On certain new exact solutions of the Einstein equations for axisymmetric rotating fields

We investigate the Einstein field equations corresponding to the Weyl–Lewis–Papapetrou form for an axisymmetric rotating field by using the classical symmetry method. Using the invariance group properties of the governing system of partial differential equations (PDEs) and admitting a Lie group of point transformations with commuting infinitesimal generators, we obtain exact solutions to the system of PDEs describing the Einstein field equations. Some appropriate canonical variables are characterized that transform the equations at hand to an equivalent system of ordinary differential equations and some physically important analytic solutions of field equations are constructed. Also, the class of axially symmetric solutions of Einstein field equations including the Papapetrou solution as a particular case has been found.