Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-10-14
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
This is a new paper
Scientific paper
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 the minimal coupling of a spin-1/2 field to STPG.
Adak Muzaffer
Kalay Mestan
Sari Murat
Sert Özcan
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