Stationary vacuum fields with a conformally flat three-space. III: Complete solution (Q1074885)

[Part II, cf. ibid. 18, 511-530 (1986; Zbl 0589.53069).] The author considers stationary vacuum spacetimes whose three-dimensional geometry of Killing trajectories is conformally flat (conformastat spacetimes). He concludes, after an elaborate analysis made possible with the use of a symbolic manipulation language, that for these (overdetermined) spacetimes the real and imaginary part of the Ernst potential should be functionally dependent. Thus, the only conformastat vacuum spacetimes are those reported by \textit{B. Lukács}, the author, \textit{A. Sebestyen}, and \textit{G. A. J. Sparling} in part I, ibid. 15, 511- 522 (1983; Zbl 0514.53028)].