Relativistic field equations and nonlinear dynamics

Yosuke Tanaka, Takefumi Shudo, Tetsutaro Yosinaga and Hiroshi Kimura

Chaos, Solitons & Fractals, 2008, vol. 37, issue 4, 941-949

Abstract: We have studied the gravitational field equations on the basis of general relativity and nonlinear dynamics. By integrating the space component of the Einstein–Friedmann equation, we have derived the Higgs-type W-shape potential [U=(1/4)(λ−κp)x2−(1/8)ζx4], and classified the solutions in the Einstein–Friedmann equation. We have shown that there occurs chaotic behaviours in case the following conditions are satisfied;(i)the expanding ratio h=x˙/x<0,(ii)the curvature ζ=−1, and(iii)the cosmological constant λ<κp.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:37:y:2008:i:4:p:941-949

DOI: 10.1016/j.chaos.2008.01.004

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