Neighbourhoods of Isolated Horizons and their stationarity
arXiv:1404.7836 · doi:10.1088/0264-9381/31/17/175012
Abstract
A distinguished (invariant) Bondi-like coordinate system is defined in the spacetime neighbourhood of a non-expanding horizon of arbitrary dimension via geometry invariants of the horizon. With its use, the radial expansion of a spacetime metric about the horizon is provided and the free data needed to specify it up to given order are determined in spacetime dimension . For the case of an electro-vacuum horizon in -dimensional spacetime the necessary and sufficient conditions for the existence of a Killing field at its neighbourhood are identified as differential conditions on the horizon data and data on null surface transversal to the horizon.
arXiv commentRevTex4.1, BibTex, 36 pages, replaced with revised version to appear in Class.Quant.Grav
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