Asymptotics of spin-0 fields and conserved charges on n-dimensional Minkowski spaces
arXiv:2408.03389 · doi:10.1016/j.geomphys.2024.105389
Abstract
We use conformal geometry methods and the construction of Friedrich's cylinder at spatial infinity to study the propagation of spin- fields (solutions to the wave equation) on -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- 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 even dimensions, we find that there are infinitely many well-defined asymptotic charges at the critical sets, while for odd higher dimensions there exists no non-trivial asymptotic charges that remain regular at the critical sets.
17 pages, 1 figure; This version incorporates changes based on comment made in arXiv:2412.05088. The technical aspects of the paper remains unchanged but the final result listed in Theorem 1 differs from previous version
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