On certain classes of exact solutions of Einstein equations for rotating fields in conventional and nonconventional form

New exact solutions of the Einstein vacuum equations for rotating axially symmetric fields

“…of the Einstein equation (3.5) lead to the Kerr space-time presented in the Boyer Lindquist coordinates [16][17][18][19] and the well-known solutions introduced in [14,15,20,21].…”

Symmetry analysis and some exact solutions of cylindrically symmetric null fields in general relativity

“…The heart of the classification schemes for the solutions of these equations are the symmetry methods based on the Lie groups. The most effective methods, for finding symmetry reductions and constructing exact solutions, include the Lie's approach [5][6][7][8][9], the nonclassical approach [10][11][12], the generalized conditional symmetry method [13,14], symmetry reduction method [6,15,16] and isovector field method [17,18]. In this paper, we will discuss system (1.11) with the aid of symmetry reduction method.…”

New exact solutions of the Einstein—Maxwell equations for magnetostatic fields

“…[15]- [17]. The effective methods for finding symmetries and constructing exact solutions include the Lie classical approach, [18−22] the symmetry reduction approach, [23,24] the nonclassical approach, [25] and the isovector field method. [26,27] In this paper, we will use the symmetry reduction approach to solve the nonlinear Eqs.…”