Weyl metrics and the generating conjecture

TL;DR

This paper explores the connection between Weyl metrics and the generating conjecture in Einstein-Maxwell theory, revealing that certain static axisymmetric fields are related to Kinnersley's transformations, and proposes new theoretical insights.

Contribution

It provides a new theoretical framework linking the generating conjecture with Kinnersley's transformations in Einstein-Maxwell fields.

Findings

Static axisymmetric Einstein-Maxwell fields are related to Kinnersley's transformations.

A new theoretical background for the generating conjecture is proposed.

Previous solutions are shown to be combinations of known transformations.

Abstract

By means of Ernst complex potential formalism it is shown, that previously studied static axisymmetric Einstein-Maxwell fields obtained though the application of the Horsky-Mitskievitch generating conjecture represent a combination of Kinnersley's transformations [W. Kinnersley: J. Math. Phys. 14 (1973) 651]. New theoretical background for the conjecture is suggested and commented.