance of introduced quantities added;
typos corrected, footnote 4 on page 9 adde
Spacetimes foliated by Killing horizons
It seems to be expected, that a horizon of a quasi-local type, like a Killing
or an isolated horizon, by analogy with a globally defined event horizon,
should be unique in some open neighborhood in the spacetime, provided the
vacuum Einstein or the Einstein-Maxwell equations are satisfied. The aim of our
paper is to verify whether that intuition is correct. If one can extend a so
called Kundt metric, in such a way that its null, shear-free surfaces have
spherical spacetime sections, the resulting spacetime is foliated by so called
non-expanding horizons. The obstacle is Kundt's constraint induced at the
surfaces by the Einstein or the Einstein-Maxwell equations, and the requirement
that a solution be globally defined on the sphere. We derived a transformation
(reflection) that creates a solution to Kundt's constraint out of data defining
an extremal isolated horizon. Using that transformation, we derived a class of
exact solutions to the Einstein or Einstein-Maxwell equations of very special
properties. Each spacetime we construct is foliated by a family of the Killing
horizons. Moreover, it admits another, transversal Killing horizon. The
intrinsic and extrinsic geometry of the transversal Killing horizon coincides
with the one defined on the event horizon of the extremal Kerr-Newman solution.
However, the Killing horizon in our example admits yet another Killing vector
tangent to and null at it. The geometries of the leaves are given by the
reflection.Comment: LaTeX 2e, 13 page
No more CKY two-forms in the NHEK
We show that in the near-horizon limit of a Kerr-NUT-AdS black hole, the
space of conformal Killing-Yano two-forms does not enhance and remains of
dimension two. The same holds for an analogous polar limit in the case of
extremal NUT charge. We also derive the conformal Killing-Yano -form
equation for any background in arbitrary dimension in the form of parallel
transport.Comment: 36 pages, 12 pdf figures, v2: minor change