Bi-twistors: An extension of twistor theory for general spacetimes

Twistor theory was initially developed to describe the geometry of Minkowski spacetime in terms of its null geodesics. The natural generalization to curved spacetimes requires the ubiquitous existence of alpha-planes, this requiring the Weyl curvature to be anti-self-dual, which for a real spacetime implies conformal flatness. A bi-twistor, however, incorporates both a twistor and a dual-twistor, together (with their canonical commutation relations), and the role of the alpha-planes is simply replaced by that of null geodesics, which are ubiquitous in any spacetime. Accordingly, bi-twistor theory can be developed so as to apply to spacetimes generally.