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

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.

29 pages, 5 figures, article to appear in the Special Issue "Teleparallel Gravity: Foundations and Observational Constraints" of the Universe

References in corpus (6)

• The teleparallel equivalent of general relativity
• The physical interpretation of the spectrum of black hole quasinormal modes
• Second Order Quasi-Normal Mode of the Schwarzschild Black Hole
• On reference frames in spacetime and gravitational energy in freely falling frames
• Gravitational Waves in Higher Order Teleparallel Gravity
• Weak field limit and gravitational waves in higher-order gravity

Cited by in corpus (4)

• Teleparallel Gravity: From Theory to Cosmology
• Ringing of a black hole in a dark matter halo
• Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity
• On the Gravitational Angular Momentum of Axial Perturbations of a Regular Black Hole