Positivity of energy inn-dimensional Lorentzian spaces

The spinor approach of Witten and Nester is used to show that in ann-dimensional Lorentzian spaceV _n , the conserved total energy-momentum vectorP is nonspace-like. It is shown thatP may be expressed in terms of an integral of an antisymmetric tensorE over ann – 2-dimensional subspace at space-like infinity inV _n .E is expressed in terms of a spinor field inV _n and its covariant derivatives. This tensor is a generalization of that used in the discussion of five-dimensional Lorentzian spaces.