Brane World black holes in Teleparallel Theory Equivalent to General Relativity and their Killing vectors, Energy, Momentum and Angular-Momentum

TL;DR

This paper investigates the energy, momentum, and angular momentum of brane world black holes within the teleparallel equivalent of general relativity, revealing non-zero angular momentum components and deriving associated Killing vectors.

Contribution

It introduces a regularized gravitational energy-momentum tensor in TEGR to reconcile energy differences in tetrad fields and derives Killing vectors for static space-times.

Findings

Different tetrad fields yield different energies without regularization.

Regularization aligns the energies of tetrad fields.

Non-zero angular momentum components are found in static space-times.

Abstract

The energy-momentum tensor, which is coordinate independent, is used to calculate energy, momentum and angular-momentum of two different tetrad fields. Although, the two tetrad fields reproduce the same space-time their energies are different. Therefore, a regularized expression of the gravitational energy-momentum tensor of the teleparallel equivalent of general relativity, (TEGR), is used to make the energies of the two tetrad fields equal. The definition of the gravitational energy-momentum is used to investigate the energy within the external event horizon. The components of angular-momentum associated with these space-times are calculated. In spite that we use a static space-times, we get a non-zero component of angular-momentum! Therefore, we derive the killing vectors associated with these space-times using the definition of the Lie derivative of a second rank tensor in the framework of the TEGR to make the picture more clear.