Regular black hole sourced by the Dehnen-type distribution of matter: The sound of the event horizon

TL;DR

This study analyzes how a Dehnen-type matter halo influences the quasinormal modes of a regular black hole, revealing mild modifications to the ringdown spectrum and breaking isospectrality without inducing strong near-horizon effects.

Contribution

It provides the first detailed analysis of quasinormal modes for a regular black hole with a Dehnen matter halo, highlighting the halo's moderate impact on the spectrum.

Findings

Halo parameter $a$ breaks isospectrality of axial modes.

Fundamental modes are moderately affected by the halo.

Overtone frequencies approach each other as the halo parameter increases.

Abstract

We compute the fundamental and overtone quasinormal modes of a regular, asymptotically flat black hole supported by a Dehnen-type matter halo. Gravitational perturbations in this background split into two distinct axial sectors, and our analysis confirms that the presence of the halo parameter $a$ breaks the isospectrality that holds in vacuum. The dependence of the quasinormal spectrum on $a$ is moderate for the fundamental modes and even weaker for the overtones, which approach one another in the complex-frequency plane as the halo parameter increases. No enhancement or rapid growth of overtone amplitudes is observed, indicating that the halo does not induce the type of strong near-horizon effects characteristic of quantum-corrected or exotic compact objects. Overall, our results show that the dark-matter halo introduces controlled and comparatively mild modifications to the ringdown spectrum while preserving its qualitative structure.