Twistor theory and the energy—momentum and angular momentum of the gravitational field at spatial infinity

Abstract

Penrose’s ‘quasi-local mass and angular momentum’ (Penrose, Proc. R. Soc. Lond . A 381, 53 (1982)) is investigated for 2-surfaces near spatial infinity in both linearized theory on Minkowski space and full general relativity. It is shown that for space-times that are radially smooth of order one in the sense of Beig & Schmidt ( Communs math. Phys . 87, 65 (1982)), with asymptotically electric Weyl curvature, there exists a global concept of a twistor space at spatial infinity. Global conservation laws for the energy—momentum and angular momentum are obtained, and the ten conserved quantities are shown to be invariant under asymptotic coordinate transformations. The relation to other definitions is discussed briefly.