Extension of bundles of null directions
Pawel Nurowski, Lane Hughston, David Robinson
Abstract
The geometry of P, the bundle of null directions over an Einstein space-time, is studied. The full set of invariants of the natural G-structure on P is constructed using the Cartan method of equivalence. This leads to an extension of P which is an elliptic fibration over the space-time. Examples are given which show that such an extension, although natural, is not unique. A reinterpretation of the Petrov classification in terms of the fibres of an extension of P is presented.
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