Generalized Teleparallel Theory

We construct a theory in which the gravitational interaction is described only by torsion, but that generalizes the Teleparallel Theory still keeping the invariance of local Lorentz transformations in one particular case. We show that our theory falls, to a certain limit of a real parameter, in the $f(\bar{R})$ Gravity or, to another limit of the same real parameter, in a modified $f(T)$ Gravity, interpolating between these two theories and still can fall on several other theories. We explicitly show the equivalence with $f(\bar{R})$ Gravity for cases of Friedmann-Lemaitre-Robertson-Walker flat metric for diagonal tetrads, and a metric with spherical symmetry for diagonal and non-diagonal tetrads. We do still four applications, one in the reconstruction of the de Sitter universe cosmological model, for obtaining a static spherically symmetric solution type-de Sitter for a perfect fluid, for evolution of the state parameter $\omega_{DE}$ and for the thermodynamics to the apparent horizon.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1503.07427, arXiv:1503.0785

Gravitational lens effect of a holonomy corrected Schwarzschild black hole

In this paper we study the gravitational lensing effect for the Schwarzschild solution with holonomy corrections. We use two types of approximation methods to calculate the deflection angle, namely the weak and strong field limits. For the first method, we calculate the deflection angle up to the fifth order of approximation and show the influence of the parameter $\lambda$ (in terms of loop quantum gravity) on it. In addition, we construct expressions for the magnification, the position of the lensed images and the time delay as functions of the coefficients from the deflection angle expansion. We find that $\lambda$ increases the deflection angle. In the strong field limit, we use a logarithmic approximation to compute the deflection angle. We then write four observables, in terms of the coefficients $b_1$, $b_2$ and $u_m$, namely: the asymptotic position approached by a set of images $\theta_{\infty}$, the distance between the first image and the others $s$, the ratio between the flux of the first image and the flux of all other images $r_m$, and the time delay between two photons $\Delta T_{2,1}$. We then use the experimental data of the black hole Sagittarius $A^{\star}$ and calculate the observables and the coefficients of the logarithmic expansion. We find that the parameter $\lambda$ increases the deflection angle, the separation between the lensed images and the delay time between them. In contrast, it decreases the brightness of the first image compared to the others.Comment: 26 pages, 17 figure