On interrelations between Sibgatullins and Alekseevs approaches to the construction of exact solutions of the Einstein-Maxwell equations

The integral equations involved in Alekseevs monodromy transform technique are shown to be simple combinations of Sibgatullins integral equations and normalizing conditions. An additional complex conjugation introduced by Alekseev in the integrands makes his scheme mathematically inconsistent; besides, in the electrovac case all Alekseevs principal value integrals contain an intrinsic error which has never been identified before. We also explain how operates a non-trivial double-step algorithm devised by Alekseev for rewriting, by purely algebraic manipulations and in a different (more complicated) parameter set, any particular specialization of the known analytically extended N-soliton electrovac solution obtained in 1995 with the aid of Sibgatullins method.