Gravitational Homeostasis and Baryonic Saturation: A Unified Field Theory of Compact Objects via Residual Metabolic Potential

AbstractWe propose a scalar-tensor extension of General Relativity where gravitational interaction emerges not as a fundamental geometric property, but as a Residual Metabolic Potential arising from the thermodynamic requirements of baryonic matter. We model the atom as a homeostatic system governed by a conserved information parameter ("Nuclear DNA"). Under extreme gravitational pressure, matter undergoes a smooth phase transition—governed by a sigmoidal saturation function η (P) —into a Zero-Entropy Neutronic Condensate (ZENC). Solving the modified Tolman-Oppenheimer-Volkoff (TOV) equations coupled to a saturation scalar field, we demonstrate that ZENCs are stable, horizonless objects that mimic Black Holes. The model predicts a specific electromagnetic signature: a luminosity cutoff in Relativistic Jets determined by the Schwinger Limit of vacuum breakdown (Ec ≈ 1. 3 × 10¹8 V/m), resolving the singularity paradox and unifying gravity with quantum vacuum electrodynamics. Python source code for the numerical simulation is included as a supplementary dataset.