Positivity and definitions of mass (general relativity)

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Abstract
This work deals with problems and properties of definitions of mass in general relativity. The author proves that it is sufficient for the spinor field determining the Nester-Witten 2-form to satisfy only one complex scalar equation in order that the integral over a convex 2-surface is positive when the dominant energy condition holds. As corollaries he shows that the quasilocal momentum of Ludvigsen and Vickers (1982) is future-pointing, and obtains a proof of the positivity of the Bondi mass which uses a different spinor propagation equation to previous proofs. As another corollary, he shows that there are infinitely many ways of defining a quasilocal 4-momentum which is future-pointing, allows definition of a corresponding positive mass, gives the Bondi and ADM momenta at infinity, is zero in flat spacetime and is correct in the linearized theory and in the spherically symmetric case.

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