On Magnetic solution to 2+1 Einstein--Maxwell gravity

TL;DR

This paper reinterprets the 2+1 dimensional magnetic solution in Einstein--Maxwell gravity, showing it is a simpler, effectively one-parameter solution with a gauge-related mass parameter, and offers an alternative source interpretation.

Contribution

It demonstrates that the magnetic solution's mass parameter is a gauge artifact, simplifying the solution to a one-parameter form and providing an alternative interpretation of its source.

Findings

The mass parameter can be rescaled to minus one, making the solution effectively one-parameter.

The magnetic solution describes a radial magnetic field in 2+1 anti-de Sitter space.

An alternative source interpretation to previous models is proposed.

Abstract

The three--dimensional magnetic solution to the Einstein--Maxwell field equations have been considered by some authors. Several interpretations have been formulated for this magnetic spacetime. Up to now this solution has been considered as a two--parameter self--consistent field. We point out that the parameter related to the mass of this solution is just a pure gauge and can be rescaled to minus one. This implies that the magnetic metric has really a simple form and it is effectively one-parameter solution, which describes a distribution of a radial magnetic field in a 2+1 anti--de Sitter background space--time. We consider an alternative interpretation to the Dias--Lemos one for the magnetic field source.