Open AccessOn the Schwarzschild solution in TEGR
Author(s) -
E. D. Emtsova,
Martin Krššák,
А. Н. Петров,
A. V. Toporensky
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2081/1/012017
Subject(s) - covariant transformation , noether's theorem , inertial frame of reference , classical mechanics , schwarzschild radius , vector field , lorentz transformation , killing vector field , physics , mathematical physics , schwarzschild metric , conserved quantity , invariant (physics) , one way speed of light , general relativity , theoretical physics , principle of relativity , gravitation , four force , lagrangian , mechanics
Conserved currents, superpotentials and charges for the Schwarzschild black hole in the Teleparallel Equivalent of General Relativity (TEGR) are constructed. We work in the covariant formalism and use the Noether machinery to construct conserved quantities that are covariant/invariant with respect to both coordinate and local Lorentz transformations. The constructed quantities depend on the vector field ξ and we consider two different possibilities, when ξ is chosen as either a timelike Killing vector or a four-velocity of an observer. We analyze and discuss the physical meaning of each choice in different frames: static and freely falling Lemaitre frame. Moreover, a new generalized free-falling frame with an arbitrary initial velocity at infinity is introduced. We derive the inertial spin connection for various tetrads in different frames and find that the “switching-off” gravity method leads to ambiguities.