Quasinormal modes of regular black holes surrounded by skewed dark matter distributions

TL;DR

This work investigates how a skewed dark matter distribution outside the innermost stable circular orbit modifies the quasinormal-mode spectrum and ringdown of regular (nonsingular) black holes arising from quantum-corrected collapse. The authors implement the DM effect as a metric correction through a radial mass function $M_\epsilon = M_{\rm BH} + M_{\rm DM}(r)$ paired with a skewed normal density profile, and they perform a QNM analysis across scalar, vector, spinor, and tensor perturbations to reveal DM-induced potential features such as shallow wells and secondary barriers that yield long-lived modes and echoes. A key finding is the strong differential sensitivity between axial and polar tensor perturbations: polar modes respond much more to DM, producing pronounced echoes at lower DM densities. The results suggest that gravitational-wave observations could probe both the interior structure of regular black holes and their DM environments, and they point to extensions to spinning regular black holes and backreaction effects for more realistic astrophysical scenarios.

Abstract

Regular black holes, nonsingular solutions to gravitational collapse with quantum corrections, offer a compelling alternative to classical black holes with curvature singularities. In this work, we investigate how the presence of skewed dark matter distributions outside the innermost stable circular orbit of regular black holes modifies the gravitational wave signals emitted by such objects. Rather than introducing corrections directly into an effective potential, we model the influence of dark matter through metric corrections, allowing a full control over the spatial distribution and abundance of dark matter. We demonstrate that a skewed normal profile generically introduces shallow potential wells or secondary barriers in the effective potential of perturbation equations, depending sensitively on the type of perturbations: scalar, spinor, or tensor. These modifications lead to distinctive quasinormal mode features, including long-lived modes, echo effects, and in some cases, altered stability behaviors. Notably, the axial and polar sectors of tensor field perturbations respond asymmetrically to identical dark matter profiles, revealing a deeper structural distinction in their perturbation dynamics. These results provide a theoretical framework for probing regular black holes in the dark matter environment through gravitational wave observations.

Figures (9)

• Figure 1: Effective potentials of different test fields with $\ell=1$.
• Figure 2: Ringdown waveform of scalar, vector and spinor field perturbations.
• Figure 3: Illustration: Gravitational wave emission from a binary black hole system immerged in a dark matter environment.
• Figure 4: Effective potentials of scalar and spinor field perturbations. The parameters are set to be $\rho_0=0.1$, $\sigma=4$, $\alpha=10$, $M=0.5$, $\xi=\xi_c$ and $\ell = 1$.
• Figure 5: Waveforms of scalar and spin field perturbations corrected by dark matter in diagram \ref{['fig:wf_modi_s0']} and diagram \ref{['fig:wf_modi_sp']}, respectively. The parameters are set to be $\rho_0=0.1$, $\sigma=4$, $\alpha=10$, $M=0.5$, and $\xi=\xi_c$.