What does this research mean for the field?

Density-dependent gravity is geometry-independent, as the stellar effective gravity formula matches the cosmological result to an O(10⁻⁵⁰) correction, demonstrating that previously observed numerical divergences were merely implementation artifacts. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To formally derive the effective gravitational constant in static spherical symmetry and demonstrate its geometry independence.

April 3, 2026Open Access

Closing the Gap: Formal Proof that CCEGA P39. Density-Dependent Gravity is Geometry-Independent

Key Points

To formally derive the effective gravitational constant in static spherical symmetry and demonstrate its geometry independence.
Applied Gauss-Codazzi projection techniques.
Examined contributions from the bulk Weyl tensor.
Evaluated effective gravitational constant under low-energy limits.
Established G_eff(ρ) = G_N·exp(−ρ/ρ_c) with significant corrections.
Resolved the open problem related to previous findings.
Identified numerical divergence in iterative Tolman-Oppenheimer-Volkoff equations as an artefact.

Abstract

Description Formal derivation of Gₑff (ρ) in static spherical symmetry via Gauss-Codazzi projection. The bulk Weyl tensor contribution E_μν is suppressed by GN·ρc/λ ~ 10⁻⁵⁰ in the RS2 low-energy limit. Gₑff^ (stellar) = GN·exp (−ρ/ρc) to O (10⁻⁵⁰) correction — identical to the cosmological result (P18). Papers P34–P38 formally consolidated. Open problem of P17 resolved. Numerical divergence in iterative TOV was implementation artefact, not physical. CCEGA Program Paper 39.

Closing the Gap: Formal Proof that CCEGA P39. Density-Dependent Gravity is Geometry-Independent

Key Points

Abstract

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