Ringdown Bounds on UV-Regularized Black-Hole Cores

Abstract

Spacetime singularities in black-hole solutions signal a breakdown of the classical description at high curvature. We analyze a minimalist UV-regularized black-hole model with a single length scale L that preserves the exterior Schwarzschild/Kerr geometry and perturbs only the light-ring scattering barrier via a Hayward-type mass function. The resulting deformation induces small, correlated shifts in the dominant quasinormal mode (QNM). Similar behavior was reported in prior studies of regular metrics: Flachi and Lemos [1] found O(10%) QNM deviations for a Minkowski-core spacetime, and Toshmatov et al. [2] showed that introducing a Hayward/Bardeen-like core increases the oscillation frequency and prolongs the damping time of test-field modes. We compute the Schwarzschild (2, 2, 0) mode using (i) double-null time-domain evolution (anchor), (ii) an audited Leaver continued-fraction solver, and (iii) a locally calibrated WKB-Pade surrogate. We then perform a covariance-aware, multi-event hierarchical analysis with ringdown-start marginalization to test fractional and absolute scaling hypotheses. We obtain 95% credible bounds e = L/rs <= 0.142 and L0 <= 47 km. Cross-checks from EHT shadow diameters and S-star dynamics are consistent with these limits. Barrier diagnostics indicate that neglected interior-gradient terms scale as (L/rs)^3 and are subdominant across the posterior support. The present constraints are Schwarzschild-calibrated - in future work we outline a Teukolsky-CF Kerr deformation map that will supersede this calibration.