QUASI-LOCAL MASS CONSTRUCTIONS WITH POSITIVE ENERGY

We propose a pair of new quasilocal constructions for the four-momentum and mass of the gravitational and matter fields within generic two-surfaces. We show that the momenta are future pointing when the dominant energy condition is satisfied on a spanning three-surface and the two-surface is suitably convex. The new definition gives zero in flat space and the correct results in linearized theory, at spacelike infinity and for round spheres. At null infinity at least one definition gives the Bondi mass. These definitions can be embedded in definitions of angular momentum.