Quasinormal Modes and Grey-Body Factors of Scalar, Electromagnetic and Dirac Fields Around Einasto-Supported Regular Black Holes

Abstract

We study quasinormal modes and grey-body factors of scalar, electromagnetic and Dirac test fields for a black hole surrounded by matter distributed according to the Einasto density profile. The quasinormal spectrum is calculated using the high-order WKB method with Padé approximants and checked by the time-domain integration. For small values of the Einasto index $\tilde n=1/2$ and $\tilde n=1$, the fundamental modes remain close to their Schwarzschild values, while for $\tilde n=5$ the oscillation frequency increases and the damping rate decreases as the halo parameter grows. Grey-body factors are much less sensitive to the halo environment: the main effect is a mild suppression at low frequencies caused by a moderate increase of the effective potential near the horizon. At higher frequencies the transmission probabilities remain close to the Schwarzschild case.

Figures (5)

• Figure 1: Typical effective potential as a function of the tortoise coordinate $r^{*}$ for small values of $\tilde{n}$. Here we have $\ell=0$ scalar perturbations; $M=1$; $h=0.1$ (blue), $h=0.3$ (black) and $h=0.38$ (red). The geometry is mostly corrected near the event horizon and quickly merge with the Schwarzschild case.
• Figure 2: Semi-logarithmic time-domain profiles for $\ell=1$ electromagnetic perturbations of the black hole model with $\tilde{n}=1$, $h=0.38$ and or $\ell=1$ scalar perturbations of the black hole model with $\tilde{n}=1/2$$h=1.05$. The Prony method allows to extract the dominant frequency $\omega = 0.288190 - 0.0895577 i$, which is very close to the WKB data $\omega = 0.288295 - 0.089840 i$.
• Figure 3: Left: Grey-body factors found by the 6th order WKB formula and by the correspondence with quasinormal modes. Right: Difference between the grey-body factors obtained by the two methods. Here we consider electromagnetic perturbations of the $\tilde{n}=1$ black-hole model at $\ell=1$, $h=0.01$ (red), and $h=0.38$ (black).
• Figure 4: Left: Grey-body factors found by the 6th order WKB formula and by the correspondence with quasinormal modes. Right: Difference between the grey-body factors obtained by the two methods. Here we consider electromagnetic perturbations of the $\tilde{n}=1$ black-hole model at $\ell=2$, $h=0.01$ (red), and $h=0.38$ (black).
• Figure 5: Left: Grey-body factors found by the 6th order WKB formula and by the correspondence with quasinormal modes. Right: Difference between the grey-body factors obtained by the two methods. Here we consider Dirac perturbations of the $\tilde{n}=1$ black-hole model at $\ell=3/2$, $h=0.01$ (red), and $h=0.38$ (black).