Finite Curvature Construction of Regular Black Holes and Quasinormal Mode Analysis

Abstract We develop a class of regular black holes by prescribing finite curvature invariants and reconstructing the corresponding spacetime geometry. Two distinct approaches are employed: one based on the Ricci scalar and the other on the Weyl scalar. In each case, we explore a variety of analytic profiles for the curvature functions, including Gaussian, hyperbolic secant, and rational forms, ensuring regularity, asymptotic flatness, and compatibility with dominant energy conditions. The resulting mass functions yield spacetime geometries free from curvature singularities and exhibit horizons depending on model parameters. To assess the stability of these solutions, we perform a detailed analysis of quasinormal modes (QNMs) under axial gravitational perturbations. We show that the shape of the effective potential, particularly its width and the presence of potential valleys, plays a critical role in determining the QNMs. Models with a large peak-to-valley ratio in the potential barrier tend to support longer-lived oscillations, since perturbations can be partially trapped in the valley region before eventually escaping. By contrast, when the ratio is small, the valley is too shallow to produce effective trapping, and the waveforms reduce to standard exponential decay without sustained oscillatory behavior. Our results highlight the significance of potential design in constructing physically viable and dynamically stable regular black holes, offering potential observational implications in modified gravity and quantum gravity scenarios.