Double harmonic mappings of Riemannian manifolds and its applications to stationary axisymmetric gravitational fields
type: Item
instance of: scholarly article
title: Double harmonic mappings of Riemannian manifolds and its applications to stationary axisymmetric gravitational fields
zbMATH Open document ID: 0826.53064
DOI: 10.1007/BF00673967
author: Ya-Bo Wu
published in: International Journal of Theoretical Physics
publication date: 1995-11-14T00:00:00Z
review text: \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.
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 58J72
Mathematics Subject Classification ID: 83C20
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 729702
zbMATH Keywords: harmonic mappings
zbMATH Keywords: stationary axisymmetric gravitational fields
zbMATH Keywords: Ernst equation
reviewed by: Volker Perlick
MaRDI profile type: Publication
Wikidata QID: Q115394953
cites work: Generation of new solutions of the stationary axisymmetric Einstein equations by a double complex function method
full work available at URL: https://doi.org/10.1007/bf00673967
OpenAlex ID: W15734236
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description: scientific article; zbMATH DE number 729702