Polyhomogeneous spin-0 fields in Minkowski spacetime

TL;DR

This paper investigates the asymptotic behavior of massless spin-0 fields near infinity in Minkowski spacetime using Friedrich's cylinder, connecting conformal and heuristic methods, and applies findings to a model related to Einstein's equations.

Contribution

It provides a detailed analysis of polyhomogeneous structures in spin-0 fields and relates conformal and heuristic approaches within the context of Minkowski spacetime.

Findings

Logarithmic terms in solutions are characterized and compared.

The relation between conformal and heuristic methods is clarified.

Results are applied to the good-bad-ugly system modeling Einstein equations.

Abstract

The asymptotic behaviour of massless spin-0 fields close to spatial and null infinity in Minkowski spacetime 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 generalised 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 H\"ormander's asymptotic system is discussed. This review article is based on Class. Quantum Grav. 40 055002 and arXiv:2304.11950.