The Bondi mass measures the total mass-energy remaining in an isolated system at a retarded time, as defined at future null infinity. It is obtained by integrating the Bondi mass aspect over a sphere, with normalization set by the metric convention.
Outgoing gravitational radiation carries energy away, so the Bondi mass decreases by a nonnegative news-squared flux in the vacuum mass-loss formula. Additional outgoing matter contributes its own flux. This is distinct from the ADM mass defined at spatial infinity: the two quantities use different asymptotic cuts and account differently for radiation that has escaped.[ref]
Bondi-Sachs Formalism by Thomas Mädler and Jeffrey Winicour. §3, mass aspect and Bondi mass-loss formula
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