Quasinormal ringing of regular black holes in asymptotically safe gravity: the importance of overtones

TL;DR

This study investigates the quasinormal modes of regular black holes in asymptotically safe gravity, highlighting the significant impact of overtones and the importance of the identification parameter choice on the spectrum.

Contribution

It reveals that overtones exhibit large deviations from Schwarzschild predictions and emphasizes the role of the near-horizon region in quasinormal mode behavior.

Findings

Overtones deviate significantly from Schwarzschild predictions.

Purely imaginary modes can appear at the second overtone.

Deviations are larger than previously claimed.

Abstract

Asymptotically safe gravity is based on the idea that the main contribution to the Schwarzschild-like black hole spacetime is due to the value of the gravitational coupling which depends on the distance from the origin and approaches its classical value in the far zone. However, at some stage this approach has an arbitrariness of choice of some identification parameter. The two cases of identification are considered here: first, by the modified proper length (the Bonanno-Reuter metric), and second, by the Kretschmann scalar (the metric for this case coincides, up to the redefinition of constants, with the Hayward metric). Even though the quasinormal modes of these metrics have been extensively studied, a number of interesting points were missed. We have found that quasinormal modes are qualitatively similar for both types of identification. The deviation of the fundamental mode from its Schwarzschild limit may be a few times larger than it was claimed in the previous studies. The striking deviation from the Schwarzschild limit occurs for overtones, being as large as hundreds of percent even when the fundamental mode is almost coinciding with the Schwarzschild one. This happens because the above metrics are very close to the Schwarzschild one everywhere, except a small region near the event horizon, which is crucial for overtones. The spectrum of both metrics contains purely imaginary (non-oscillatory) modes, which, for some values of parameters, can appear already at the second overtone.