Gauge Approach to The Symmetric Teleparallel Gravity

We discuss a gauge invariant gravity model in a non-Riemannian geometry in which the curvature and the torsion both are zero, the nonmetricity is nonzero. We also argue that only a metric ansatz is enough to start finding solutions to the field equations. As an application we obtain explicitly a conformally flat solution.Comment: This is the improved version of our manuscript arXiv:0810.2388v1. To appear in International Journal of Geometric Methods in Modern Physic

Spinor coupling to the weak Poincare gauge theory of gravity in three dimensions

Minimal coupling of a Dirac field to gravity with the most general non-propagating torsion is considered in (1+2)-dimensions. The field equations are obtained from a lagrangian by a variational principle. The space-time torsion is calculated algebraically in terms of a quadratic spinor condensate plus coupling coefficients. Firstly we give circularly symmetric rotating exact solutions that collapse to $AdS_3$ geometry in the absence of the Dirac condensate. Secondly we investigate a BTZ-like solution.Comment: We added a new subsection, corrected syntax errors, extended dicussion. To be published in Phys. Rev.

Non-minimal RF2RF^2-type corrections to holographic superconductor

We study $(2+1)$-dimensional holographic superconductors in the presence of non-minimally coupled electromagnetic field to gravity by considering an arbitrary linear combination of $RF^2$-type invariants with three parameters. Our analytical analysis shows that the non-minimal couplings affect the condensate and the critical temperature.Comment: Accepted for publication in Modern Physics Letters

Non-minimally coupled Dirac equation with torsion: Poincar\'e gauge theory of gravity with even and odd parity terms

We take a Dirac field non-minimally coupled to the gravitational field within the framework of the Poincar\'e gauge theory of gravity with torsion and curvature. We study the subcase of "weak" gravity, that is, the gravitational Lagrangian depends only linearly on the curvature and quadratically on the torsion. We include all pieces in curvature and torsion that are of odd parity. The second field equation of gravity is derived by varying the Lorentz connection. We solve it with respect to the torsion and decompose the first field equation of gravity and the Dirac equation into Einsteinian pieces and post-Riemannian terms.Comment: Title and content have been changed. To appear in CQ

Anisotropic cosmological solutions to the Y(R)F2Y(R)F^2 gravity

We investigate anisotropic cosmological solutions of the theory with non-minimal couplings between electromagnetic fields and gravity in $Y(R) F^2$ form. After we derive the field equations by the variational principle, we look for spatially flat cosmological solutions with magnetic fields or electric fields. Then we give exact anisotropic solutions by assuming the hyperbolic expansion functions. We observe that the solutions approach to the isotropic case in late-times.Comment: 16 pages, 5 figure

Weyl-Lorentz-U(1)-invariant symmetric teleparallel gravity in three dimensions

We consider a Weyl-Lorentz-U(1)-invariant gravity model written in terms of a scalar field, electromagnetic field and nonmetricity tensor in three dimensions. Firstly we obtain variational field equations from a Lagrangian. Then, we find some classes of circularly symmetric rotating solutions by exploiting the coincident gauge of symmetric teleparallel spacetime

The non-minimally coupled symmetric teleparallel gravity with electromagnetic field

We construct a symmetric teleparallel gravity model which is non-minimally coupled with electromagnetic field in four dimensions inspired by its Riemannian equivalent. We derive the field equations by taking the variation of this model, which is written here for the first time. Then, we find some classes of spherically symmetric static solutions by the coincident gauge of symmetric teleparallel spacetime.Comment: 16 page

Symmetric Teleparallel Gravity: Some exact solutions and spinor couplings

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.Comment: Accepted for publication in the International Journal of Modern Physics