On a modified-Lorentz-transformation based gravity model confirming basic GRT experiments

TL;DR

This paper introduces a scalar Lorentz-covariant gravity model based on modified Lorentz transformations that aligns with basic tests of General Relativity, using a background geometry and a gravitational affecting function.

Contribution

It develops a gravity model rooted in Poincaré's conventionalism with modified Lorentz transformations, unifying elements from previous theories and confirming basic GRT experiments.

Findings

Model reproduces light deflection, perihelion precession, radar delay, and spectral line shifts.

Uses a covariant Hamiltonian framework for particles and photons.

Recovers Lorentz-Poincaré gravity Lagrangian and incorporates variable speed of light and mass concepts.

Abstract

Implementing Poincar\'e's `geometric conventionalism' a scalar Lorentz-covariant gravity model is obtained based on gravitationally modified Lorentz transformations (or GMLT). The modification essentially consists of an appropriate space-time and momentum-energy scaling ("normalization") relative to a nondynamical flat background geometry according to an isotropic, nonsingular gravitational `affecting' function Phi(r). Elimination of the gravitationally `unaffected' S_0 perspective by local composition of space-time GMLT recovers the local Minkowskian metric and thus preserves the invariance of the locally observed velocity of light. The associated energy-momentum GMLT provides a covariant Hamiltonian description for test particles and photons which, in a static gravitational field configuration, endorses the four `basic' experiments for testing General Relativity Theory: gravitational i) deflection of light, ii) precession of perihelia, iii) delay of radar echo, iv) shift of spectral lines. The model recovers the Lagrangian of the Lorentz-Poincar\'e gravity model by Torgny Sj\"odin and integrates elements of the precursor gravitational theories, with spatially Variable Speed of Light (VSL) by Einstein and Abraham, and gravitationally variable mass by Nordstr\"om.