ИСТИНА

On constructing conserved quantities in TEGR and STEGR A.N.Petrov Sternberg Astronomical Institute, Moscow MV Lomonosov State University, Universitetskii pr., 13, Moscow 119992, Russia The teleparallel equivalent of general relativity (TEGR) and the symmetrical teleparallel equivalent of general relativity (STEGR) are studied. Lagrangians of TEGR and STEGR include both dynamical fields (tetrads and metric, respectively) and external fields (inertial spin connection, ISC, and symmetric teleparallel connection, STC, respectively). Applying directly the Noether theorem to covariant Lagrangians, one constructs new expressions for conserved currents and related superpotentials both in TEGR and in STEGR. Because both the dynamical fields and external fields are geometrical objects all of them are objects for diffeomorphisms. The new conserved quantities are covariant under coordinate transformations (and local Lorentz rotations in TEGR), and allow us to construct well defined conserved charges, unlike many earlier approaches. The advantage is achieved by an explicit presence of displacement vectors (defined for diffeomorphisms) in the new expressions that can be interpreted as a Killing vector, as a proper vector of an observer, etc., and of a presence of ISCs and STCs. To define external (undetermined from the start) fields, ISCs and STCs, the generalized principle “turning off” gravity is introduced generalizing earlier ones. Theoretical results are applied for constructing charges and currents in numerous models, like Schwarzschild and Kerr black holes, Friedmann–Lemaitre–Robertson–Walker world, (anti-)de Sitter space, flat gravitational waves.