Conserved quantities in STEGR and applications

Abstract

We derive conservation laws in Symmetric Teleparallel Equivalent of General Relativity (STEGR) with direct application of Noether's theorem. This approach allows us to construct covariant conserved currents, corresponding superpotentials and invariant charges. A necessary component of our constructions is the concept of "turning off" gravity, introduced in the framework of STEGR to define the flat and torsionless connection. By calculating currents, one can obtain local characteristics of gravitational field like energy density. Surface integration of superpotentials gives charges which correspond to global quantities of the system like mass, momentum, etc. To test our results for the obtained currents and superpotentials, we calculate the energy density measured by freely falling observer in the simple solutions (Friedman universe, Schwartzchild black hole) and total mass of the Schwartzchild black hole. We find ambiguities in obtaining the connection, which explicitly affect the values of conserved quantities, and discuss possible solutions to this problem.

arXiv commentPublished Version

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Cited by in corpus (9)

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• Equivalence of $f(Q)$ cosmology with quintom-like scenario: the phantom field as effective realization of the non-trivial connection
• The equivalence principle for a plane gravitational wave in torsion based and non-metricity based teleparallel equivalents of general relativity
• Conventionalism, cosmology and teleparallel gravity
• The Hamiltonian constraint in the symmetric teleparallel equivalent of general relativity
• Mass and angular momentum for the Kerr black hole in TEGR and STEGR
• The gravitational energy-momentum pseudo-tensor in $f(Q)$ non-metric gravity
• Hamiltonian surface charges in General Parallel Relativity