About reduction of Einstein-Friedman equations to a system of Abel & Riccati ordinary differential equations

Details About reduction of Einstein-Friedman equations to a system of Abel & Riccati ordinary differential equations About reduction of Einstein-Friedman equations to a system of Abel & Riccati ordinary differential equations

2010-12-24

arxiv.org/abs/1012.5374v1

Physics

General Physics

4 pages

Scientific paper

Here is presented a method how to reduce Einstein-Friedman equations (including an equation for law of energy saving) to a proper Abel & Riccati ordinary differential equations. Due to a very special character of Riccati's type equation, it's general solution could be represented as gravitational shock wave or shock wave of gravitating inter-stellar matter in physical sense (i.e., a proper gap of density of inter-stellar matter). Thus, sudden change of an evolutionary stage of expansion - a compression stage (or on the contrary) in the Universe is possible at its evolution, which is caused by sudden changing of radius of curvature (which is proved to be of a Riccati type's). The reason can be both gravitational shock waves, and compression shock waves of gravitating inter-stellar matter at Universe evolution.

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