Perturbations, eikonal limit and Hawking radiation of diverse external fields in a non-minimal charged black hole

Abstract

We compare the quasinormal modes (QNMs), greybody factors, and Hawking emission of massless scalar, electromagnetic, and Dirac test fields propagating on a non-minimal Einstein--Yang--Mills black hole. The QNMs are calculated using WKB and pseudospectral methods, while greybody factors are estimated with sixth-order WKB method. All computed modes are damped within the parameter range considered. Higher overtones generally exhibit stronger dependence on the non-minimal coupling $ξ$ than the fundamental mode, including non-monotonic behavior in the scalar and Dirac sectors. For large multipole numbers, all three fields follow a common leading eikonal description governed by the unstable circular null orbit. Increasing $ξ$ raises the orbital angular velocity and reduces the Lyapunov exponent, leading to higher oscillation frequencies and weaker damping rate. The greybody factors depend strongly on the multipole number, with weaker field dependent corrections from $ξ$. The partial-wave emission powers generally decrease with increasing $ξ$, while the lowest scalar mode shows mild non-monotonic behavior. This comparison reveals enhanced overtone sensitivity alongside comparatively small changes in transmission, whereas the Hawking emission reflects changes in both the greybody factors and the black hole temperature.