A Spatially-VSL Gravity Model with 1-PN Limit of GRT

Abstract

In the static field configuration, a spatially-Variable Speed of Light (VSL) scalar gravity model with Lorentz-Poincaré interpretation was shown to reproduce the phenomenology implied by the Schwarzschild metric. In the present development, we effectively cover configurations with source kinematics due to an induced sweep velocity field w. The scalar-vector model now provides a Hamiltonian description for particles and photons in full accordance with the first Post-Newtonian (1-PN) approximation of General Relativity Theory (GRT). This result requires the validity of Poincaré's Principle of Relativity, i.e. the unobservability of 'preferred' frame movement. Poincaré's principle fixes the amplitude of the sweep velocity field of the moving source, or equivalently the 'vector potential' ξ of GRT (e.g.; S. Weinberg, Gravitation and cosmology, 1972), and provides the correct 1-PN limit of GRT. The implementation of this principle requires acceleration transformations derived from gravitationally modified Lorentz transformations. A comparison with the acceleration transformation in GRT is done. The present scope of the model is limited to weak-field gravitation without retardation and with gravitating test bodies. In conclusion the model's merits in terms of a simpler space, time and gravitation ontology -in terms of a Lorentz-Poincaré-type interpretation-are explained (e.g. for 'frame dragging', 'harmonic coordinate condition').

A Lorentz-Poincaré Type Interpretation of the Weak Equivalence Principle

“…Notwithstanding that Lorentz's electromagnetic preliminary gravitation theory [18] nor Poincaré's Newtonian Lorentz-covariant gravitation theory [20] were not conceived along the line here presented; we introduce the term L-P type because of the continuity with the Lorentz-Poincaré interpretation of SRT originally pertaining to physical effects on configurations of matter due to motion. Now however, these effects are due both to position in the gravitation field as well as a relative kinematics [5,6]. This L-P type of development will explicitly use two levels of description: gravitationally affected observations versus gravitationally unaffected "observations".…”

A look at the abandoned contributions to cosmology of Dirac, Sciama, and Dicke

“…[25,26,27]), the representations in terms of a spatially varying speed of light (e.g. [20,28,15,29,30]) have to gain yet broad acceptance.…”

“…Dicke's proposal belongs to the 'conservative' VSL theories that do not postulate exotic dependencies of c but widely agree with general relativity (GR) in the sense that a variable c in a flat background metric generates a curved space. While recent VSL theories had to suffer a couple of objections, these do not apply to the present 'bimetric' type, since the notion of VSL is implicitly present in GR (see [15], ref. 70, with numerous excerpts of GR textbooks).…”

“…Vice versa, when ∇c vanishes,ċ will change f and leave λ constant. Therefore, assuming an isotropic DSD universe 15 This describes approximately the evolution, since detailed assumptions for 0 < t < t 0 cannot be given. 16 In the matter-dominated epoch.…”

“…Defining c with respect to the latter scales, one can equivalently say that c is lowered 24 in the gravitational field (cfr. [37], p. 111, and [15], ref. 70).…”