Some Total Invariants of Asymptotically Flat Space-Times

Abstract

The total energy, momentum, supermomentum, and angular momentum of asymptotically flat space‐times are calculated in terms of coordinate and conformally invariant expressions by taking the limit in an invariant way of the asymptotic symmetry linkages through a sequence of finite closed two‐spaces which converge to a sphere at null infinity. The resulting expressions consist of integrals over the sphere at null infinity of cordinate and conformally invariant quantities. In the case of energy and momentum these integrals may be reduced to expressions previously proposed by Penrose.