Long-lived quasinormal frequencies for regular black hole supported by the Einasto profile in the presence of the magnetic field

Abstract

We investigate quasinormal modes, grey-body factors, and absorption cross-sections of a massive scalar field in regular black-hole spacetimes supported by the Einasto density profile. The analysis is performed for $\tilde n=1/2$, $1$, and $5$, where the scalar mass $μ$ is treated as an effective parameter induced by an external environment. Quasinormal frequencies are computed with high-order WKB expansions and Padé resummation, and are cross-checked by time-domain evolution. We show that increasing the effective mass and varying the Einasto parameters can strongly suppress the damping rate, leading to long-lived modes and clear quasi-resonant behavior. Grey-body factors obtained from direct WKB transmission and from the QNM-based correspondence agree well in the considered regimes, while their differences remain controlled. Using the transmission coefficients, we derive partial and total absorption cross-sections and demonstrate the expected transition from low-frequency suppression to efficient high-frequency absorption. Our results show that regularity of the core together with environmental parameters leaves a noticeable imprint on both ringdown and scattering observables. Within this setup, the magnetic field acts as the physical agent that controls the effective mass scale and therefore governs how close the system can approach the quasi-resonant regime.

Figures (7)

• Figure 1: Model with $\tilde{n}=1/2$, $h=1.05$. Effective potential as a function of the tortoise coordinate $r^{*}$ for scalar perturbations with $M=1$: left panel $\ell=0$, $\mu=0,0.2,0.4$ (blue, black, red); middle panel $\ell=1$, $\mu=0,0.2,0.6$ (blue, black, red); right panel $\ell=2$, $\mu=0,0.2,0.8$ (blue, black, red).
• Figure 2: Model with $\tilde{n}=1$, $h=0.38$. Effective potential as a function of the tortoise coordinate $r^{*}$ for scalar perturbations with $M=1$: left panel $\ell=0$, $\mu=0,0.2,0.4$ (blue, black, red); middle panel $\ell=1$, $\mu=0,0.2,0.6$ (blue, black, red); right panel $\ell=2$, $\mu=0,0.2,0.8$ (blue, black, red).
• Figure 3: Left: Semi-logarithmic time-domain profile for $\tilde{n}=1/2$, $\ell=1$, $h=1$, and $\mu=0.2$. The ringing period is modified by intermediate asymptotic tails. The QNM obtained by the Prony method from the time-domain integration is $\omega_{n=0} = 0.3084 - 0.0823063 i$. Right: Semi-logarithmic time-domain profile for $\tilde{n}=1$, $\ell=1$, $h=0.38$, and $\mu=0.2$. QNM given by the time-domain profile is $\omega_{n=0} =0.314732 - 0.0737021 i$.
• Figure 4: Extrapolation of the damping rate $|Im(\omega)|$ versus effective mass $\mu$ for the fundamental scalar mode with $\ell=1$, using only tabulated WKB16 data. Left: $\tilde{n}=1/2$ (Table \ref{['tab:qnm_wkb_comparison_nhalf']}), yielding $\mu_c\approx0.554$. Right: $\tilde{n}=1$ (Table \ref{['tab:qnm_wkb_comparison']}), yielding $\mu_c\approx0.545$. The solid curves are quadratic fits to the tabulated points.
• Figure 5: Partial and total absorption cross-sections for the scalar field in the Einasto-supported regular black-hole model with $\tilde{n}=1$ and $\mu=0.1$ ($M=1$). The QNM extracted from the time-domain profile $\omega = 0.3084 - 0.08231 i$ differs from that obtained by the WKB by a small fraction of one percent.