Weyl–Lorentz-U(1)-invariant symmetric teleparallel gravity in three dimensions

Abstract

We consider a Weyl–Lorentz-U(1)-invariant gravity model written in terms of a scalar field, electromagnetic field and nonmetricity without torsion and curvature, the so-called symmetric teleparallel geometry, in three dimensions. Firstly, we obtain variational field equations from a Lagrangian. Then, we find some classes of circularly symmetric rotating solutions by making only a metric ansatz. The coincident gauge of symmetric teleparallel spacetime allows us for doing so.

The non-minimally coupled symmetric teleparallel gravity with electromagnetic field

“…Therefore, STPG model was later constructed and its spherically symmetric solutions were founded in the papers [7][8][9]. This model has subsequently become a remarkable research topic, which has been extensively studied in many papers [10][11][12][13][14][15][16][17] and the references therein.…”