On Global Conservation Laws at Null Infinity

Abstract

The ``standard'' expressions for total energy, linear momentum and also angular momentum of asymptotically flat Bondi metrics at null infinity are also obtained from differential conservation laws on asymptotically flat backgrounds, derived from a quadratic Lagrangian density by methods currently used in classical field theory. It is thus a matter of taste and commodity to use or not to use a reference spacetime in defining these globally conserved quantities. Backgrounds lead to Nœther conserved currents; the use of backgrounds is in line with classical views on conservation laws. Moreover, the conserved quantities are in principle explicitly related to the sources of gravity through Einstein's equations, while standard definitions are not. The relations depend, however, on a rule for mapping spacetimes on backgrounds.