A novel approach to autoparallels for the theories of symmetric teleparallel gravity

Abstract

Although the autoparallel curves and the geodesics coincide in the Riemannian geometry in which only the curvature is nonzero among the nonmetricity, the torsion and the curvature, they define different curves in the non-Riemannian ones. We give a novel approach to autoparallel curves and geodesics for theories of the symmetric teleparallel gravity written in the coincident gauge. Then we apply our autoparallel equation to a Schwarzschild-type metric and give remarks about dark matter and orbit equation.

We added a new section titled "An application to a stationary, spherically axisymmetric metric". Dedicated to Tekin Dereli in honour of his 72nd birthday

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Cited by in corpus (7)

• FLRW solutions in $f(Q)$ theory: the effect of using different connections
• Nonmetricity theories and aspects of gauge symmetry
• Weyl covariance, second clock effect and proper time in theories of symmetric teleparallel gravity
• Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity
• The non-minimally coupled symmetric teleparallel gravity with electromagnetic field
• Degrees of Freedom of New General Relativity I: Type 2, Type 3, Type 5, and Type 8
• Mass and angular momentum for the Kerr black hole in TEGR and STEGR