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

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Contrary to common belief, (electro)vacuum Brans-Dicke gravity does not reduce to general relativity for large Brans-Dicke coupling $\ensuremath{\omega}$, a problem which has never been fully solved. Two new approaches, independent… Click to show full abstract

Contrary to common belief, (electro)vacuum Brans-Dicke gravity does not reduce to general relativity for large Brans-Dicke coupling $\ensuremath{\omega}$, 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 $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\infty}$ 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.

Keywords: two new; new approaches; limit; ensuremath; gravity; brans dicke

Journal Title: Physical Review D
Year Published: 2019

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