Newman-Penrose constants of the Kerr-Newman metric

The Newman-Unti formalism of the Kerr-Newman metric near future null infinity is developed, with which the Newman-Penrose constants for both the gravitational and electromagnetic fields of the Kerr-Newman metric are computed and shown to be zero. The multipole structure near future null infinity in the sense of Janis-Newman of the Kerr-Newman metric is then further studied. It is found that up to the $2^4$-pole, modulo a constant dependent upon the order of the pole, these multipole moments agree with those of Geroch-Hansen multipole moments defined at spatial infinity.