Quasinormal Modes and Thermodynamics of Regular Black Holes

TL;DR

This paper analytically investigates quasinormal modes and phase transitions in three types of regular black holes, revealing universal deviations in thermodynamics and unique behaviors of quasinormal modes not seen in singular black holes.

Contribution

It provides the first analytical study linking quasinormal modes, phase transitions, and thermodynamic deviations in regular black holes, highlighting universal properties and novel spiral-like mode shapes.

Findings

Universal deviations to the first law of black hole mechanics.

Existence of second order phase transitions and Davies points.

Non-vanishing imaginary parts of QNMs at extremality in regular black holes.

Abstract

By applying the dimensionless scheme, we investigate the quasinormal modes and phase transitions analytically for three types of regular black holes. The universal deviations to the first law of mechanics in regular black holes are proved. Meanwhile, we verify that second order phase transitions and Davies points still exist in these three models. In addition, we calculate their quasinormal modes in the eikonal limit by applying the light ring/quasinormal mode correspondence, and discuss the spiral-like shapes and the relations between the quasinormal modes and phase transitions. As the main result, we show that spiral-like shapes in the complex frequency plane are closely related to the parameterization, namely in some particular units the spiral-like shapes will emerge in the models, which may not be of the spiral behaviors reported by other authors. We also discover a universal property of regular black holes, i.e., the imaginary parts of their QNMs do not vanish for the extreme cases, which does not appear in singular black holes, such as the Reissner-Nordstr\"om and Kerr black holes, etc.