New improved massive gravity

Abstract

We derive the field equations for topologically massive gravity coupled with the most general quadratic curvature terms using the language of exterior differential forms and a first-order constrained variational principle. We find variational field equations both in the presence and absence of torsion. We then show that spaces of constant negative curvature (i.e. the anti de-Sitter space AdS3) and constant torsion provide exact solutions.