Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-06-26
J.Phys.Conf.Ser.229:012050,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
7 pages, no figures, section II extended
Scientific paper
10.1088/1742-6596/229/1/012050
The integral equations involved in Alekseev's "monodromy transform" technique are shown to be simple combinations of Sibgatullin's 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 Alekseev's 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 Sibgatullin's method.
Ernst Frederick J.
Manko Vladimir S.
Ruiz Eduardo
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