Einstein-Maxwell-Anti-de-Sitter spinning solitons

TL;DR

This paper constructs and analyzes smooth, finite-energy Einstein-Maxwell-AdS solitons with various angular momentum properties, using both analytical and numerical methods, revealing new spinning solutions in AdS spacetime.

Contribution

It introduces new classes of regular, finite-energy Einstein-Maxwell-AdS solitons with different angular momentum configurations, including spinning solutions, through perturbative and non-perturbative approaches.

Findings

Existence of regular, finite-energy electric and magnetic fields on AdS in three classes.

Construction of Einstein-Maxwell-AdS solitons with non-zero total angular momentum.

Explicit relation between boundary data and soliton energy and angular momentum.

Abstract

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 (arXiv:1507.04370). 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, $T^t_\varphi$; $(III)$ with vanishing $J$ and $T^t_\varphi$. 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.