Perturbations of massless external fields on magnetically charged black holes in string-inspired Euler-Heisenberg theory

TL;DR

This work investigates how massless external fields perturb magnetically charged black holes in a string-inspired Euler–Heisenberg framework. It derives the scalar and electromagnetic perturbation equations, casts them in Schrödinger-like form with explicit potentials $V_s(r)$ and $V_e(r)$, and solves for quasinormal frequencies (QNFs) using AIM and a 6th‑order WKB method under standard QNM boundary conditions; it also computes the scalar greybody factor via WKB. The results show that increasing the magnetic charge $Q_m$ generally increases the real parts of the QNFs and, depending on the horizon-structure parameter $$, can enhance or suppress damping, with $$ largely exerting a smaller effect on the QNFs; the greybody factor decreases with $Q_m$ and increases with $$, both consistent with the behavior of the effective potentials. The analysis reveals how horizon structure controlled by $=-$ and magnetic charge influence ringdown signatures and emission spectra, contributing to black hole spectroscopy in nonlinear electrodynamics-inspired gravity and informing potential gravitational-wave phenomenology in strong-field string-inspired contexts.

Abstract

In this paper, we study the perturbations of massless scalar and electromagnetic fields on the magnetically charged black holes in string-inspired Euler-Heisenberg theory. We calculate the quasinormal frequencies (QNFs) and discuss influences of black hole magnetic charge $Q_m$, coupling parameter $ε$ and angular momentum $l$ on QNFs, emphasizing the relationship between these parameters and QNMs behavior. We find these results obtained through the AIM method are in good agreement with those of obtained by WKB method. The greybody factor is calculated by WKB method. The effects of these parameters $Q_m$ and $ε$ on the greybody factor are also studied.

Figures (13)

• Figure 1: The effective potential $V_s(r)$ for massless scalar field perturbation on black hole with $M=1$ and $\epsilon>0$.
• Figure 2: The effective potential $V_s(r)$ for massless scalar field perturbation on black hole with $M=1$ and $\epsilon<0$.
• Figure 3: The effective potential $V_e(r)$ for massless electromagnetic field on black hole with $M=1$ and $\epsilon>0$.
• Figure 4: The effective potential $V_e(r)$ for massless electromagnetic field on black hole with $M=1$ and $\epsilon<0$.
• Figure 5: Variation of fundamental QNFs with respect to the different$l$ with $M=1$ and $Q_m=0.3$.