Scale invariant Einstein–Cartan theory in three dimensions

Abstract

We retreat the well-known Einstein–Cartan theory by slightly modifying the covariant derivative of spinor field by investigating double cover of the Lorentz group. We first write the Lagrangian consisting of the Einstein–Hilbert term, Dirac term and a scalar field term in a non-Riemannian spacetime with curvature and torsion. Then by solving the affine connection analytically we reformulate the theory in the Riemannian spacetime in a self-consistent way. Finally we discuss our results and give future perspectives on the subject.

A class of static spherically symmetric solutions in f(Q)-gravity

“…automatically satisfies the equations of motion ( 14)- (15). Here, T0 is a constant value (eventually vanishing) of the torsion scalar.…”

“…It is now well understood that GR is just a vertex of a geometrical trinity of dynamically equivalent gravity theories in which the other vertexes are the Teleparallel Equivalent to General Relativity (TEGR) [3][4][5][6][7][8][9][10][11][12][13], and the Symmetric Teleparallel Equivalent of General Relativity (STEGR) [14][15][16][17][18][19][20][21]. The former is characterized by vanishing curvature and nonmetricity and the connection reduces to the Weitzenböck connection, while in the latter, the curvature and the torsion vanish.…”

A class of static spherically symmetric solutions in f(T)-gravity

“…It is now well understood that GR is just a vertex of a geometrical trinity of dynamically equivalent gravity theories in which the other vertexes are the Teleparallel Equivalent to General Relativity (TEGR) [3][4][5][6][7][8][9][10][11][12][13], and the Symmetric Teleparallel Equivalent of General Relativity (STEGR) [14][15][16][17][18][19][20][21]. The former is characterized by vanishing curvature and non-metricity and the connection reduces to the Weitzenböck connection, while in the latter, the curvature and the torsion vanish.…”

Anisotropic charged stellar models with modified Van der Waals EoS in f(Q) gravity

“…One way to generalize GR is to improve the Ricci scalar R to its functional form, i.e., f (R) gravity [1,9]. Choosing the T (torsion) or Q (nonmetricity) results in similar but different explanations of gravity, famed as (TEGR) teleparallel equivalent of general relativity [10,11] and (STGR) symmetric teleparallel general relativity [12][13][14][15]. In STGR definition of gravity is based on nonmetricity instead of curvature and torsion.…”