Paper IV: Geodesic Regularity and Global Structure of the Bühring Interior Metric Deformation Model

This paper studies the geodesic structure and global regularity of the Bühring interior metric deformation model. The framework replaces the classical Schwarzschild singularity by a regular interior core while preserving the exact Schwarzschild exterior geometry. We analyze timelike, null, and spacelike geodesics and demonstrate that the regular core removes the classical singular geodesic endpoint. The resulting spacetime is geodesically extendible and free of curvature divergences in the interior region. The global causal structure is examined, including horizon crossing behaviour, interior continuation, and completeness properties. The analysis shows that the Bühring model provides a regular interior completion of the Schwarzschild solution without modifying the exterior geometry. This distinguishes the model from many regular black hole constructions that alter the photon sphere or outer potential. Paper IV establishes the mathematical consistency of the Bühring framework at the level of geodesic structure and global spacetime regularity. These results form the foundation for the perturbative and observational analysis developed in subsequent papers.