Complex Ernst-Harrison potential and nonrelativistic limits of stationary vacuum gravitational fields

Expressions are derived for determining the potentials of the nonrelativistic gravitational fields corresponding to stationary vacuum gravitational fields described by given complex Ernst-Harrison potentials E or ξ on a definite region of the three-space ¯V3 with given metric tensork (¯V3, is determined by the set of trajectories of a timelike Killing field). The dependence of the form of the nonrelativistic potentials on the parameters of the symmetry group SL(2, R) of the equations of the stationary vacuum gravitational fields with respect to transformations of the form of E is found.