The Galactic Core Metamorphosis: Supermassive Black Holes as Localized Thermodynamic Precursors and Phase-Space Regulators in Finsler-Mucini TR Gravity

This paper formalizes a foundational postulate of Finsler-Maxwell Thermo-Relativistic (TR) Gravity: the topological and energetic equivalence between transformed baryonic matter and the residual primordial thermo-quantum fluid within the expanding universe. Rather than treating supermassive black holes (SMBHs) as passive gravitational singularities where physical laws break down, we model them as localized homoeostatic regulators—establishing a strict law of "one regulator per galaxy." We present explicit analytical and numerical derivations coupling the global infrared invariant (Omega_IR = 14.75%) directly to macro-galactic mass scales (M_spiral approx 2.87 * 10^11 M_odot), omitting the need for dark matter halos. Furthermore, we evaluate the internal micro-state velocity dispersion floor within the frozen event horizon, proving it stabilizes at precisely sigmaTRᶜᵒʳᵉ approx 1.503 * c under strict causal protection. This framework provides a deterministic mechanism for synchronized global cosmic recycling, resolving the Tolman and black hole information loss paradoxes through phase-space metric co-saturation.