Some exact solutions of all $f(R_{\mu \nu })$ theories in three dimensions

We find constant scalar curvature Type-N and Type-D solutions in all higher curvature gravity theories with actions of the form $f(R_{\mu \nu })$ that are built on the Ricci tensor, but not on its derivatives. In our construction, these higher derivative theories inherit some of the previously studied solutions of the cosmological topologically massive gravity and the new massive gravity field equations, once the parameters of the theories are adjusted. Besides the generic higher curvature theory, we have considered in some detail the examples of the quadratic curvature theory, the cubic curvature theory, and the Born-Infeld extension of the new massive gravity.