A model of non-minimally coupled gravitation and electromagnetism in (1+2) dimensions

TL;DR

This paper explores a three-dimensional gravity-electromagnetism model with non-minimal $RF^2$ couplings, deriving field equations and identifying conditions for exact self-dual solutions on constant negative curvature spaces.

Contribution

It extends topologically massive gravity with electrodynamics by incorporating the most general non-minimal $RF^2$-type couplings and finds exact self-dual solutions.

Findings

Derived variational field equations for the model.

Identified conditions for the existence of self-dual solutions.

Provided explicit solutions on constant negative curvature backgrounds.

Abstract

Following earlier works of Dereli and collaborators, we study a three dimensional toy model where we extend the topologically massive gravity with electrodynamics by the most general $RF^2$-type non-minimal coupling terms. Here $R$ denotes the possible curvature terms and $F$ denotes the electromagnetic 2-form. We derive the variational field equations and look for exact solutions on constant negative curvature space-times with a constant, self-dual electromagnetic field. The notion of self-dual electromagnetic fields in three dimensions is introduced by Dereli and collaborators in the study of exact solutions of models with gravity-electromagnetism couplings. We note the conditions that the parameters of the model have to satisfy for these self-dual solutions to exist.