The Collapse Origin of the Bühring Interior Metric Deformation Model: A Phenomenological Formation Mechanism for a Regular Black Hole Core

This paper develops a collapse-based interpretation of the Bühring Interior Metric Deformation Model. Starting from a bounded-density spherical collapse core, we derive the effective mass function, reconstruct the metric, and obtain the deformation factor β (r) from the resulting interior structure. We show that regularity of the center forces a cubic mass scaling m (r) ~ r³, which naturally leads to a de Sitter-like core. From this mass profile the Bühring deformation factor follows directly, yielding the characteristic scaling β (r) ~ r^-3/2 near the origin. The work demonstrates that the deformation factor is not an arbitrary ansatz but emerges from a regularized collapse scenario with finite central density and vacuum-like pressure. A minimal effective action is also introduced to describe the core phenomenologically. This paper provides a physical formation mechanism for the static interior geometry introduced in Paper I, while keeping the exterior spacetime exactly Schwarzschild. This is Paper II in the Bühring Interior Metric Deformation Model series. Contact: Fbuehring62@gmail. com