On Conserved Quantities for the Schwarzschild Black Hole in Teleparallel Gravity

Understand

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.