A comment on differential identities for the Weyl spinor perturbations (Q1385321)

The author shows that in a vacuum spacetime of Petrov type \(D\), with cosmological constant, the components of the perturbations of the Weyl spinor along the principal spinors of the background conformal curvature satisfy differential identities which are valid in all normalized spin frames for which basic spinors are double spinors of the background conformal curvature. These identities are exhibited, and it is noted that they are applicable to the energy flux at infinity, or on the horizon, when the background spacetime is the Kerr or Schwarzschild metric.