3,293 research outputs found
Degenerate Sectors of the Ashtekar Gravity
This work completes the task of solving locally the Einstein-Ashtekar
equations for degenerate data. The two remaining degenerate sectors of the
classical 3+1 dimensional theory are considered. First, with all densitized
triad vectors linearly dependent and second, with only two independent ones. It
is shown how to solve the Einstein-Ashtekar equations completely by suitable
gauge fixing and choice of coordinates. Remarkably, the Hamiltonian weakly
Poisson commutes with the conditions defining the sectors. The summary of
degenerate solutions is given in the Appendix.Comment: 19 pages, late
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
CR Structures and Asymptotically Flat Space-Times
We discuss the unique existence, arising by analogy to that in algebraically
special space-times, of a CR structure realized on null infinity for any
asymptotically flat Einstein or Einstein-Maxwell space-time.Comment: 6 page
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
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