The Petrov algebraic classification and phase transitions in gravitational fields

A. M. Baranov

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 29-41

Résumé

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.

Détail

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

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