Ringing Regularity: Gravitational Perturbations and Quasinormal Modes of Einasto-Supported Black Holes

Abstract

We investigate axial gravitational perturbations and quasinormal modes of regular black holes supported by an Einasto distribution of matter. Halo matter not only removes the central singularity but also modifies the quasinormal spectrum. We show that the resulting quasinormal spectrum deviates systematically from the Schwarzschild case, with shifts in both oscillation frequencies and damping rates that grow with the halo scale parameter and the Einasto index. In near-extremal configurations, the damping rate can be significantly suppressed, leading to long-lived modes. The effects of regularity and environmental factors on the spectrum are found to be substantially larger than the estimated numerical uncertainty, as confirmed independently by high-order WKB calculations with Padé resummation and time-domain integration.

Figures (2)

• Figure 1: Effective potential as a function of the tortoise coordinate $r^{*}$ for $\ell=2$ up perturbations; $M=1$. Left: $n=1/2$, $h=0.1$ (blue), $h=0.5$ (black) and $h=0.9$ (red). Right: $n=1$, $h=0.1$ (blue), $h=0.3$ (black) and $h=0.38$ (red).
• Figure 2: Time domain profile for up-potential $\ell=2$, $n=1$, $h=0.3$. Left: The up-potential for which the 16th WKB result $\omega=0.384390-0.079386 i$ perfectly agrees with the extraction of the frequency from the time-domain profile via the Prony method $\omega = 0.384389 - 0.079382 i$. Right: Down potential for which the 16th WKB result $\omega= 0.382115-0.072757 i$ perfectly agrees with the extraction of the frequency from the time-domain profile via the Prony method $\omega = 0.382115 - 0.0727567 i$.