Invariant stationary vacuum solutions by symmetry analysis and Jacobi elliptic rational expansion method

In this paper, new explicit exact solutions for the stationary static Einstein’s vacuum field equation are obtained. Symmetry analysis, based on Lie point transformations, is used to derive different similarity solutions. These transformations are used to reduce the equation under investigation into solvable ordinary differential equations, and then some interesting invariant solutions are presented. In addition, some of the solutions are obtained as a result of applying the Jacobi elliptic function expansion method to one of the reduced systems. Graphical representations of the obtained solutions are also shown.