Noether formalism for constructing conserved quantities in teleparallel equivalents of general relativity

E.D. Emtsova^†^a, b, A.N. Petrov^‡^c, A.V. Toporensky^§^c
^aDepartment of Physics, Ariel University, Ramat HaGolan Str. 65, Ariel, 40700, Israel
^bDepartment of Physics, Bar Ilan University, Max ve-Anna Webb Str. 1, Ramat Gan, 5290002, Israel
^cLomonosov Moscow State University, Shternberg State Astronomical Institute, Universitetskii prosp. 13, Moscow, 119234, Russian Federation

This paper has a methodological character, where we present a comprehensive formalism for constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR) and Symmetric Teleparallel Equivalent of General Relativity (STEGR). It was developed in a series of our earlier studies. and here, we combine them into a complete form. By employing the Noether method within a tensor formalism, conserved currents, superpotentials, and charges are constructed. These are shown to be covariant under coordinate transformations and local Lorentz rotations in TEGR, while, in STEGR, they are covariant under coordinate transformations. The teleparallel (flat) connections in both theories are defined using the 'turning off gravity' principle. Uniting such defined flat connections with the tetrad in TEGR and metric in STEGR, a new notion — 'gauge' — fruitful in applications, is introduced. The choice of various initial tetrads in TEGR or initial coordinates in STEGR leads to different gauges, giving different conserved quantities. Finally, we discuss an appropriate choice of gauges from a possible set of them.

Correspondence should be addressed to
Keywords: teleparallel gravity, Noether theorem, conserved currents, superpotentials, conserved charges, gauges
PACS: 04.20.−q, 04.20.Cv, 04.50.Kd (all)
DOI: 10.3367/UFNe.2025.05.039924
URL: https://ufn.ru/en/articles/2025/11/i/
Web of Science

001644067100008
Scopus

2-s2.0-105027335500
ADS NASA

2025PhyU...68.1164E
Citation: Emtsova E D, Petrov A N, Toporensky A V "Noether formalism for constructing conserved quantities in teleparallel equivalents of general relativity" Phys. Usp. 68 1164–1172 (2025)

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Received: 5th, February 2025, accepted: 20th, May 2025

Оригинал: Емцова Е Д, Петров А Н, Топоренский А В «Формализм Нётер в построении сохраняющихся величин в телепараллельных эквивалентах общей теории относительности» УФН 195 1235–1244 (2025); DOI: 10.3367/UFNr.2025.05.039924

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