Matter–Sector Admissibility Regulation in General Relativity (MSAR-GR) investigates whether curvature growth during gravitational collapse can be regulated without modifying the Einstein–Hilbert structure of General Relativity. The framework introduces a canonical multi-scalar matter sector in which a regulator field modulates the effective interaction strength of coupled scalar fields through a purely algebraic, diffeomorphism-invariant interaction. In this construction, the gravitational sector remains completely unchanged, preserving the standard propagator, Lorentz structure, and field equations of classical GR. MSAR-GR derives the full Einstein–scalar field system for static, spherically symmetric configurations and formulates the collapse problem as a nonlinear boundary-value system of coupled differential equations. A dominant-balance analysis of the near-origin behavior reveals an important structural constraint: algebraic regulators cannot modify the leading kinetic scaling of canonical scalar collapse under analytic expansion. This result places strong theoretical limits on curvature-suppression mechanisms that rely solely on potential-sector interactions while preserving canonical kinetic structure. Rather than proposing a resolution of gravitational singularities, MSAR-GR establishes a mathematically consistent regulator framework that defines the conditions under which finite-curvature collapse solutions may exist. The theory identifies the precise analytical and numerical criteria required to evaluate such solutions, including boundary conditions, curvature diagnostics, and stability considerations. Within the broader Stellar Resonance Framework (SRF), MSAR-GR serves as a conservative gravitational foundation, exploring the limits of curvature regulation through matter-sector dynamics while maintaining the full structure of classical General Relativity.
Nathaniel Salisbury (2025) studied this question.