New solutions to Einstein's equations to find Walker manifolds

In this paper, we investigate the Einsteinian manifolds with parallel null distribution. For this, we first obtain the equations that lead to finding the mentioned manifolds. These equations are known as Einstein's equations. Then we reduce these equations by using Lie symmetry method. These equations are known as Einstein's equations. In this method, we first obtain the generators of the symmetry algebra and then calculate the differential invariants for each of the generators and calculate the group invariant solutions of this equation. In addition to this, we also obtain the optimal system of the one-dimensional sub-algebras of these equations. This optimal system helps us to have a classification on group invariant solutions using conjugate mapping.