Abstract
The asymptotic behaviour of massless spin-0 fields close to spatial and null infinity in Minkowski space-time is studied by means of Friedrich's cylinder at spatial infinity. The results are applied to a system of equations called the good-bad-ugly which serves as a model for the Einstein field equations in generalized harmonic gauge. The relation between the logarithmic terms (polyhomogeneity) appearing in the solution obtained using conformal methods and those obtained by means of a heuristic method based on Hörmander's asymptotic system is discussed. This review article is based on Duarte et al. (Duarte et al. 2023 Class. Quantum Gravity 40, 055002. (doi:10.1088/1361-6382/acb47e)); Gasperín & Pinto (Gasperín & Pinto 2023 Spin-0 fields and the NP-constants close to spatial infinity in Minkowski spacetime. J. Math. Phys. 64, 082502. (doi:10.1063/5.0158746)). This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'.
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