We derive conservation laws in Symmetric Teleparallel Equivalent of General
Relativity (STEGR) with direct application of Noether’s theorem. This approach
allows us to construct covariant conserved currents, corresponding
superpotentials and invariant charges. A necessary component of our
constructions is the concept of “turning off” gravity, introduced in the
framework of STEGR to define the flat and torsionless connection. By
calculating currents, one can obtain local characteristics of gravitational
field like energy density. Surface integration of superpotentials gives charges
which correspond to global quantities of the system like mass, momentum, etc.
To test our results for the obtained currents and superpotentials, we calculate
the energy density measured by freely falling observer in the simple solutions
(Friedman universe, Schwartzchild black hole) and total mass of the
Schwartzchild black hole. We find ambiguities in obtaining the connection,
which explicitly affect the values of conserved quantities, and discuss
possible solutions to this problem.
