Finite Curvature Construction of Regular Black Holes and Quasinormal Mode Analysis

TL;DR

This paper constructs regular black holes with finite curvature invariants using analytic profiles and analyzes their stability through quasinormal modes, revealing how potential shape influences stability.

Contribution

It introduces a novel class of regular black holes based on prescribed curvature invariants and studies their stability via detailed QNM analysis.

Findings

Regular black holes with no curvature singularities are constructed.

The shape of the effective potential affects the stability and decay of QNMs.

Potential valleys can lead to late-time instabilities in black hole perturbations.

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 exhibit stable, exponentially decaying waveforms, while a small ratio may induce late-time instabilities. 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.