Topologically massive gravito-electrodynamics: Exact solutions

We construct two classes of exact solutions to the field equations of topologically massive electrodynamics coupled to topologically massive gravity in 2+1 dimensions. The self-dual stationary solutions of the first class are horizonless, asymptotic to the extreme BTZ black-hole metric, and regular for a suitable parameter domain. The diagonal solutions of the second class, which exist if the two Chern-Simons coupling constants exactly balance, include anisotropic cosmologies and static solutions with a pointlike horizon.