Double harmonic mappings of Riemannian manifolds and its applications to stationary axisymmetric gravitational fields
\textit{A. Eris} [J. Math. Phys. 18, 824-829 (1977)] applied harmonic mappings of Riemannian manifolds to study the Ernst equation governing stationary axisymmetric gravitational fields. In the paper under review the author gives an extension of these techniques to the ``double complex'' Ernst equation of \textit{Z.-Z. Zhong} [J. Math. Phys. 26, 2589- 2595 (1985; Zbl 0598.58044)] combining ordinary complex numbers with hyperbolic complex numbers. In this formalism solutions for the gravitational field are always obtained in pairs. The paper presents two different methods of how to obtain the Ernst solution and its dual. Unfortunately, there is almost no discussion of the result and its relevance in view of general relativity remains obscure to the reviewer.
stationary axisymmetric gravitational fields
scientific article; zbMATH DE number 729702