 Parallel spinors and vanishing ADM mass

A nonzero spacetime parallel spinor makes the Nester two-form vanish, so its ADM boundary charge vanishes. For complete regular spin initial data in an asymptotically flat spacetime under the dominant energy condition, the ADM momentum is future causal. Its contraction with the spinor's nonzero future causal Dirac current cannot vanish if the momentum is timelike. Thus the invariant ADM mass is zero; in a rest frame this gives zero energy. Local parallel-spinor existence without asymptotic/global hypotheses does not establish this mass conclusion.