Quasinormal modes and greybody factors of magnetically charged de Sitter black holes probed by massless external fields in Einstein Euler Heisenberg gravity

Abstract

This paper investigates the perturbation dynamics of massless scalar and electromagnetic fields on magnetically charged de Sitter (dS) black holes within the framework of string-inspired Euler-Heisenberg (EH) gravity. We calculate the quasinormal frequencies (QNFs) and discuss the influences of black hole magnetic charge $Q_{\mathrm{m}}$, the cosmological constant $Λ$, coupling parameter $ε$ and multipole number $l$ on QNFs, emphasizing the relationships between these parameters and quasinormal modes (QNMs) behavior. We find that the results obtained through the asymptotic iteration method (AIM) are in good agreement with those obtained by the WKB method. Importantly, the Bernstein spectral method is employed as a rigorous cross-check for QNFs in the $l=0$ scalar perturbation sector, where the WKB approximation is often unreliable. The greybody factor (GFs) is calculated using WKB method. The effects of the parameters $Q_{\mathrm{m}}$ and $ε$ on the greybody factor are also studied.

Figures (21)

• Figure 1: The metric function $B(r)$ as a function of the radial coordinate $r$ for different values of magnetic charge $Q_{\mathrm{m}}$ with fixed $M=1$ and $\Lambda=0.05$. Panels (a), (b), and (c) correspond to $\epsilon=-1$, $\epsilon=0$, and $\epsilon=1$, respectively. The zeros of $B(r)$ indicate horizons depending on parameters, there can be $0$--$3$ horizons (cosmological horizon $r_{\mathrm{c}}$, event horizon $r_{\mathrm{h}}$, and possibly Cauchy horizon $r_-$).
• Figure 2: The metric function $B(r)$ versus $r$ for different values of the coupling parameter $\epsilon$, with fixed $M=1$ and $\Lambda=0.05$. Panels (a), (b), and (c) correspond to $Q_{\mathrm{m}}=0.3$, $Q_{\mathrm{m}}=0.5$, and $Q_{\mathrm{m}}=0.7$, respectively. The zeros of $B(r)$ indicate horizons depending on parameters, there can be $0$--$3$ horizons (cosmological horizon $r_{\mathrm{c}}$, event horizon $r_{\mathrm{h}}$, and possibly Cauchy horizon $r_-$).
• Figure 3: The metric function $B(r)$ versus $r$ for different values of the cosmological constant $\Lambda$, with fixed $M=1$ and $Q_{\mathrm{m}}=0.3$. Panels (a), (b), and (c) correspond to $\epsilon=-1$, $\epsilon=0$, and $\epsilon=1$, respectively. The zeros of $B(r)$ indicate horizons depending on parameters, there can be $0$--$3$ horizons (cosmological horizon $r_{\mathrm{c}}$, event horizon $r_{\mathrm{h}}$, and possibly Cauchy horizon $r_-$).
• Figure 4: The effective potential $V_{\mathrm{s}}(r)$ for massless scalar field perturbation ($l=1$) as a function of the radial coordinate $r$ for different values of magnetic charge $Q_{\mathrm{m}}$. In all cases, we set $M=1$ and $\Lambda=0.05$. Panels (a), (b), and (c) correspond to $\epsilon=-1$, $\epsilon=0$, and $\epsilon=1$, respectively. As $Q_{\mathrm{m}}$ decreases, the peak of the potential barrier shifts outward and its height is significantly suppressed.
• Figure 5: The effective potential $V_e(r)$ for electromagnetic field perturbation ($l=1$) as a function of the radial coordinate $r$ for different values of magnetic charge $Q_{\mathrm{m}}$. In all cases, we set $M=1$ and $\Lambda=0.05$. Panels (a), (b), and (c) correspond to $\epsilon=-1$, $\epsilon=0$, and $\epsilon=1$, respectively. As $Q_{\mathrm{m}}$ decreases, the peak of the potential barrier shifts outward and its height is significantly suppressed.