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

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.

💡 Research Summary

This research paper presents a rigorous investigation into the gravitational wave signatures—specifically the quasinormal modes (QNMs)—of a regular, asymptotically flat black hole embedded within a Dehnen-type matter distribution. The study addresses the fundamental question of how a dark matter halo, modeled via the Dehnen-type distribution, modifies the characteristic “ringdown” signal of a black hole, which is a crucial component in gravitational wave astronomy.

The core of the analysis lies in the computation of both fundamental modes and higher-order overtones of the gravitational perturbations. A significant finding of this study is the breaking of isospectrality. In the standard vacuum Schwarzschild black hole, the axial and polar perturbations share the same spectrum of quainormal modes. However, the introduction of the halo parameter $a$, which characterizes the Dehnen-type matter distribution, disrupts this symmetry, leading to distinct spectra for the two axial sectors.

Furthermore, the paper provides a detailed examination of the sensitivity of the QNM spectrum to the halo parameter $a$. The researchers observed that while the fundamental modes exhibit a moderate dependence on $a$, the overtones show an even weaker sensitivity. Interestingly, as the halo parameter increases, the overtones tend to converge toward each other within the complex-frequency plane.

Crucially, the study distinguishes this Dehnen-type regular black hole from more exotic theoretical constructs, such as quantum-corrected black holes or exotic compact objects (ECOs). In those models, the presence of near-horizon structures often leads to an enhancement or rapid growth in the amplitudes of overtones, signaling strong-field effects. In contrast, this study demonstrates that the Dehnen-type halo induces only controlled and relatively mild modifications to the ringdown spectrum, preserving the qualitative structural integrity of the black hole’s gravitational signature. This suggests that while dark matter halos influence the spacetime geometry, they do not introduce the radical instabilities or extreme near-horizon phenomena associated with more radical departures from general relativity.