Invariant solutions of Einstein field equations in pure radiation fields

General form of axially symmetric stationary metric: exact solutions and conservation laws in vacuum fields

“…The solutions of special forms of metric can be derived from the solutions of general metric (1) by using some transformations (like mentioned in above remarks). Similarly, the conservation laws for Einstein vacuum field equations corresponding to some special forms of axially symmetric stationary metric, can also be derived from the conservation laws (17) that are obtained in correspond to most general form of axially symmetric stationary line element.…”

“…By approaching through the classical symmetry method, we have reduced the derived PDEs into ODEs. The conservation laws (17) have been obtained for Einstein vacuum equations in axially symmetric gravitational fields. The solutions of Lewis metric and Chandrasekhar metric, have also been derived from the obtained solutions.…”

“…This semi-Riemannian manifold [24] is not conformally flat. The Lie symmetry method [9,10,[16][17][18]30] is used to find the symmetry groups [3,15], performing symmetry reduction and for getting the exact solutions in terms of integrable arbitrary functions. On letting the doubly periodic Jacobi elliptic functions in place of arbitrary functions, the 3D plots and 2D plots are shown.…”

Non-static plane symmetric perfect fluid solutions and Killing symmetries in f(R, T) gravity

“…However, when it comes to non-linearity of DEs, the Lie symmetry method [9] has been proved most effective. Many authors have derived exact solutions of FEs in GR using this method [10][11][12][13][14]. Jyoti et al [15] has used symmetry analysis in order to find the perfect fluid solutions for Einstein field equations.…”