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The catastrophe theory, Petrov’s algebraic classification and gravitational phase transitions. (English) Zbl 1232.83076
Summary: A close relationship is demonstrated between the catastrophe theory, Petrov’s algebraic classification of the gravitational fields and the theory of phase transitions.
MSC:
83E05 Geometrodynamics and the holographic principle
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
58K35 Catastrophe theory
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References:
[1] A. Z. Petrov, New Methods in General Relativity (Nauka, Moscow, 1966, in Russian).
[2] A. Z. Petrov, Einstein Spaces (Pergamon Press, 1969).
[3] T. Poston and I. Stewart, Catastrophe Theory and Its Applications (Pitman, 1978). · Zbl 0382.58006
[4] A. M. Baranov, Dep. VINITI USSR, No. 2632-76 (1976) (in Russian).
[5] A. M. Baranov, Abstr. of the Conference ”200 Years of Kazan University” (in Russian), p. 107 (2004).
[6] A. M. Baranov, Grav. Cosmol. 12, 100 (2006).
[7] A. M. Baranov, Zh. SibFU. Mat. Fiz. 4(1), 3 (2011).
[8] A. M. Baranov, Transactions of the Russian School-Seminar GRACOS-2010 (in Russian), p. 132 (2010).
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