Gravitational perturbations of nonsingular black holes in conformal gravity

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.

Lessons from black hole quasinormal modes in modified gravity

“…The first example that we will show here is the QNMs of non-singular black holes in conformal gravity [13,14,46]. One can imagine that when the curvature scale is extremely high, the universe may respect the conformal invariance and it is described by some conformal theories of gravity.…”

“…In this respect, one can directly consider a particular mode, by fixing the multiple l and the overtone n, and compare their mode frequencies with those in GR. This turns out to be the most straightforward way of exhibiting how the QNMs would be altered when going beyond GR, and has been widely investigated in the literature [14,15,[32][33][34][35][36][37][38][39][40][41][42][43][44][45].…”

“…Furthermore, assuming that the non-singular black hole is governed by the Einstein equations coupled with an anisotropic fluid, the axial gravitational perturbations have been discussed in Ref. [14]. It was found that the master equations of the perturbations mentioned above can be expressed in the form of…”

“…where the effective potentials for the scalar field, electromagnetic fields, and the axial gravitational perturbations are [13,14]…”

“…The first feature is based on the aforementioned property of QNMs that they respect the no-hair theorem. In particular, we will take the non-singular black holes in conformal gravity [13,14] and the charged black holes in the Eddingtoninspired-Born-Infeld (EiBI) gravity [15] as examples to demonstrate that, due to the existence of the additional parameters in the theory, the QNM frequencies of these black holes are different from their GR counterparts.…”