Scalar gravity with preferred frame: asymptotic post-Newtonian scheme and the weak equivalence principle

TL;DR

This paper introduces a scalar gravity theory with a preferred frame, extending Newtonian dynamics, and demonstrates that a revised isotropic space metric version respects the weak equivalence principle in weak gravitational fields.

Contribution

It presents a new scalar gravity model with an isotropic space metric that maintains energy conservation and adheres to the weak equivalence principle.

Findings

Weak equivalence principle violated in v1 with anisotropic metric

Weak equivalence principle valid in v2 with isotropic metric

Application of post-Newtonian approximation to extended body motion

Abstract

A scalar theory of gravity with a preferred reference frame is presented. It is insisted on the dynamics, which involves a (non-trivial) extension of Newton's second law, and on the new version (v2) with isotropic space metric. We display the energy conservation equation obtained with v2. Then the principles of the asymptotic post-Newtonian approximation are discussed in some detail. The results of its application to the motion of a small extended body in a weakly-gravitating system are given and discussed: the weak equivalence principle was violated in v1, due to its anisotropic space metric (as the standard Schwarzschild metric), but is valid with v2.