Open AccessOn conservation laws in teleparallel gravity
Author(s) -
E. D. Emtsova,
А. Н. Петров,
A. V. Toporensky
Publication year - 2020
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 - 10.1088/1742-6596/1557/1/012017
Subject(s) - noether's theorem , conserved quantity , conservation law , covariant transformation , lorentz transformation , observer (physics) , classical mechanics , inertial frame of reference , physics , conserved current , killing vector field , principle of relativity , general relativity , mathematical physics , four force , quantum mechanics , lagrangian
Applying directly the Noether theorem in the framework of the Teleparallel Equivalent of General Relativity (TEGR), we construct conserved quantities, currents and superpotentials. They are covariant both under coordinate transformations and under local Lorentz rotations, unlike earlier approaches. This advantage is achieved by a presence in expressions of conservation laws of a displacement vector that can be interpreted as a Killing vector, as a proper vector of an observer, etc. We introduce, as well, a principle for a definition of an inertial spin connection that is an undetermined quantity in TEGR in the original formulation. The new expressions for conserved quantities and the introduced principle are applied to calculate mass for the Schwarzschild black hole and energy density for an observer freely falling in spatially flat Friedmann world.