A Solution to Symmetric Teleparallel Gravity(6)

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

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