Spectral Bifurcations in Quasinormal Modes of Regular BTZ Black Holes

TL;DR

This paper investigates how regularized BTZ black holes affect the quasinormal mode spectrum of scalar fields, revealing bifurcations and mode reordering as the regularization parameter varies, thus providing insights into black hole stability and spectral structure.

Contribution

It introduces a detailed analysis of quasinormal modes in regular BTZ black holes, demonstrating bifurcations and spectral reordering due to Lovelock regularization effects.

Findings

Regular BTZ black holes remain linearly stable.

Spectral bifurcations occur as the regularization parameter increases.

Mode reordering and purely imaginary branches emerge with increasing regularization.

Abstract

We study the quasinormal spectrum of massless scalar fields propagating on a family of regular BTZ black holes arising from an infinite tower of dimensionally regularized Lovelock corrections. These geometries are asymptotically AdS, reduce to the standard BTZ solution in the limit $\ell \to 0$, and resolve the central singularity by introducing a smooth core controlled by the new length scale $\ell$. The scalar quasinormal modes are computed using both Leaver's continued-fraction method and the Horowitz-Hubeny power-series method; the two approaches agree to high accuracy across the parameter space. We find that the regularization preserves linear stability ($\omega_I < 0$) while qualitatively reshaping the spectrum: as $\ell$ increases, BTZ-like complex branches collide with the imaginary axis and undergo a hierarchy of bifurcations into multiple purely imaginary branches, leading to mode switching and a nontrivial reordering of overtones as functions of $\ell$ and the harmonic index $m$. Our results place regular BTZ black holes within the emerging family of bifurcating quasinormal spectra known from nearly extremal and asymptotically AdS black holes, and highlight these $(2+1)$-dimensional geometries as a controlled arena for exploring geometric mechanisms behind spectral branching and late-time ringdown in regular black hole spacetimes.