Quadratic curvature gravity with second order trace and massive gravity models in three dimensions

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.

Impulsive gravitational waves in general massive 3D gravity

“…The field equations given by Eq. (20) for the CGMG model are valid relative to both an orthonormal coframe [24,25] as well as to the seminull coframe to be defined in the preliminary section above.…”

Multi-scalar-tensor equivalents for modified gravitational actions

“…In this section the scheme of calculation of variational derivatives relative to an orthonormal coframe will briefly be presented [29][30][31][32]. In the subsequent sections, the general formulas of this section will be applied to all the modified gravitational actions considered below.…”

“…The QC Lagrangians having this particular property in arbitrary dimension n ! 3 have been constructed in [31].…”

“…However, intending the modification of the quadratic curvature Lagrangian densities in the fðRÞ spirit, it is convenient to work with all three scalars. For further calculational details for the variational derivatives of the Lagrangians relative to an orthonormal coframe considered here, see [30][31][32].…”

“…relative to an orthonormal coframe [31]. Equation (70) can be considered to be an extension of the field equations (22).…”