Asymptotics of spin-0 fields and conserved charges on n-dimensional Minkowski spaces

We use conformal geometry methods and the construction of Friedrich's cylinder at spatial infinity to study the propagation of spin-\(0\) fields (solutions to the wave equation) on \(n\)-dimensional Minkowski spacetimes in a neighbourhood of spatial and null infinity. We obtain formal solutions...

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Bibliographic Details
Published inarXiv.org
Main Authors Gasperín, Edgar, Ali Mohamed, Mariem Magdy, Mena, Filipe C
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 08.08.2024
Subjects
Asymptotic methods
Asymptotic properties
Asymptotic series
Infinity
Minkowski space
Series expansion
Spatial data
Wave equations
Wave propagation
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Summary:We use conformal geometry methods and the construction of Friedrich's cylinder at spatial infinity to study the propagation of spin-\(0\) fields (solutions to the wave equation) on \(n\)-dimensional Minkowski spacetimes in a neighbourhood of spatial and null infinity. We obtain formal solutions written in terms of series expansions close to spatial and null infinity and use them to compute non-trivial asymptotic spin-\(0\) charges. It is shown that if one considers the most general initial data within the class considered in this paper, the expansion is poly-homogeneous and hence of restricted regularity at null infinity. Furthermore, we derive the conditions on the initial data needed to obtain regular solutions and well-defined limits for the asymptotic charges at the critical sets where null infinity and spatial infinity meet. In four dimensions, we find that there are infinitely many well-defined asymptotic charges at the critical sets, while for higher dimensions there is only a finite number of non-trivial asymptotic charges that remain regular at the critical sets.
ISSN:2331-8422