This assumption is justified because we are ultimately interested in the radiation field at some given finite
post-Newtonian precision like 3PN, and because only a finite number of multipole moments can contribute at
any finite order of approximation. With a finite number of multipoles in the linearized metric (26, 27, 28),
there is a maximal multipolarity
at any post-Minkowskian order
, which grows linearly with
.