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

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 $R{F}^2$-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.