Conserved Currents and Superpotentials in Teleparallel Equivalent of General Relativity

Abstract

We study the Teleparallel Equivalent of General Relativity (TEGR) with Lagrangian that includes the flat (inertial) spin connection and that is evidently invariant with respect to local Lorentz rotations. Applying directly the Noether theorem, we construct new expressions for conserved currents and related superpotentials. They are covariant both under coordinate transformations and local Lorentz rotations, and allow us to construct well defined conserved charges, unlike earlier approaches. The advantage is achieved by an explicit presence of a displacement vector in the new expressions that can 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 an inertial spin connection that is undetermined one in the TEGR from the start. Theoretical results are applied to calculate mass for the Schwarzschild black hole and densities of conserved quantities for freely falling observers both in Friedmann-Lemaitre-Robertson-Walker world of all the three signs of curvature and in (anti-)de Sitter space.

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• Exploring Axial Symmetry in Modified Teleparallel Gravity
• On Conserved Quantities for the Schwarzschild Black Hole in Teleparallel Gravity
• On spherically symmetric vacuum solutions and horizons in covariant $f(T)$ gravity theory
• Conserved quantities in STEGR and applications
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• Conventionalism, cosmology and teleparallel gravity
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• Kerr-Schild metrics in teleparallel gravity
• Noether currents in theories with higher derivatives and theories with differential field transformation in action (DFTA)
• On Gravitational Stefan-Boltzmann Law and Casimir Effect in FRW Universe
• Off-Shell ADT Conserved Quantities in Palatini Gravity