On Global Conservation Laws at Null Infinity

TL;DR

This paper explores the derivation of total energy, momentum, and angular momentum at null infinity in asymptotically flat spacetimes, emphasizing the role of background spacetimes and conservation laws from a Lagrangian perspective.

Contribution

It presents a derivation of conserved quantities at null infinity from differential conservation laws using a quadratic Lagrangian, highlighting the significance of background spacetimes.

Findings

Conserved quantities can be derived from a quadratic Lagrangian density.

Background spacetimes lead to N oether conserved currents.

Relations between conserved quantities and sources depend on the mapping rule.

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 N\oe ther 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.