Abstract: 

We present an algorithm for deriving the precise asymptotics of both linear and non-linear wave propagation in asymptotically flat spacetimes, inclusive of non-stationary spacetimes without any spherical symmetry assumptions. Our method combines local energy decay, the r^p method, and a spectral analysis using resolvent expansions near zero energy, complemented with geometric singular analysis. We position certain prior results related to Price's law (from general relativity in three spatial dimensions) as special cases within our broader framework. This research carries implications for the Strong Cosmic Censorship Conjecture in general relativity and for the interactions of waves with spatially-localized entities, notably solitons.