Conditions of Equivalence of Spinor and Tensor Methods in the Problem of Positive Definiteness of the Gravitational Problem

Abstract

It is demonstrated that J. Nester's tensor method for proving the theorem on the positive definiteness of gravitational energy in an asymptotically Minkowsky space is equivalent to E. Witten's spinor method, in which the Saint–Witten equation must be completed with a linear term that includes the gradient of a certain scalar potential. A new proof of the theorem on the positive definiteness of energy is proposed.