Perturbations of the Gravitational Energy in the TEGR: Quasinormal Modes of the Schwarzschild Black Hole

TL;DR

This paper calculates the gravitational energy spectrum of Schwarzschild black hole perturbations using TEGR, revealing discretized energy levels and providing insights into gravitational radiation flux decrease.

Contribution

It introduces a general formula for gravitational energy in TEGR for black hole perturbations and analyzes the discretization of energy spectrum based on quasinormal modes.

Findings

Energy spectrum depends on mode integers n and l

Energy perturbations are discretized

Derived a simple expression for gravitational radiation flux decrease

Abstract

We calculate the gravitational energy spectrum of the perturbations of a Schwarzschild black hole described by quasinormal modes, in the framework of the teleparallel equivalent of general relativity (TEGR). We obtain a general formula for the gravitational energy enclosed by a large surface of constant radius $r$, in the region $m\,<<\,r\,<<\infty$, where $m$ is the mass of the black hole. Considering the usual asymptotic expression for the perturbed metric components, we arrive at finite values for the energy spectrum. The perturbed energy depends on the two integers $n$ and $l$ that describe the quasinormal modes. In this sense, the energy perturbations are discretised. We also obtain a simple expression for the decrease of the flux of gravitational radiation of the perturbations.