Quantum-modified Regge–Wheeler formalism for black holes with phantom global monopoles: Potential profiles and Quasinormal modes

In this study, we present a thorough analysis of the effective potential and its reliance on critical parameters in the spacetime surrounding a static, spherically symmetric black hole (BH) represented by an AdS–Schwarzschild-like metric with a quantum correction. This BH also features phantom global monopoles, which modify the structure of the BH spacetime. We extend our study to include the spin-dependent Regge–Wheeler (RW)-potential, which characterizes the dynamics of perturbations in this quantum-corrected BH background. By examining this RW-potential for various spin fields, we show how quantum corrections affect its form in the presence of both phantom and ordinary global monopoles. Our analysis demonstrates that quantum corrections significantly alter the nature of the RW-potential, influencing the stability and behavior of test particles and perturbations around the BH. Furthermore, we investigated quasinormal modes (QNMs) using sixth-order WKB approximations for scalar and electromagnetic perturbations with zero cosmological constant. The influence of the quantum corrections on the QNMs is investigated in detail.