Teleparallel gravity models, in which the curvature and the nonmetricity of spacetime are both set zero, are widely studied in the literature. We work a different teleparallel theory, in which the curvature and the torsion of spacetime are both constrained
Thenfrom(37)and(38)
G(r)=1/F(r)(41)
andfrom(39)and(40)
F2(r)=1 C
e10,R02(ω)=F′
rFG2e30,
R12(ω)(G 1F)′G=rGe31,R23(ω)=1
G2)e32.(43)
ThusthequadraticinvariantoftheRiemanniancurvaturereads
R)∧ Rab(ω)= 2 (F′G 1)′ 2 (G 1)′
ab(ωrFG2+4r2 1 1
r61(44)
andthespacetimegeometryisnaturallycharacterizedbythequadraticinvariantofthenon-metricity
Qab∧ Qab= F′
r 1 1
4r3(r C) 3C
r2 1 1 C