# Gravitational perturbations of non-singular black holes in conformal gravity

## TL;DR

This paper studies the quasinormal modes of non-singular black holes in conformal gravity, showing their potential to be distinguished from Schwarzschild black holes via gravitational wave observations.

## Contribution

It derives the master equation for axial gravitational perturbations of conformally related non-singular black holes and evaluates their QNM frequencies using WKB method.

## Key findings

- QNM spectra differ from Schwarzschild black holes.
- Deviations in QNM frequencies could be observable.
- Potential to test conformal gravity theories with gravitational waves.

## Abstract

It is believed that in the near future, gravitational wave detections will become a promising tool not only to test gravity theories, but also to probe extremely curved spacetime regions in our universe, such as the surroundings of black holes. In this paper, we investigate the quasinormal modes (QNMs) of the axial gravitational perturbations of a class of non-singular black holes conformally related to the Schwarzschild black hole. These non-singular black holes can be regarded as the vacuum solution of a family of conformal gravity theories which are invariant under conformal transformations. After conformal symmetry is broken, these black holes produce observational signatures different from those of the Schwarzschild black hole, such as their QNM frequencies. We assume that the spacetime is described by the Einstein equation with the effective energy momentum tensor of an anisotropic fluid. The master equation describing the QNMs is derived, and the QNM frequencies are evaluated with the Wentzel-Kramers-Brillouin (WKB) method up to the 6th order. As expected, the QNM spectra of these non-singular black holes deviate from those of the Schwarzschild black hole, indicating the possibility of testing these black hole solutions with the help of future gravitational wave detections.