Arbitrarily long-lived quasinormal modes of proper-time flow black holes

Peoples’ Friendship University of Russia (RUDN University) - 6 Miklukho-Maklaya Street, Moscow, 117198, Russia

Received: 16 March 2026
Accepted: 10 April 2026

Abstract

We investigate the quasinormal modes (QNMs) of a massive scalar field in the background of a regular black hole arising from the proper-time flow in asymptotically safe gravity. This quantum-corrected geometry, characterized by a deformation parameter q , smoothly interpolates between a near-extremal regular black hole and the Schwarzschild solution. Employing both the WKB approximation with Padé resummation and time-domain integration, we compute the complex frequencies for various values of the scalar field mass μ, multipole number ℓ, and deformation parameter q. We observe that the real parts of the QNMs increase with the field mass, while the imaginary parts exhibit behavior indicative of long-lived modes. Although quasi-resonances are not detected in the time-domain profiles due to the dominance of late-time tails, we find that the asymptotic decay follows an oscillatory slowly decaying behavior with the power-law envelope.