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 ally rea l value of the deformation parameter delta, the solution of the Ernst equation ill an axially symmetric gravitational field caused by a rota ting source is given in a perturbative expansion of the variables lamb da(= q(2)/p(2)) and b(= y(2)-1) for a real value of delta. The proof o f the validity of the solution is given to first order in lambda and a ll orders in b.