Gravitational Spectra and Wave Propagation in Regular Black Holes Supported by a Dehnen Halo

TL;DR

This work analyzes gravitational perturbations of a regular, asymptotically flat black hole embedded in a Dehnen-type galactic halo. Using high-order WKB with Padé resummation and time-domain evolution, the authors compute axial QNMs for two inequivalent perturbation schemes ('up' and 'down'), and they evaluate grey-body factors and absorption cross-sections from the corresponding scattering problem. They find that increasing the halo scale $a$ gently increases $\mathrm{Re}(\omega)$ while leaving $\mathrm{Im}(\omega)$ nearly unchanged, breaking isospectrality at the percent level; GBFs and $\sigma_{\rm abs}$ are suppressed with larger $a$, whereas late-time Price tails remain identical to Schwarzschild. The results demonstrate measurable imprint of astrophysical environments on black-hole dynamics and provide a robust framework for future tests of gravity in realistic galactic contexts, including potential extensions to polar perturbations and rotating configurations.

Abstract

We investigate gravitational perturbations, quasinormal modes, grey-body factors, and absorption cross-sections of the recently proposed regular and asymptotically flat black hole supported by a Dehnen-type dark-matter halo. This geometry provides a remarkably simple analytic model of supermassive black holes embedded in galactic environments, having a lapse function $ f(r)=1-2 M r^{2}/(r+a)^{3}, $ [R. A. Konoplya, A. Zhidenko, 2511.03066]. The regularizing parameter $a$ is the characteristic scale of the halo. We compute the quasinormal spectrum for both axial "up" and "down" perturbations using the WKB method and verify the results through time-domain integration. The two sectors are no longer isospectral, and the deviations grow with the halo scale parameter. The grey-body factors and absorption cross-sections are extracted via standard scattering boundary conditions and the WKB approach, and their behaviour is fully consistent with the structure of the effective potentials. Altogether, our analysis demonstrates that a dark-matter halo imprint induces modifications in the gravitational response, while the employed approximation schemes remain sufficiently accurate for quantitative predictions. At asymptotically late times, the presence of the halo does not alter the Price-law decay, which remains identical to that of a Schwarzschild black hole in vacuum.

Figures (10)

• Figure 1: Effective potential as a function of the tortoise coordinate $r^{*}$ for $\ell=2$ up perturbations: $M=1$; $a=0$ (blue), $a=0.05$ (black) and $a=0.15$ (red).
• Figure 2: Effective potential as a function of the tortoise coordinate $r^{*}$ for $\ell=2$ down perturbations: $M=1$; $a=0$ (blue), $a=0.05$ (black) and $a=0.15$ (red).
• Figure 3: The logarithmic time-domain profile for $\ell=2$ up-perturbations (left) and down-perturbations (right) at $a=0.25$, $M=1$. The fundamental QNMs given by the Prony extraction method are $\omega = 0.58167 - 0.09089 i$ (for up - modes) and $\omega = 0.54474 - 0.09191 i$ (for down - modes), which coincide with the WKB data. The asymptotic tail is $\sim t^{-7}$ in both cases, which coincides with the Price law for the Schwarzschild spacetime.
• Figure 4: Grey-body factors for $\ell=2$ up perturbations at $a=0$ (blue), $a=0.2$ (red) and $a=0.25$ (green).
• Figure 5: Difference between GBFs obtained by the 6th order WKB formula and the correspondence for $\ell=2$ up perturbations at $a=0$ (blue), $a=0.2$ (red) and $a=0.25$ (green).