Tensorial Accessibility and the Schwarzschild Exterior: Constitutive Completion of Finite-Accessibility Gravity

Arc V — Gravity & Quantum Theory Paper 2 Title Tensorial Accessibility and the Schwarzschild Exterior: Constitutive Completion of Finite-Accessibility Gravity Zenodo DOI 10.5281/zenodo.18225945 Description This paper provides the first constitutive completion of the finite-accessibility gravity framework in the empirically decisive case of the static, spherically symmetric vacuum exterior. Building on the structural results of Paper V.1, it demonstrates explicitly why scalar accessibility models fail and derives the minimal tensorial accessibility response required to reproduce observed gravitational phenomena. The work proves that any scalar accessibility field yields a conformally flat effective metric, eliminating Weyl curvature and forbidding gravitational light bending. This “scalar trap” necessitates direction-dependent (tensorial) accessibility. Introducing distinct temporal and spatial accessibility factors, the paper derives their weak-field behavior using operational principles: finite state-change budgets, conservation of accessible information flux, and independence of temporal and spatial transport limitations. Without assuming Einstein’s equations or inserting known solutions, the resulting effective metric reproduces the post-Newtonian parameters γ = 1 and β = 1. The Schwarzschild exterior thus emerges as a consequence of accessibility modulation rather than geometric postulate. This paper completes the weak-field constitutive sector of the program and establishes tensorial accessibility as unavoidable for any operational theory of gravity consistent with observation. Keywords emergent gravity; Schwarzschild metric; tensorial accessibility; Weyl curvature; post-Newtonian parameters; operational gravity Notes Arc V — Gravity & Quantum Theory (constitutive, weak-field) Completes the PPN sector without assuming GR Establishes necessity of anisotropic accessibility Strong-field extensions follow in Papers V.3–V.4