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 firstorder 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.

Weyl covariant theories of gravity in 3-dimensional Riemann–Cartan–Weyl space-times

“…This way, one can introduce dimensionful quantities to the theory. Alternatively, the same method can be applied to other three dimensional massive gravity theories with an action formulation such as New Massive Gravity [16,17], Minimal Massive Gravity [18,19] or New Improved Massive Gravity [20,21] theories. Three dimensional applications are also important because of novel topological and geometrical properties of three dimensional Einstein-Weyl spaces [22,23].…”

“…In our earlier papers[12,13], using an identy we replaced one of the three quadratic curvature invariants in terms of the other two. Here, we do not do this and keep all three quadratic curvature invariants.…”

Thin-shells and thin-shell wormholes in new massive gravity

“…Studying thinshells with double layers may also be of interest, as for these ones demand some other JCs [90]. As another subject for further studies one may have a look into extended theories of NMG and solutions therein [68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83].…”

“…Exploiting the NMG action, a new bi-gravity model is constructed in 3 dimensions in [81]. Finally, a novel work by Dereli and Yetişmişoglu suggests a model (new improved massive gravity (NIMG)) which includes TMG, NMG and minimal massive gravity (MMG) as subclasses of the theory [82,83].…”

The Variational Field Equations of Cosmological Topologically Massive Supergravity

“…A formulation using a first order constrained variational formalism in Riemann‐Cartan spaces in the language of exterior differential forms has been described by us before. [ 8–10 ]…”