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We study the Teleparallel Equivalent of General Relativity (TEGR) withLagrangian that includes the flat (inertial) spin connection and that isevidently invariant with respect to local Lorentz rotations. Applying directlythe Noether theorem, we construct new expressions for conserved currents andrelated superpotentials. They are covariant both under coordinatetransformations and local Lorentz rotations, and allow us to construct welldefined conserved charges, unlike earlier approaches. The advantage is achievedby an explicit presence of a displacement vector in the new expressions thatcan be interpreted as a Killing vector, as a proper vector of an observer, etc.The new expressions are used to introduce a principle for definition of aninertial spin connection that is undetermined one in the TEGR from the start.Theoretical results are applied to calculate mass for the Schwarzschild blackhole and densities of conserved quantities for freely falling observers both inFriedmann-Lemaitre-Robertson-Walker world of all the three signs of curvatureand in (anti-)de Sitter space.

Conserved Currents and Superpotentials in Teleparallel Equivalent of General Relativity