= Parallel spinors and vanishing ADM mass
{title2=$EV_\infty^0-P_iV_\infty^i=0\ \Longrightarrow\ M_{\rm ADM}=0$}
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.
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