Paper VII: Quasinormal Mode Structure and Spectral Sensitivity of the Bühring Interior Metric Deformation Model

This paper analyzes the quasinormal-mode structure of the Bühring interior metric deformation model, a regular black hole construction that preserves the exact Schwarzschild exterior while replacing the interior singularity with a regular core. Because the exterior geometry remains unchanged, the dominant quasinormal-mode structure is expected to remain close to the Schwarzschild reference case. The regular interior modifies the global boundary-value problem and introduces subleading spectral deviations tied to the interior completion. The analysis distinguishes between single-horizon and multi-region interior seeds, identifies the hierarchy of mode sensitivity, and examines the role of overtone structure and angular sectors. The resulting picture is that deviations from Schwarzschild arise primarily in subleading modes and late-time ringdown behaviour. This work establishes the structural spectral framework and identifies observational channels for testing the Bühring interior model. Fully converged numerical frequency tables are left for future dedicated numerical computation. This work is part of the Bühring Interior Metric Deformation Model series (Papers I–VII).