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arXiv · 0908.0751

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

T. M. Adamo·E. T. Newman
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Abstract

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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T. M. Adamo, E. T. Newman. 2009-08-05. Vacuum non-expanding horizons and shear-free null geodesic congruences. https://doi.org/10.1088/0264-9381%2F26%2F23%2F235012

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