Exact self dual vortices in $d=3$ Majumdar-Papapetrou dilaton gravity

TL;DR

This paper constructs exact solutions in 3D Einstein-Maxwell-Dilaton gravity using self-dual Nielsen-Olesen vortices, revealing unique properties like zero total energy and long-range fields due to 2D Green's functions.

Contribution

It introduces a novel class of exact solutions coupling NO vortices with Einstein-Maxwell-Dilaton gravity under the MP relation, highlighting their unique asymptotic and energetic properties.

Findings

Solutions are explicit in terms of vortex functions.

Vortices have zero total ADM energy.

Electric fields are long-range with zero net charge.

Abstract

We show that self-dual Nielsen Olesen (NO) vortices in $3$ dimensions give rise to a class of exact solutions when coupled to Einstein Maxwell Dilaton gravity obeying the Majumdar-Papapetrou(MP) relation between gravitational and Maxwell couplings , provided certain Chern-Simons type interactions are present. The metric may be solved for explicitly in terms of the NO vortex function and is asymptotic to Euclidean space with signature (-1,-1,-1). The MP electric field is long range but, strictly speaking, the charge of the vortices is zero since the field dies off as $O(1/r (ln r)^2)$. The total ADM energy integral of such vortices is {\it{zero}}. These peculiarities are due to the nature of the two dimensional Greens function.