Quadratic Curvature Gravity with Second Order Trace and Massive Gravity Models in Three Dimensions

TL;DR

This paper constructs quadratic curvature gravity models in three and higher dimensions with second order trace field equations, relating massive gravity theories and exploring their mathematical properties.

Contribution

It introduces new quadratic curvature gravity models with second order trace equations and connects massive gravity theories through specific conditions in arbitrary dimensions.

Findings

Pure quadratic curvature lagrangians with second order trace contain three free parameters.

Field equations of these models can be expressed using the Schouten tensor.

Conditions under which topologically massive gravity is a 'square root' of new massive gravity are identified.

Abstract

The quadratic curvature lagrangians having metric field equations with second order trace are constructed relative to an orthonormal coframe. In $n>4$ dimensions, pure quadratic curvature lagrangian having second order trace constructed contains three free parameters in the most general case. The fourth order field equations of some of these models, in arbitrary dimensions, are cast in a particular form using the Schouten tensor. As a consequence, the field equations for the New massive gravity theory are related to those of the Topologically massive gravity. In particular, the conditions under which the latter is "square root" of the former are presented.