Some remarks on finite-gap solutions of the Ernst equation

TL;DR

This paper demonstrates that the finite-gap solutions of the Ernst equation, previously constructed using algebro-geometric methods, include the solutions recently developed by Meinel and Neugebauer, showing their broader mathematical context.

Contribution

It reveals that the earlier algebro-geometric solutions encompass the more recent solutions by Meinel and Neugebauer, unifying different approaches to the Ernst equation.

Findings

Finite-gap solutions include Meinel and Neugebauer's solutions

Algebro-geometric solutions form a broader class

Unification of solution methods for the Ernst equation

Abstract

It is shown that the class of algebro-geometrical (finite-gap) solutions of the Ernst equation constructed several years ago in [D.Korotkin, Theor.Math.Phys., 77 (1989), p. 1018] contains the solutions recently constructed by R.Meinel and G.Neugebauer as a subset.