  All strategies for the treatment of future null-infinity in numerical
relativity involve some form of regularization of the field equations. In a
recent proposal that relies on the dual foliation formalism this is achieved by
the use of an asymptotically Minkowskian generalized harmonic tensor basis. For
the scheme to work however, derivatives of certain coordinate light-speeds must
decay fast enough. Presently, we generalize the method of asymptotic expansions
for nonlinear wave equations to treat first order symmetric hyperbolic systems.
We then use this heuristic tool to extract the expected rates of decay of the
metric near null-infinity in a free-evolution setting. We show, within the
asymptotic expansion, that by carefully modifying the non-principal part of the
field equations by the addition of constraints, we are able to obtain optimal
decay rates even when the constraints are violated. The light-speed condition
can hence be satisfied, which paves the way for the explicit numerical
treatment of future null-infinity. We then study the behavior of the
Trautman-Bondi mass under the decay results predicted by the asymptotic
expansion. Naively the mass seems to be unbounded, but we see first that the
divergent terms can be replaced with a combination of the constraints and the
Einstein field equations, and second that the Bondi mass loss formula is
recovered within the framework. Both of the latter results hold in the presence
of small constraint violations.
