Parametrizations in scalar-tensor theories of gravity and the limit of general relativity

TL;DR

This paper analyzes scalar-tensor theories of gravity, showing that the conditions for these theories to reduce to general relativity are independent of scalar field parametrizations and can be examined in different conformal frames.

Contribution

It demonstrates that the limits of general relativity in scalar-tensor theories are invariant under scalar field transformations and can be studied in both Jordan and Einstein frames.

Findings

Limits of general relativity are independent of scalar field parametrization.

Transformation between scalar fields may be singular at the limit.

The limit can be analyzed in multiple conformal frames.

Abstract

We consider a general scalar-tensor theory of gravity and review briefly different forms it can be presented (different conformal frames and scalar field parametrizations). We investigate the conditions under which its field equations and the parametrized post-Newtonian parameters coincide with those of general relativity. We demonstrate that these so-called limits of general relativity are independent of the parametrization of the scalar field, although the transformation between scalar fields may be singular at the corresponding value of the scalar field. In particular, the limit of general relativity can equivalently be determined and investigated in the commonly used Jordan and Einstein frames.