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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2011, Volume 153, Book 3, Pages 29–41 (Mi uzku1052)  

The Petrov algebraic classification and phase transitions in gravitational fields

A. M. Baranov

Institute of Engineering Physics and Radioelectronics, Siberian Federal University, Krasnoyarsk

Abstract: This article shows the connection of the Petrov algebraic classification of gravitational fields with the theory of catastrophes as a generalized theory of phase transitions. We demonstrate the analogy between the transitions of the algebraic types of space-times and the phase transitions at the curvature tensor level (Weyl's matrices level) by the examples of the Petrov classification, the algebraic classification of four-dimensional local Euclidean spaces, and the derivation of the gravitational fields of lightlike sources.

Keywords: Petrov algebraic classification, gravitational fields, catastrophe theory, phase transitions, lightlike sources, lighton, helixon.

Full text: PDF file (262 kB)
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UDC: 530.12+530.51
Received: 19.06.2011

Citation: A. M. Baranov, “The Petrov algebraic classification and phase transitions in gravitational fields”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 153, no. 3, Kazan University, Kazan, 2011, 29–41

Citation in format AMSBIB
\Bibitem{Bar11}
\by A.~M.~Baranov
\paper The Petrov algebraic classification and phase transitions in gravitational fields
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2011
\vol 153
\issue 3
\pages 29--41
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1052}


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