Static, cylindrically symmetric solutions in symetric teleparallel gravity

In this thesis, based on the theorem called 'Symmetric Teleparallel (STEGR)', which has been shown to be equivalent to General Relativity (GR), f (Q) gravity is studied, which is an alternative to GR and a generalised version of STEGR. Additionally, f (Q) theory, which has not been previously examined in a static, cylindrically symmetric spacetime, was investigated in this spacetime to assess the consistency of this theory. In order to obtain the non-metricity scalar Q for f (Q) theory, which corresponds to the Ricci scalar in GR, the components of non-metricity, disformation, and superpotential tensors were calculated from the most general static, cylindrically symmetric metric. According the field equations, f (Q) should be zero in vacuum solutions. However, unlike the vacuum solutions and the widely studied spherically symmetric solutions in the literature, there are no constraints on the scalar Q and the function f (Q) in perfect fluid solutions. In this regard, to obtain the most general result, the f (Q) function was chosen as a power series which is both coherent with cosmological solutions and in its simplest form, and equation of action was constructed accordingly. The energy density ρ and the directional pressures pm are obtained by the field equations which are derived from the variation of the action with respect to metric and affine connections and the energy momentum tensor of the anisotropic perfect fluid. Corresponding solutions of f (Q)-gravity are discussed for few known solutions of static, cylindrically symmetric spacetime. By determining the constants that would provide positive energy density, the numerical values of the directional pressures were obtained, and the graphs were analyzed accordingly. Furthermore, to analyze the consistency of the obtained solution, the energy conditions null energy condition (NEC), weak energy condition (WEC), dominant energy condition (DEC), and strong energy condition (SEC) inequalities were calculated, and their behaviors were graphed on positive energy density coefficients.