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

TL;DR

This paper derives field equations for a generalized massive gravity theory in three dimensions, incorporating quadratic curvature terms, and identifies exact solutions with constant negative curvature and torsion.

Contribution

It introduces a new formulation of topologically massive gravity with quadratic curvature terms using differential forms and finds exact solutions with constant curvature and torsion.

Findings

Exact solutions in $AdS_3$ with constant negative curvature

Solutions with constant torsion

Field equations derived in presence and absence of 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 $AdS_3$) and constant torsion provide exact solutions.