On the solutions of field equations due to rotating bodies in General Relativity

A metric, describing the field due to bodies in stationary rotation about their axes and compatible with a stationary electromagnetic field, has been studied in present paper. Using Lie symmetry reduction approach we have herein examined, under continuous groups of transformations, the invariance of field equations due to rotation in General Relativity, that are expressed in terms of coupled system of partial differential equations. We have exploited the symmetries of these equations to derive some ans$\ddot{a}$tz leading to the reduction of variables, where the analytic solutions are easier to obtain by considering the optimal system of conjugacy inequivalent subgroups. Furthermore, some solutions are considered by using numerical methods due to complexity of reduced ordinary differential equations.