Electrodynamic field at spatial infinity

Abstract: The treatment of spatial infinity is one of the remaining major open problems in the theory of isolated self-gravitating systems. Especially when one wants to model scattering of gravitational radiation in spacetime. In this thesis the conformal theory is used to study simple electromagnetic fields, close to spatial infinity. In particular, the trajectory of the moving Coulomb field is studied in compactified Minkowski space. In the formalism, introduced by Penrose, Minkowski metric is rescaled g = Ω^2η to Einstein’s universe, R × S^3. A dual particle, passing through spatial infinity in Einstein’s Universe, emerges from the conformally extended Coulomb field. The particle pair moves antipodally with respect to the retarded and advanced directions. Furthermore, a more recent treatment of spatial infinity, proposed by Friedrich, is studied in conjunction with the electromagnetic field. In this treatment, spatial infinity is blown-up to a cylinder that is a total characteristic of the spacetime. The Newman-Penrose formalism is central to the theory and is used here to rewrite Maxwell’s equations. The blow-up is linked to the sigma-process, a process used to treat singularities in the theory of differential equations. Boosted space-like curves are linked to points on the cylinder via a bijective function. The Newman-Penrose scalars are studied on the cylinder. Finally, a global treatment of spacetime, using global coordinates for adS2 ×S^2, is proposed for further study of spatial infinity in e.g. numerical codes and Newman-Penrose formalism.