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

Erdinç Ulaş Saka

TL;DR

This paper addresses how a Dehnen-type galactic halo surrounding a regular, asymptotically flat black hole alters the gravitational quasinormal spectrum. Using axial gravitational perturbations with two gauge-invariant formulations and numerical techniques including Leaver's Frobenius method and Padé-improved WKB, they compute the fundamental and overtone frequencies $\omega$ and analyze their dependence on the halo scale $a$. They find moderate shifts, breaking of isospectrality between the up and down sectors, and a mild compression of the overtone spacing as $a$ grows, with no explosive growth of higher overtones. The results support a perspective that environmental matter deforms the ringdown gently, offering a physically motivated testbed for environmental effects on black-hole spectroscopy.

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.

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

TL;DR

This paper addresses how a Dehnen-type galactic halo surrounding a regular, asymptotically flat black hole alters the gravitational quasinormal spectrum. Using axial gravitational perturbations with two gauge-invariant formulations and numerical techniques including Leaver's Frobenius method and Padé-improved WKB, they compute the fundamental and overtone frequencies and analyze their dependence on the halo scale . They find moderate shifts, breaking of isospectrality between the up and down sectors, and a mild compression of the overtone spacing as grows, with no explosive growth of higher overtones. The results support a perspective that environmental matter deforms the ringdown gently, offering a physically motivated testbed for environmental effects on black-hole spectroscopy.

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 breaks the isospectrality that holds in vacuum. The dependence of the quasinormal spectrum on 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.

Paper Structure

This paper contains 6 sections, 19 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Black-hole geometry and axial gravitational perturbations
  3. WKB method
  4. Leaver (Frobenius) method
  5. Quasinormal modes
  6. Conclusions

Figures (3)

  • Figure 1: Quasinormal modes found by the precise Leaver method for the down channel: the fundamental mode and the first five overtones as a function of the regularization parameter $a$.
  • Figure 2: Quasinormal modes found by the precise Leaver method for the down channel: the fundamental mode and the first five overtones as a function of the regularization parameter $a$.
  • Figure 3: Quasinormal modes found by the precise Leaver method for both up and down channels, so that the broken iso-spectrality of up and down perturbations can be seen: the fundamental mode and the first five overtones as a function of the regularization parameter $a$.