  We discuss electrostatics in Anti-de-Sitter ($AdS$) spacetime, in global
coordinates. We observe that the multipolar expansion has two crucial
differences to that in Minkowski spacetime. First, there are everywhere regular
solutions, with finite energy, for every multipole moment except for the
monopole. Second, all multipole moments decay with the same inverse power of
the areal radius, $1/r$, as spatial infinity is approached. The first
observation suggests there may be regular, self-gravitating, Einstein-Maxwell
solitons in $AdS$ spacetime. The second observation, renders a
Lichnerowicz-type no-soliton theorem inapplicable. Consequently, we suggest
Einstein-Maxwell solitons exist in $AdS$, and we support this claim by
computing the first order metric perturbations sourced by test electric field
multipoles, which are obtained analytically in closed form.
