Structural Admissibility Regimes (SAR): Gravity and Cosmology from Finite Admissibility

This paper develops the gravitational and cosmological regime of the Structural Admissibility Regimes (SAR) framework under finite admissibility capacity. Building on the algebraic foundations of the SAR series and the Unified Structural Admissibility System, we derive gravitational dynamics, black hole structure, and cosmological expansion as large-scale manifestations of admissibility redistribution under compatibility constraints. The framework begins from a single structural principle: finite admissibility capacity constrained by compatibility load. Geometry emerges as the accessibility structure of admissible refinements, characterized by an accessibility potential whose second covariant variation induces an effective Lorentzian compatibility metric in the weak admissibility-strain regime. Spatial gradients of compatibility load generate curvature as the structural response of accessibility geometry, yielding a covariant field equation governing admissibility strain. Event horizons arise as admissibility saturation boundaries where effective capacity vanishes and cross-boundary compatibility collapses. The resulting boundary commutant capacity reproduces the entropy–area relation as a structural counting invariant without invoking thermodynamic postulates. Black holes therefore appear as finite saturated admissibility regimes rather than geometric singularities, and curvature remains bounded due to finite capacity. Residual compatibility load stabilizing geometric regimes manifests as an effective non-radiative load component corresponding structurally to dark matter phenomena. Incomplete global relaxation of admissibility capacity produces persistent accessibility bias, yielding negative structural pressure and accelerated cosmological expansion without introducing a cosmological constant. In the weak admissibility-strain limit, the structural field equation reduces exactly to the Einstein field equations, ensuring agreement with General Relativity in the post-Newtonian regime. In strong regimes, the framework predicts bounded curvature, nonsingular collapse, and structural corrections to classical solutions. Gravity and cosmology therefore emerge as regime-level expressions of admissibility redistribution under finite structural capacity within the Structural Admissibility Regimes framework. Part of the Structural Admissibility Regimes (SAR) Applied Series, completing the SAR program following the quantum–thermodynamic regime analysis.