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

PALA Ç., Adak M.

A Life in Mathematical Physics: Conference in Honour of Tekin Dereli, DERELI-FS 2021, Virtual, Online, 26 - 28 November 2021, vol.2191 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 2191
  • Doi Number: 10.1088/1742-6596/2191/1/012017
  • City: Virtual, Online
  • Keywords: Autoparallel curve, Geodesic, Non-Riemannian geometry
  • Kayseri University Affiliated: No

Abstract

© 2021 Published under licence by IOP Publishing Ltd.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.