Bang-Time Perturbations and Redshift Drift in LTB Cosmology: Regularity, Distance Compensation, and Light-Cone Response

We study how radial variations in the bang time affect redshift drift in Lemaître–Tolman–Bondi cosmologies. Starting from the neighboring-light-cone equations, we derive a linear response system and evaluate it for regular dust and Λ-bearing model families. In the sampled parabolic dust models, hump-shaped bang-time profiles develop shell crossings, while a monotonic profile avoids them and gives a positive drift response at all sampled redshifts. A corresponding flat Λ-LTB family shows the same response sign in our calculations. We also solve a local first-order curvature compensation problem that holds luminosity distance fixed; the solution becomes sharply varying near the angular-diameter-distance maximum, limiting finite-amplitude control. These are model-specific numerical results, not observational detections or a universal theorem.