On conserved quantities for the Schwarzschild black hole in teleparallel gravity

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 4 and we consider two different options where 4 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 an 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.

Automated summary

This study examines various methods of constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR), with a focus on Noether charges in the covariant formulation. The physical implications of choosing the observer's four-velocity or a Killing vector as 4 in different frames, based on the example of the Schwarzschild solution, are discussed. Additionally, an analysis of determining inertial spin connections for different tetrads used in calculations is presented, revealing some ambiguity in the method of switching-off gravity.