Einstein–Maxwell–Anti-de-Sitter spinning solitons

Electrostatics on global Anti-de-Sitter (AdS) spacetime is sharply different from that on global Minkowski spacetime. It admits a multipolar expansion with everywhere regular, finite energy solutions, for every multipole moment except the monopole [1]. A similar statement holds for global AdS magnetostatics. We show that everywhere regular, finite energy, electric plus magnetic fields exist on AdS in three distinct classes: (I) with non-vanishing total angular momentum J; (II) with vanishing J but non-zero angular momentum density  , Tφt; (III) with vanishing J and  Tφt. Considering backreaction, these configurations remain everywhere smooth and finite energy, and we find, for example, Einstein–Maxwell–AdS solitons that are globally – Type I – or locally (but not globally) – Type II – spinning. This backreaction is considered first perturbatively, using analytical methods and then non-perturbatively, by constructing numerical solutions of the fully non-linear Einstein–Maxwell–AdS system. The variation of the energy and total angular momentum with the boundary data is explicitly exhibited for one example of a spinning soliton.