Spinor propagation and quasilocal momentum for the Kerr solution

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Abstract
One of the problems associated with defining quasilocal momentum PAA' in general relativity is that of introducing a canonical spin space S on which PAA' acts. It is shown that for a Kerr spacetime, S may be identified with the solution space of an integrable spinor propagation law Del AA' lambda B=0 where is a natural covariant derivative with torsion. The momentum contained within a closed spacelike 2-surface Sigma is shown to have the form PAA'( Sigma ) lambda A lambda A'= integral Sigma F( lambda in S) where F a closed 2-form obtained from the spinor field lambda A corresponding to lambda A. Finally, PAA'( Sigma ) is shown to agree with the Bondi momentum if Sigma surrounds the black hole.

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