A Lorentz-Poincar\'e type interpretation of the Weak Equivalence Principle

TL;DR

This paper presents a Lorentz-Poincaré type scalar-vector gravity model that interprets the Weak Equivalence Principle within a local inertial frame, aligning with General Relativity at the first Post-Newtonian order and offering a new perspective on parallel transport.

Contribution

It introduces a scalar-vector gravitation model with a Lorentz-Poincaré interpretation that explains the Weak Equivalence Principle and provides a physical understanding of parallel transport.

Findings

Model is compatible with General Relativity at first Post-Newtonian order

Provides a physical interpretation of parallel transport within the model

Develops a geodesic deviation concept in the scalar-vector framework

Abstract

The validity of the Weak Equivalence Principle relative to a local inertial frame is detailed in a scalar-vector gravitation model with Lorentz-Poincar\'e type interpretation. Given the previously established first Post-Newtonian concordance of dynamics with General Relativity, the principle is to this order compatible with GRT. The gravitationally modified Lorentz transformations, on which the observations in physical coordinates depend, are shown to provide a physical interpretation of \emph{parallel transport}. A development of ``geodesic'' deviation in terms of the present model is given as well.