Polyhomogeneous spin-0 fields in Minkowski space–time

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’.

At the interface of asymptotics, conformal methods and analysis in general relativity

“…That quite generally the situation is no worse was recently confirmed by Hintz & Vasy [ 34 ]. Work to understand these issues sharply is ongoing, and the detailed structure of the polyhomogeneities exhibited by massless scalar fields on Minkowski space is reviewed in Gasperín’s [ 35 ] contribution to this issue.…”

Relativistic Formulation in Dual Minkowski Spacetime

“…That research work discovered that within quantum perturbation, because of quantum gravitational effects, a point particle cannot be modeled as an infinitely sharp Gaussian. In Gasperin (2024) [7], the research was focused on the investigation of the asymptotic behaviour of massless spin-0 fields close to spatial and null infinity in Minkowski spacetime. In that work, Friedrich's cylinder at spatial infinity was a key framework utilized in that investigation.…”