The good-bad-ugly system near spatial infinity on flat spacetime

TL;DR

This paper analyzes a simplified model of Einstein's equations near spatial infinity in flat spacetime using conformal methods, revealing insights into the asymptotic structure and polyhomogeneous expansions.

Contribution

It applies Friedrich's cylinder construction to the good-bad-ugly system, connecting rigorous conformal analysis with heuristic asymptotic methods near spatial infinity.

Findings

Established the relation between polyhomogeneous expansions and asymptotic systems.

Demonstrated the effectiveness of conformal rescaling in analyzing Einstein-like systems.

Provided a framework for studying gravitational fields near spatial infinity in Minkowski spacetime.

Abstract

A system of equations that serves as a model for the Einstein field equation in generalised harmonic gauge called the good-bad-ugly system is studied in the region close to null and spatial infinity in Minkowski spacetime. This analysis is performed using H. Friedrich's cylinder construction at spatial infinity and defining suitable conformally rescaled fields. The results are translated to the physical set up to investigate the relation between the polyhomogeneous expansions arising from the analysis of linear fields using the $i^0$-cylinder framework and those obtained through a heuristic method based on H\"ormander's asymptotic system.