Vacuum non-expanding horizons and shear-free null geodesic congruences

Details Vacuum non-expanding horizons and shear-free null geodesic congruences Vacuum non-expanding horizons and shear-free null geodesic congruences

2009-08-05

arxiv.org/abs/0908.0751v1

Class.Quant.Grav.26:235012,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages

Scientific paper

10.1088/0264-9381/26/23/235012

We investigate the geometry of a particular class of null surfaces in space-time called vacuum Non-Expanding Horizons (NEHs). Using the spin-coefficient equation, we provide a complete description of the horizon geometry, as well as fixing a canonical choice of null tetrad and coordinates on a NEH. By looking for particular classes of null geodesic congruences which live exterior to NEHs but have the special property that their shear vanishes at the intersection with the horizon, a good cut formalism for NEHs is developed which closely mirrors asymptotic theory. In particular, we show that such null geodesic congruences are generated by arbitrary choice of a complex world-line in a complex four dimensional space, each such choice induces a CR structure on the horizon, and a particular world-line (and hence CR structure) may be chosen by transforming to a privileged tetrad frame.

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