A detailed first-order post-Newtonian analysis of massive Brans-Dicke theories: numerical constraints and the $\beta$ parameter meaning

Abstract

Massive Brans-Dicke (BD) theory is among the simplest general relativity extensions. It is commonly found as the weak-field limit of other gravitational theories. Here we do a detailed post-Newtonian analysis of massive BD theories. We start by expanding the massive BD field equations following the Will-Nodtvedt Parameterized-Post-Newtonian (PPN) formalism, without point-particle approximations. A single potential that is not present in the standard PPN formalism is found. This new potential hinders immediate PPN conclusions. To proceed, we do a complete first-order post-Newtonian analysis and explicitly derive all the conserved quantities. After demanding that there exists a Newtonian limit by requiring the BD mass to be sufficiently large, we find, as expected, that $\gamma =1$; but there is no effective $\beta$ parameter that can have the same physical role of the standard $\beta$ in PPN formalism. All the others standard PPN parameters can be extended to the massive BD case without issues and are shown to have the same values of general relativity. At last, we consider numerical relations on the periastron advance and the BD mass in two different physical contexts, the orbit of Mercury about the Sun and the orbit of the star S2 about the expected supermassive black hole in the Milky Way.

v2: 12 pages, 5 figures. Accepted in PRD

References in corpus (9)

• The Confrontation between General Relativity and Experiment
• Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole
• de Sitter space and the equivalence between f(R) and scalar-tensor gravity
• Progress in Measurements of the Gravitational Bending of Radio Waves Using the VLBA
• Palatini $f(R)$ gravity in the solar system: post-Newtonian equations of motion and complete PPN parameters
• Post-Newtonian parameter $\gamma$ for multiscalar-tensor gravity with a general potential
• On the Newtonian and Spin-induced Perturbations felt by the Stars Orbiting around the Massive Black Hole in the Galactic Center
• Post-Newtonian $\gamma$-like parameters and the gravitational slip in scalar-tensor and $f(R)$ theories
• Parameterized Post-Newtonian coefficients for Brans-Dicke gravity with d+1 dimensions

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• A note on Gravitational radiation in generalized Brans-Dicke theory: compact binary systems