Einstein-Maxwell gravity coupled to a scalar field in 2+1-dimensions

We consider Einstein-Maxwell-self-interacting scalar field theory described by a potential $V\left(\varphi \right)$ in $2+1-$dimensions. The self-interaction potential is chosen to be a highly non-linear double-Liouville type. Exact solutions, including chargeless black holes and singularity-free non-black hole solutions are obtained in this model.