A spatially-VSL gravity model with 1-PN limit of GRT

TL;DR

This paper develops a scalar gravity model based on Poincare's approach, offering an alternative interpretation of GRT with a variable speed of light and matching the first Post-Newtonian approximation.

Contribution

It introduces a scalar gravity model with spatially variable light speed, derived from a geometric conventionalist perspective, aligning with GRT's phenomenology and Post-Newtonian limits.

Findings

Model reproduces Schwarzschild phenomenology in static fields.

Incorporates a 'sweep velocity' for source kinematics.

Aligns with first Post-Newtonian approximation of GRT.

Abstract

A scalar gravity model is developed according the 'geometric conventionalist' approach introduced by Poincare (Einstein 1921, Poincare 1905, Reichenbach 1957, Gruenbaum1973). In principle this approach allows an alternative interpretation and formulation of General Relativity Theory (GRT), with distinct i) physical congruence standard, and ii) gravitation dynamics according Hamilton-Lagrange mechanics, while iii) retaining empirical indistinguishability with GRT. In this scalar model the congruence standards have been expressed as gravitationally modified Lorentz Transformations (Broekaert 2002). The first type of these transformations relate quantities observed by gravitationally 'affected' (natural geometry) and 'unaffected' (coordinate geometry) observers and explicitly reveal a spatially variable speed of light (VSL). The second type shunts the unaffected perspective and relates affected observers, recovering i) the invariance of the locally observed velocity of light, and ii) the local Minkowski metric (Broekaert 2003). In the case of a static gravitation field the model retrieves the phenomenology implied by the Schwarzschild metric. The case with proper source kinematics is now described by introduction of a 'sweep velocity' field w: The model then provides a hamiltonian description for particles and photons in full accordance with the first Post-Newtonian approximation of GRT (Weinberg 1972, Will 1993).