Illusions of general relativity in Brans-Dicke gravity

TL;DR

This paper challenges the common belief that Brans-Dicke theory reduces to general relativity as omega approaches infinity, showing this is false when the matter energy-momentum tensor trace vanishes, using conformal transformations.

Contribution

It introduces a new approach with conformal transformations to clarify the limiting behavior of Brans-Dicke gravity, especially for radiation-like sources.

Findings

Brans-Dicke theory does not always reduce to general relativity in the limit of large omega.

Conformal invariance explains the unaccountable limiting behavior.

The asymptotic behavior of the scalar field is computed using this new approach.

Abstract

Contrary to common belief, the standard tenet of Brans-Dicke theory reducing to general relativity when omega tends to infinity is false if the trace of the matter energy-momentum tensor vanishes. The issue is clarified in a new approach using conformal transformations. The otherwise unaccountable limiting behavior of Brans-Dicke gravity is easily understood in terms of the conformal invariance of the theory when the sources of gravity have radiation-like properties. The rigorous computation of the asymptotic behavior of the Brans-Dicke scalar field is straightforward in this new approach.