Quasinormal Modes of a Massive Scalar Field in 4D Einstein--Gauss--Bonnet Black Hole Spacetimes

Abstract

We analyze quasinormal modes, grey-body factors, and absorption cross-sections of a massive scalar field in four-dimensional Einstein--Gauss--Bonnet black-hole spacetimes within a stability-constrained coupling window. High-order WKB-Padé spectra show that increasing field mass typically reduces damping and drives the system toward long-lived, quasi-resonant behavior. The scattering sector follows the same potential-barrier physics: larger effective barriers suppress transmission and low-frequency absorption, while the Gauss--Bonnet coupling has a comparatively mild impact over the stable range. These results provide a compact baseline for massive-field spectroscopy in higher-curvature black-hole backgrounds.

Figures (7)

• Figure 1: Effective potential profiles $V_\ell(r)$ for fixed Gauss--Bonnet coupling $\alpha=0.01$ and $\ell=0$, with several scalar masses $\mu$. For small $\mu$, the potential has a clear barrier maximum; as $\mu$ increases, the barrier flattens and disappears (here around $\mu\approx0.2$), marking the onset of a no-peak regime.
• Figure 2: Effective potential profiles $V_\ell(r)$ for fixed scalar mass $\mu=0.1$ and $\ell=1$, with different Gauss--Bonnet couplings $\alpha\in[-0.2,0.2]$. The overall potential shape changes only weakly across this range, illustrating the mild $\alpha$-dependence compared with the stronger $\mu$-dependence in Fig. \ref{['fig:veff_mu_scan']}.
• Figure 3: Absolute damping rate $|\mathrm{Im}(\omega)|$ versus scalar mass $\mu$ ($M=1$) for fixed multipole $\ell=0,1,2$ and three Gauss--Bonnet couplings $\alpha=-0.5,\,0.01,\,0.5$ (WKB16 data points). Dashed curves show quadratic extrapolations in $\mu$ to the formal zero-damping limit $|\mathrm{Im}(\omega)|\to 0$, illustrating the quasi-resonant trend of progressively longer-lived modes at larger $\mu$. We can see that for $\ell=0$ and $\alpha=-0.5$ the quadratic fit is inaccurate, yet the damping rate evidently approaches zero in this case as well.
• Figure 4: Time-domain ringdown profile for the massive scalar perturbation with $(\ell,\mu,\alpha)=(2,0.1,0.5)$ (with $M=1$). The oscillatory tail is fitted by the Prony method, yielding $\omega_{\rm Prony}=0.496502-0.0917142\,i$. For the same parameter set, the frequency-domain WKB16 value from the QNM table is $\omega_{\rm WKB}=0.496501-0.091715\,i$. Taking the time-domain/Prony result as the reference benchmark, the relative complex error of WKB is $|\omega_{\rm WKB}-\omega_{\rm Prony}|/|\omega_{\rm Prony}|\times100\%\approx2.54\times10^{-4}\%$, confirming very good agreement while indicating that the direct time-domain extraction is the more accurate estimate.
• Figure 5: Grey-body factors $\Gamma_{\ell=1}(\Omega)$ for the 4D-EGB black hole ($M=1$) at three Gauss--Bonnet couplings: (a) $\alpha=-1$ (left), (b) $\alpha=0.01$ (center), and (c) $\alpha=0.5$ (right). In each panel, the curves correspond to scalar masses $\mu=0$ (blue), $\mu=0.2$ (red), and $\mu=0.3$ (black). The comparison shows how both coupling and field mass shape the transmission probability in the $\ell=1$ channel.