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On Global Conservation Laws at Null Infinity
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