On Conserved Quantities for the Schwarzschild Black Hole in Teleparallel Gravity

TL;DR

This paper investigates conserved quantities in teleparallel gravity, emphasizing covariant Noether charges for the Schwarzschild black hole, and explores their physical interpretation in different frames and tetrad choices.

Contribution

It demonstrates the use of covariant Noether charges as invariant conserved quantities in TEGR and analyzes their physical meaning across various observer frames and tetrad configurations.

Findings

Noether charges are true invariants in covariant TEGR.

Different observer frames yield distinct physical interpretations of conserved quantities.

Ambiguity exists in choosing inertial spin connections for tetrads.

Abstract

We examine various methods of constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR). We demonstrate that in the covariant formulation the preferred method are the Noether charges that are true invariant quantities. The Noether charges depend on the vector field $\xi$ and we consider two different options where $\xi$ is chosen as either a Killing vector or a four-velocity of the observer. We discuss the physical meaning of each choice on the example of the Schwarzschild solution in different frames: static, freely falling Lemaitre frame, and a newly obtained generalised freely falling frame with an arbitrary initial velocity. We also demonstrate how to determine the inertial spin connection for various tetrads used in our calculations, and find a certain ambiguity in the "switching off" gravity method where different tetrads can share the same inertial spin connection.