Illusions of general relativity in Brans-Dicke gravity

Abstract

Contrary to common belief, the standard tenet of Brans-Dicke theory reducing to general relativity in the ω → ∞ limit is false when 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.

Brans–dicke Theory: Jordan Versus Einstein Frame

“…The scalar field couples to both matter and spacetime geometry and the strength of the coupling is represented by a single dimensionless constant parameter ω. It is generally considered that under the limit ω → ∞, the vacuum (or for traceless matter field) BD theory (and its dynamic generalization) reduces to the GR but the recent finding suggests that such a convergence is not always true [18][19][20][21][22]. In the Jordan conformal frame, the BD action takes the form…”

Field Equations and Lagrangian for the Kaluza Metric Evaluated with Tensor Algebra Software

“…The expression given for̃5 is similar to (10) but is missing the term iñ5 5 and is divided by 2 . The expression given for̃] is similar to (12) but is missing all the terms iñ5 5 and̃] 5 . Interestingly, during his discussion of the 5D Einstein tensor̃, Thiry fails to write down an expression for̃5 5 .…”

Averaging inhomogeneities in scalar–tensor cosmology

“…Inserting this relationship into the equation of motion for φ, it is possible to solve with respect to a(t). The effective gravitational coupling is finite for both small and large times t, and the corresponding averaged scale factor is a D (t) = e is indeed correct (see [31] and references therein).…”