Abstract
In spinorial proofs of the positive energy theorem in general relativity the total energy is expressed as the integral of a certain 3-form over a spacelike hypersurface in spacetime. The 3-form depends on a spinor field and by assuming that this spinor field satisfies the Sen--Witten equation, the 3-form becomes everywhere positive. By writing part of the 3-form as a quadratic form in first order derivatives of the spinor field, it is here shown that the Sen--Witten equation can be replaced by a large class of other differential equations, all of which can be used to prove the positive energy theorem. The class is naturally represented by eight complex functions restricted by two inequalities but otherwise arbitrary.
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