New Improved Massive Gravity and Three Dimensional Spacetimes of Constant Curvature and Constant Torsion

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 $Ad{S}_3$) and constant torsion provide exact solutions.

16 pages

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• Weyl Covariant Quadratic Curvature Gravity in 3-Dimensional Riemann-Cartan-Weyl Space-Times
• A model of non-minimally coupled gravitation and electromagnetism in (1+2) dimensions
• A note on the pp-wave solution of Minimal Massive 3D Gravity coupled with Maxwell-Chern-Simons theory