Angular momentum in general relativity I. Definition and asymptotic behaviour

Abstract

Angular momentum in axisymmetric space-times is investigated. The conclusions lead to a general definition suitable for all asymptoticallyflat spaces which is valid both at infinity and on the event horizon of a black hole. This first paper restricts attention to considerations at infinity. Working in terms of the spin coefficient formalism, the field equations are solved asymptotically at large distances and the definition is evaluated. A conservation law is derived and finally the effect on the angular momentum of a supertranslation of the coordinates is discussed.