Comment on F.J.Ernst, V.S.Manko and E.Ruiz "On interrelations between Sibgatullin's and Alekseev's approaches to the construction of exact solutions of the Einstein-Maxwell equations" (J.Phys.:Conf.Ser.229(2010)012050; arXiv:1006.5118)

TL;DR

This paper corrects misconceptions and errors in a previous work on solution methods for Einstein-Maxwell equations, clarifying derivations and emphasizing prior related solutions to prevent misinformation.

Contribution

It clarifies the correct derivation of Sibgatullin's reduction within the monodromy transform approach and refutes claims of novelty regarding certain electrovac solutions.

Findings

Identifies and corrects errors in the discussed paper.

Provides proper derivation of integral equations.

Shows earlier solutions encompass those claimed as new.

Abstract

The necessity of this Comment was invoked by numerous mistakes, erroneous discussions and misleading citations curiously collected in the paper of F.J.Ernst, V.S.Manko and E.Ruiz and concerning the interrelations between two integral equation methods developed for solution of Einstein - Maxwell equations more than twenty five years ago. At first, we clarify the origin of the errors in the paper of F.J.Ernst, V.S.Manko and E.Ruiz which gave rise to so curious authors "conclusions" as that the monodromy transform integral equations "...are simple combinations of Sibgatullin's integral equations and normalizing conditions..." or even that "...in the electrovac case Alekseev's integral equations are erroneous...". In the Comment, the way of correct derivation of Sibgatullin's reduction of the Hauser and Ernst integral equations in the context of the monodromy transform approach is briefly outlined. In response to various speculations and priority claims collected in the section 3 of the F.J.Ernst, V.S.Manko and E.Ruiz paper, the concrete references are given here to the papers which were ignored completely by these authors and which show that the so called "extended electrovacuum N-soliton solutions" considered by E.Ruiz, V.S. Manko and J. Martin in 1995, are not new because all these solutions are the particular cases of a larger class of solutions constructed much earlier in explicit (determinant) form using the monodromy transform equations, and that the real story of construction of the solution for superposition of fields of two Reissner - Nordstr\"om sources and of corresponding equilibrium configurations found in our papers with V.Belinski differs crucially from that, which one can read in the paper of F.J.Ernst, V.S.Manko and E.Ruiz.