Among modified theories of gravity, the teleparallel f (T ) gravity is an intensively discussed model in the literature. The best way to investigate its viability is to derive observable predictions which yield evidence or constraints for the model, when compared with actual observations. In this paper we derive the photon sphere and the perihelion shift for weak f (T ) perturbations of general relativity. We consistently calculate first order teleparallel perturbations of Schwarzschild and Minkowski spacetime geometry, with which we improve and extend existing results in the literature. * Electronic address: sbahamonde@ut.ee † Electronic address: kai.flathmann@uni-oldenburg.de ‡ Electronic address: christian.pfeifer@ut.ee

In this article we derive the post-Newtonian limit of a class of teleparallel theories of gravity, where the action is a free function L(T, X, Y, φ) of the Torsion scalar T and scalar quantities X and Y built from the dynamical scalar field φ. We restrict the analysis to a massless scalar field in order to use the parameterized post-Newtonian formalism without modifications, such as introducing an effective gravitational constant which depends on the distance between the interacting masses. In particular the results show a class of fully-conservative theories of gravity, where the only nonvanishing parameters are γ and β. For a particular choice of the function L(T, X, Y, φ) the theory cannot be distinguished from General Relativity in its post-Newtonian approximation.

In this article we analyze the post-Newtonian approximation of a generalization of the symmetric teleparallel gravity with the help of the parameterized post-Newtonian (PPN) formalism. This class of theories is based on a free function of the five independent quadratic contractions of the non-metricity tensor. By calculating the PPN metric of these theories, we can restrict the Taylor coefficients of the free function with the help of the PPN parameters and their observational bounds. We find two families of theories whose PPN parameters are identical to those of general relativity, and thus in full agreement with observations. For three further families, we find that only the PPN parameters β and γ deviate, but can be brought arbitrarily close to their general relativity values by an appropriate choice of the Lagrangian, so that also these families contain candidate theories which agree with observations. The remaining theories either possess no well-defined solution of the post-Newtonian field equations, or possess a post-Newtonian limit which exceeds the form assumed in the PPN formalism.

In this article we derive the geodesic equations in the U(1) 2 dyonic rotating black hole spacetime. We present their solutions in terms of the Kleinian σ-function and in special cases in terms of the Weierstraß ℘-, σ-and ζ-functions. To give a list of all possible orbits, we analyse the geodesic motion of test particles and light using parametric diagrams and effective potentials.

In this article we study the geodesic motion of test particles and light in the Einstein-Maxwelldilaton-axion black hole spacetime. We derive the equations of motion and present their solutions in terms of the Weierstraß ℘-, σ-and ζ-functions. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and give a list of all possible orbit types.