http://arxiv.org/abs/2210.04657
Based on mathematically rigorous analysis of nonlinear differential equations studied in our companion article [1], we construct a model which describes the \textit{nonlinear} gravitational instability on a local portion of the universe characterized by the expanding Newtonian universe. In this portion, the perturbations are homogeneous and isotropic. This result, to some extent, can be viewed as a nonlinear version of the Jeans instability. The growth rate of the relative density due to the nonlinear effects is much faster (at least $\sim \exp(t^{\frac{2}{3}})$ or blowup at a finite time according to the data) than the one predicted by the classical linear version of the Jeans instability ($\sim t^{\frac{2}{3}}$), and it leads to a better, or potentially substantial impacts on, understanding of the formation of the nonlinear structures in the universe and stellar systems. This article associated with [1] provides a new window into the rigorously mathematical and robust method, instead of the most used approximations and numerical calculations, of the fully nonlinear analysis of the Jeans instability for general cases.
C. Liu
Tue, 11 Oct 22
53/92
Comments: 15 pages