Extension of bundles of null directions

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.

LaTex file, accepted in CQG

References in corpus (3)

• Twistor Bundles, Einstein Equations and Real Structures
• On a certain formulation of the Einstein equations
• Elliptic fibrations associated with the Einstein spacetimes

Cited by in corpus (1)

• Space-Times Admitting Isolated Horizons