What question did this study set out to answer?

The research aims to compare the gravitational stability and maximum mass predictions between General Relativity and the CCEGA framework using TOV equations.

April 14, 2026Open Access

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Part V 1.1 TOV Integration Code: GR vs CCEGA Numerical Comparison

MSMarc López Sánchez

Key Points

The research aims to compare the gravitational stability and maximum mass predictions between General Relativity and the CCEGA framework using TOV equations.
Implemented TOV equations for both General Relativity (GR) and CCEGA (Information-Driven Gravity) frameworks in Python.
Conducted Bardeen stability analysis to identify stable and unstable regions.
Included visualizations of mass-radius diagrams and stability parameters.
Used RK45 numerical integration for accurate solutions.
Maximum mass for GR calculated as 1.9893 ± 0.0012 M_☉ and 4.3493 ± 0.0085 M_☉ for CCEGA.
CCEGA exhibits an enhancement factor of 2.19× in maximum mass predictions compared to GR.
The stability density limit is higher in CCEGA (5.76 × ρ_nuc) than in GR (5.15 × ρ_nuc), aiding in resolving the mass gap problem.

Abstract

Complete Python implementation of TOV equations for General Relativity baseline and CCEGA (Information-Driven Gravity) framework with full stability analysis via Bardeen criterion. Supplementary material for: López Sánchez, M. (2026). CCEGA: Information-Driven Gravity and the Mass Gap Problem. Zenodo. doi: 10. 5281/zenodo. 19539744 VERSION 1. 1: - Complete Bardeen stability analysis (dM/dρc criterion) - Stability branch identification (stable vs unstable regions) - Enhanced visualization (4 plots: M-R, dM/dρ, convergence, interpretation) - Full physical interpretation of stability results NUMERICAL RESULTS (v1. 1 verified): - GR Mₘax = 1. 9893 ± 0. 0012 M_☉ (26/30 convergences) - CCEGA Mₘax = 4. 3493 ± 0. 0085 M_☉ (30/30 convergences) - Enhancement factor: 2. 19× (118. 6% increase) - GR stability: up to ρc = 5. 15 × ρₙuc- CCEGA stability: up to ρc = 5. 76 × ρₙuc- Theory vs numerical deviation: 2. 1% FILES INCLUDED: 1. GRᵥsCCEGACOMPLETEᵥ1₁. py (executable Python code) 2. CCEGAPARTVCODERESULTSᵥ1₁COMPLETE. txt (results + analysis) KEY FEATURES: - APR4 equation of state (piecewise polytropic, Read et al. 2009) - GR TOV equations (4 variables) - CCEGA TOV equations (5 variables with information field) - RK45 numerical integration (Dormand-Prince 5th order) - Bardeen stability analysis- Comparative M-R diagrams- Four-panel visualization PHYSICAL FRAMEWORK: CCEGA modifies Einstein equations via Gₑff (ρ) = GN/ (1 + I (ρ) ) where I (ρ) = exp (-ρ/ρc). This reduces gravity at supranuclear densities, allowing larger stable masses via curvature braking. REPRODUCIBILITY: - All results fully reproducible from code- APR4 EOS parameters hardcoded (Read et al. 2009) - No external data files required- Tolerances: rtol=1e-5, atol=1e-11 USAGE: Option A (Google Colab): Copy code into cell, execute, 2-3 minutes runtimeOption B (Local): pip install numpy scipy matplotlib, then python code REQUIREMENTS: Python 3. 8+ with numpy, scipy, matplotlib STABILITY INTERPRETATION: Maximum mass Mₘax occurs where dM/dρc = 0 (Bardeen criterion). CCEGA allows larger stable density range (5. 76 vs 5. 15 × ρₙuc), explaining resolution of mass gap problem. FALSIFICATION CRITERIA: (1) NICER 2026-2029: If M > 4. 35 M_☉ → falsified (2) Einstein Telescope 2035: No echoes at τ ≈ 14 ms → falsified (3) EM surveys: Accretion in mass-gap objects → falsified VERSION: 1. 1AUTHOR: Marc López SánchezORCID: 0009-0005-6356-3702DATE: April 12, 2026

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Marc López Sánchez (Sun,) studied this question.

synapsesocial.com/papers/69ddda22e195c95cdefd7994 https://doi.org/https://doi.org/10.5281/zenodo.19543673

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