Solution with Real Value of Deformation Parameter for Ernst Equation in Gravitational Field Caused by Rotating Source

Starting with the Weyl solution that is known to be valid for any real value of the deformation parameter δ, the solution of the Ernst equation in an axially symmetric gravitational field caused by a rotating source is given in a perturbative expansion of the variables λ(= q^2 / p^2) and b(= y^2 -1) for a real value of δ. The proof of the validity of the solution is given to first order in λ and all orders in b.