Classification of Petrov Type D Empty Einstein Spaces with Diverging Null Geodesic Congruences

In terms of Eddington-Finkelstein coordinates, we give the most general from of the line element for all type D empty spaces. The merits of our form are that this metric contains special space-times without a uniform acceleration in a non-singular form and this form makes it possible a systematic survey for the type D spaces. We perform a classification of all type D empty spaces as Lorentz space-times. In the most general case, the classification leads to nine classes, some of which can be reduced to the four classes of the Kinnersley class II in a limiting case. Moreover in another limiting case the most general case can be reduced to the Kinnersley class IIIA, some of which can cover all static classes discussed by Ehlers and Kundt.