Anti-de-Sitter regular electric multipoles: towards Einstein-Maxwell-AdS solitons

TL;DR

This paper explores the unique electrostatic multipole solutions in Anti-de-Sitter spacetime, revealing the potential existence of regular Einstein-Maxwell solitons due to their distinct decay properties and regularity, supported by analytical perturbation calculations.

Contribution

It demonstrates the possibility of regular, self-gravitating Einstein-Maxwell solitons in AdS spacetime by analyzing multipole decay and regularity, challenging previous no-soliton theorems.

Findings

All multipoles except monopole are regular and finite energy in AdS.

Multipole moments decay as 1/r at infinity, unlike in Minkowski.

First-order metric perturbations for electric multipoles are analytically derived.

Abstract

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.