Newtonian Gravity in the Density-Suppressed Weak-Field Regime: A GETT Reconstruction.

The GETT Correspondence Series Paper 2: Newtonian Gravity as the Density-Suppressed Weak-Field Limit of General Expanse Tension Theory

This paper presents the second study in the GETT Correspondence Series, a programme designed to demonstrate that established physical laws emerge as domain-limit solutions of General Expanse Tension Theory (GETT).

A fundamental requirement of any candidate theory of physics is that it reproduce existing empirical laws within the regimes where those laws have been confirmed experimentally. Paper 1 of the series demonstrated that the density-suppressed weak-field regime of GETT reproduces the full structure of classical kinematics, including Galilean reference frames and the standard equations of inertial motion.

The present work extends this correspondence analysis to the gravitational sector.

Within GETT, gravity arises as an emergent phenomenon associated with gradients in the Holland scalar field, a real scalar field coupled to the Higgs sector through a density-dependent portal interaction. The strength of this coupling is controlled by a density-gate function that determines the dynamical regime of the theory.

In environments characterised by relatively high coarse-grained baryonic density—such as terrestrial laboratories, planetary systems, and the Solar System—the density-gate function is effectively suppressed. Under these conditions the governing scalar-field equation reduces to the classical Poisson equation for the gravitational potential, and the resulting acceleration law becomes identical to the Newtonian inverse-square relation.

From this recovered potential the complete structure of classical gravitational mechanics follows directly. The paper demonstrates the recovery of:

• the Poisson equation for gravitational potential
• the Newtonian inverse-square acceleration law
• conservation of angular momentum in central-force motion
• planar orbital dynamics
• Kepler’s three laws of planetary motion
• mechanical energy relations for gravitational systems
• escape velocity relations
• the virial theorem for bound systems

Illustrative numerical examples drawn from Solar-System dynamics confirm that the reconstructed equations reproduce observed orbital periods and gravitational behaviour across multiple scales.

A systematic correspondence audit confirms that all tested structural elements of Newtonian gravitational theory are reproduced exactly within the density-suppressed weak-field regime of GETT.

Newtonian gravity therefore appears not as a fundamental interaction, but as a domain-limit solution of the underlying scalar-field dynamics of GETT.

Subsequent papers in the GETT Correspondence Series will examine regimes in which the density-gate function becomes active, including low-density environments associated with galactic rotation curves and large-scale cosmological dynamics.