A class of exact solutions to the Einstein field equations

Abstract

The Einstein–Rosen metric is considered and a class of new exact solutions of the field equations for stationary axisymmetric Einstein–Maxwell fields is obtained. The Lie classical approach is applied to obtain exact solutions. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of Einstein–Maxwell equations.