2008/10/31 by Muzaffer Adak, Özcan Sert, Mestan Kalay +1 · 2 citations
Physics and Astronomy · #gr-qc
paper · pdf · doi:10.1142/s0217751x13501674
published as International Journal of Modern Physics A Vol. 28 (2013) 1350167 · Accepted for publication in the International Journal of Modern Physics A
arxiv created 2013/11/25 · arxiv updated 2016/08/14
In this paper we elaborate on the symmetric teleparallel gravity (STPG) written in a non-Riemannian spacetime with nonzero nonmetricity, but zero torsion and zero curvature. Firstly we give a prescription for obtaining the nonmetricity from the metric in a peculiar gauge. Then we state that under a novel prescription of parallel transportation of a tangent vector in this non-Riemannian geometry the autoparallel curves coincides with those of the Riemannian spacetimes. Subsequently we represent the symmetric teleparallel theory of gravity by the most general quadratic and parity conserving lagrangian with lagrange multipliers for vanishing torsion and curvature. We show that our lagrangian is equivalent to the Einstein-Hilbert lagrangian for certain values of coupling coefficients. Thus we arrive at calculating the field equations via independent variations. Then we obtain in turn conformal, spherically symmetric static, cosmological and pp-wave solutions exactly. Finally we discuss a minimal coupling of a spin-1/2 field to STPG.