2024/08/06 by Gasperín, Edgar, Magdy, Mariem, Mena, Filipe C. · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2408.03389
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 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.