On the Gravitational Energy of Axial Perturbations in Regular Black Holes

TL;DR

This paper investigates the gravitational energy of axial perturbations in regular black holes using TEGR, linking the dynamical response of these black holes to the energy carried by their gravitational waves.

Contribution

It introduces a method to compute gravitational energy of axial perturbations in regular black holes using TEGR, connecting quasinormal modes to energy content.

Findings

Gravitational energy can be expressed in terms of quasinormal mode functions.

Regular black holes are stable under axial perturbations.

Energy content relates to the dynamical response of the black hole.

Abstract

The article deals with the gravitational energy associated with axial perturbations of regular black holes. We review the stability of the geometry under odd-parity perturbations and the corresponding quasinormal modes, previously obtained for this class of spacetimes. The perturbative functions describing the metric fluctuations are reconstructed from the master equation. To evaluate the energy content of these perturbations, we employ the Teleparallel Equivalent of General Relativity (TEGR), which provides a well-defined expression for gravitational energy. The gravitational energy is computed up to second order in the perturbation parameter and expressed in terms of the quasinormal mode functions. Our results establish a direct connection between the dynamical response of regular black holes and the energy carried by their gravitational perturbations.