Geodesic
The Petrov algebraic classification and phase transitions in gravitational fields
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 29-41

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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, lightlike sources, lighton, helixon.
Mots-clés : phase transitions 
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     title = {The {Petrov} algebraic classification and phase transitions in gravitational fields},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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     publisher = {mathdoc},
     volume = {153},
     number = {3},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a2/}
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A. M. Baranov. The Petrov algebraic classification and phase transitions in gravitational fields. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 29-41. http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a2/