SIMILARITY SOLUTIONS OF FIELD EQUATIONS WITH AN ELECTROMAGNETIC STRESS TENSOR AS SOURCE

We study the general relativity with an electromagnetic stress tensor, as source, and Maxwell's equations in curved space. We investigate the similarity solutions of field equations of these two areas by using the generalized symmetry method based on Frechet derivative of the differential operators. Metrics and electromagnetic fields as functions of two independent variables are considered. The field equations are presented in a scientific form and certain exact solutions of these equations are systematically derived. The results are achieved by obtaining the infinitesimals of the group of transformations, which leave the system of field equations invariant. An optimal system of conjugacy inequivalent subgroups is then identified with the adjoint action of the symmetry group. This is further used to reduce the system of field equations into a system of ordinary differential equations with the aim of deriving certain exact solutions.