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.

UDC: 530.12+530.51

Received: 19.06.2011