Axially symmetric black hole solutions in f(T) gravity

The f(T) theory of gravity seems to have the capacity to explain cosmological phenomena such as the early inflation and the cosmic acceleration of the universe. When considering its success at the weak field limit (infrared scale), the black hole solutions of f(T) theory gain importance in order to understand the strong field or ultraviolet scale behaviour. Besides the axially symmetric ones, spherically symmetric solutions for $f(T)$ theory are obtained in the scope of this thesis. Firstly, by using the most general scalar - tensor equivalent of the f(T) theory, Einstein frame Lagrangian is obtained via conformal transformations. After that, tetrad potentials are obtained in terms of conserved quantities in both the Jordan and the Einstein frames for spherical and cylindrical tetrads. New solutions are gathered for both spherical and cylindrical tetrads by solving the Euler - Lagrange equations corresponding to the Jordan frame Lagrangians. By computing and analyzing the singularities, the cases that these solutions correspond to black holes are determined.