https://doi.org/10.1140/epjc/s10052-021-09505-x
Regular Article - Theoretical Physics
On conserved quantities for the Schwarzschild black hole in teleparallel gravity
1
Sternberg Astronomical Institute, Lomonosov Moscow State University, Universitetskii pr., 13, 119992, Moscow, Russia
2
Faculty of Physics, Lomonosov Moscow State University, 119991, Moscow, Russia
3
Bangkok Fundamental Physics Group, Department of Physics, Chulalongkorn University, 10330, Bangkok, Thailand
4
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, 225009, Yangzhou, China
5
Kazan Federal University, Kremlevskaya 18, 420008, Kazan, Russia
Received:
7
June
2021
Accepted:
28
July
2021
Published online:
17
August
2021
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 
and we consider two different options where 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.
© The Author(s) 2021
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