The Bondi mass is an asymptotic mass associated with null infinity or with compatible hyperboloidal initial data. For an energy-momentum charge that is future timelike, its invariant normalization
is
An initial-data functional must be distinguished from a charge of a cut of null infinity, whose identification requires a compatible spacetime development.
Chruściel, P. T.; Jezierski, J.; and Łęski, S. "The Trautman-Bondi Mass of Hyperboloidal Initial Data Sets." Adv.
Theor. Math. Phys.8, 83-139, 2004. https://doi.org/10.4310/ATMP.2004.v8.n1.a2.