Two new approaches to the anomalous limit of Brans-Dicke to Einstein gravity

Abstract

Contrary to common belief, (electro)vacuum Brans-Dicke gravity does not reduce to general relativity for large Brans-Dicke coupling $ω$, a problem which has never been fully solved. Two new approaches, independent from each other, shed light on this issue producing the same result: in the limit $ω\rightarrow \infty $ an (electro)vacuum Brans-Dicke spacetime reduces to a solution of the Einstein equations sourced, not by (electro)vacuum, but by a minimally coupled scalar field. The latter is shown to coincide with the Einstein frame scalar field. The first method employs a direct analysis of the Einstein frame, while the second (complementary and independent) method uses an imperfect fluid representation of Brans-Dicke gravity together with a little known 1-parameter symmetry group of this theory.

Explanation and bibliography expanded, matches version published in Phys. Rev. D