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

The Weak Null Condition in Free-evolution Schemes for Numerical Relativity: Dual Foliation GHG with Constraint Damping