Long-lived quasinormal modes, grey-body factors and absorption cross-section of the black hole immersed in the Hernquist galactic halo

TL;DR

This work addresses how a Hernquist dark-matter halo surrounding a Schwarzschild black hole modifies the quasinormal spectrum, grey-body factors, and absorption cross-sections of a massive scalar perturbation. The authors model the spacetime with an analytically specified Hernquist halo, compute QNMs using a high-order WKB–Padé scheme and validate them with time-domain Prony analysis, and analyze GBFs and $\sigma_{\rm abs}$ across halo and field-mass parameters. They find that in the astrophysically relevant hierarchy $M_{\rm BH}\ll M\ll a_{0}$ the halo induces only mild shifts in QNM frequencies, while increasing the field mass $\mu$ yields longer-lived, quasi-resonant modes; GBFs and absorption cross-sections remain dominated by the near-horizon geometry with mild corrections from the halo. The results support the robustness of black-hole ringdown against typical dark-matter environments and delineate regimes where halo effects might become observable.

Abstract

We analyze quasinormal modes, grey-body factors, and absorption cross-sections of a massive scalar field in the background of a Schwarzschild black hole surrounded by a Hernquist dark-matter halo. The quasinormal spectrum is obtained through the higher-order WKB method and verified by time-domain evolution, showing consistent results. The field mass increases the oscillation frequency and reduces the damping rate, producing longer-lived modes, while variations in the halo parameters lead to moderate shifts in the spectrum. The grey-body factors reveal a suppression of low-frequency transmission and a displacement of their main features toward higher frequencies, resulting in a corresponding shift in the absorption cross-section.

Figures (9)

• Figure 1: Effective potentials for $\ell=0$ perturbations at $M_{BH}=1$, $M=10 M_{BH}$$a_{0}=0.1$, $\mu=0$ (black), $\mu=0.2$ (blue) and $\mu=0.3$ (red).
• Figure 2: Effective potentials for $\ell=1$ perturbations at $M_{BH}=1$, $M=10 M_{BH}$$a_{0}=0.1$, $\mu=0$ (black), $\mu=0.3$ (blue) and $\mu=0.5$ (red).
• Figure 3: Effective potentials for $\ell=0$ perturbations at $M_{BH}=1$, $M=8 M_{BH}$, $a_{0}=5$, $\mu=0$. The double peak potential does not appear in the regime of realistic galactic halos.
• Figure 4: Semi-logarithmic time-domain profile for $\ell=1$, $M_{BH}=1$, $M=10 M_{BH}$, $a=100$, $\mu=0$. The Prony method allows one to find the fundamental QNM $\omega = 0.264892 - 0.0881029 i$, which is very close to the WKB value $\omega = 0.264887 -0.088108 i$.
• Figure 5: Semi-logarithmic time-domain profile for $\ell=1$, $M_{BH}=1$, $M=10 M_{BH}$, $a=10^5$, $\mu=0.1$. The Prony method allows one to find the fundamental QNM $\omega = 0.297391 - 0.0949604 i$, which is very close to the WKB value $\omega = 0.297382 - 0.094948 i$.