Quasinormal modes and tidal Love numbers of covariant effective quantum black holes with cosmological constant

Abstract

This paper systematically investigates the quasinormal modes (QNMs) and tidal Love numbers of covariant quantum-modified black holes (BHs) within two cosmological constant-dependent metric frameworks. By deriving axial/polar perturbation equations and employing pseudospectral methods (for QNMs) and numerical integration (for Love numbers), we quantify the quantum parameter $\zeta$'s influence. We find that, higher overtones exhibit enhanced $\zeta$ sensitivity. Solution 1 maintains purely imaginary QNMs under $\zeta$ variation, whereas Solution 2 demonstrates mode transitions from real to complex for polar/axial perturbations. Furthermore, for Love number, axial perturbations show non-monotonic $\zeta$ dependence, with $\Delta\mathcal{T}^a_l$ peaking at specific $\ell$ values before decay. While for polar perturbation of the same metric displays strictly monotonic $\zeta$ effects on $\Delta\mathcal{T}^p_l$. These results highlight quantum gravity's role in BH perturbation dynamics and cosmological BH phenomenology.