Conserved Currents and Superpotentials in Teleparallel Equivalent of General Relativity

TL;DR

This paper develops covariant conserved currents and superpotentials in TEGR, enabling well-defined conserved charges and applying these to calculate mass and densities in various spacetimes.

Contribution

It introduces new covariant expressions for conserved currents in TEGR that incorporate a displacement vector, improving the definition of conserved charges.

Findings

Derived covariant conserved currents and superpotentials.

Calculated black hole mass and conserved densities in different cosmological models.

Provided a principle for defining the inertial spin connection in TEGR.

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.