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

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, selfdual 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 gravityelectromagnetism couplings. We note the conditions that the parameters of the model have to satisfy for these self-dual solutions to exist.