1. Asymptotics of spin-0 fields and conserved charges on n-dimensional Minkowski spaces
- Author
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Gasperín, Edgar, Mohamed, Mariem Magdy Ali, and Mena, Filipe C.
- Subjects
General Relativity and Quantum Cosmology ,Mathematical Physics ,Mathematics - Differential Geometry - Abstract
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., Comment: 17 pages, 1 figure
- Published
- 2024