We are interested in the development of spherically symmetric geometries inF(T) teleparallel gravity which are of physical importance. We first express the general forms for the spherically symmetric frame and the zero curvature, metric compatible, spin connection. We then analyse the antisymmetric field equations (the solutions of which split into two cases, which we subsequently consider separately), and derive and analyse the resulting symmetric field equations. In order to further study the applications of spherically symmetric teleparallel models, we study 3 subcases in which there is an additional affine symmetry so that the resulting field equations reduce to a system of ordinary differential equations. First, we study static spherical symmetric geometries and solve the antisymmetric field equations and subsequently derive the full set of symmetric field equations. In particular, we investigate vacuum spacetimes and obtain a number of new solutions. Second, we consider an additional affine frame symmetry in order to expand the affine frame symmetry group to that of a spatially homogeneous Kantowski–Sachs geometry. Third, we study the special case of spherical symmetry with an additional fourth similarity affine vector.

Theories of gravity based on teleparallel geometries are characterized by the torsion, which is a function of the coframe, derivatives of the coframe, and a zero curvature and metric compatible spin-connection. The appropriate notion of a symmetry in a teleparallel geometry is that of an affine symmetry. Due to the importance of the de Sitter geometry and Einstein spaces within General Relativity, we shall describe teleparallel de Sitter geometries and discuss their possible generalizations. In particular, we shall analyse a class of Einstein teleparallel geometries which have a 4-dimensional Lie algebra of affine symmetries, and display two one-parameter families of explicit exact solutions.

In this paper, we investigate static spherically symmetric teleparallel $F\left(T\right)$ gravity containing a perfect isotropic fluid. We first write the field equations and proceed to find new teleparallel $F\left(T\right)$ solutions for perfect isotropic and linear fluids. By using a power-law ansatz for the coframe components, we find several classes of new non-trivial teleparallel $F\left(T\right)$ solutions. We also find a new class of teleparallel $F\left(T\right)$ solutions for a matter dust fluid. After, we solve the field equations for a non-linear perfect fluid. Once again, there are several new exact teleparallel $F\left(T\right)$ solutions and also some approximated teleparallel $F\left(T\right)$ solutions. All these classes of new solutions may be relevant for future cosmological and astrophysical applications.

We investigate the gravitational effect on Landau levels. We show that the familiar infinite Landau degeneracy of the energy levels of a quantum particle moving inside a uniform and constant magnetic field is removed by the interaction of the particle with a gravitational field. Two independent approaches are used to solve the relevant Schrödinger equation within the Newtonian approximation. It is found that both approaches yield qualitatively similar results within their respective approximations. With the goal of clarifying some results found in the literature concerning the use of a third independent approach for extracting the quantization condition based on a similar differential equation, we show that such an approach cannot yield a general and yet consistent result. We point out to the more accurate, but impractical, way to use such an approach; a way which does in principle yield a consistent quantization condition. We discuss how our results could be used to contribute in a novel way to the existing methods for testing gravity at the tabletop experiments level as well as at the astrophysical observational level by deriving the corrections brought by Yukawa-like and power-law deviations from the inverse-square law. The full relativistic regime is also examined in detail.

In this paper, we investigate time-dependent Kantowski–Sachs spherically symmetric teleparallel $F\left(T\right)$ gravity in vacuum and in a perfect isotropic fluid. We begin by finding the field equations and solve for new teleparallel $F\left(T\right)$ solutions. With a power-law ansatz for the co-frame functions, we find new non-trivial teleparallel $F\left(T\right)$ vacuum solutions. We then proceed to find new non-trivial teleparallel $F\left(T\right)$ solutions in a perfect isotropic fluid with both linear and non-linear equations of state. We find a great number of new exact and approximated teleparallel $F\left(T\right)$ solutions. These classes of new solutions are relevant for future cosmological applications.