Parameterization of the Kerr solution

In this thesis we are exploring basic properties of the Kerr solution using se- veral coordinate systems. Later on, we are deriving general metric form of the spacetime foliated by null hypersurfaces. Employing the formalism of optical sca- lars we shall see, that geometry of a such a spacetime is non-twisting, that is it admits existence of a non-twisting affinely parametrized null geodesic congru- ence. Subsequently, we are trying to express the Kerr solution in the form of non-twisting coordinates. This form would have many applications e.g. in forma- lism of weakly isolated horizons (WHIs) for use in more realistic astrophysical models of black holes