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 permit 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 permit 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.

中文翻译：

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GR 的远平行等效中的守恒电流和超电势

我们研究了广义相对论的 Teleparallel Equivalent (TEGR) 与拉格朗日，其中包括平面（惯性）自旋连接，并且对于局部洛伦兹旋转显然是不变的。直接应用诺特定理，我们构建了守恒电流和相关超电势的新表达式。它们在坐标变换和局部洛伦兹旋转下都是协变的，并且允许构建定义明确的守恒电荷，这与早期的方法不同。优点是通过在新表达式中明确存在位移向量来实现的，该向量可以解释为 Killing 向量、观察者的固有向量等。 新表达式允许引入定义惯性自旋连接的原理从一开始就在 TEGR 中未确定。