Properties of a model Einstein equation
Although chaos is almost a generally property of nonlinear systems of equations its existence in the case of the solution of Einstein's equations is still an open question. The author, starting from the Einstein equations on \(T^ 3\times {\mathbb{R}}\) with one Killing vector, makes a series of justified approximations and develops a nice toy model to analyse using numerical methods, the chaotic behavior of the vacuum-type solutions for a closed space-time with a Killing vector symmetry. An exact solution exhibits chaos if its behavior for smooth initial data, mixes the Fourier decomposition modes and presents an exponential phase-space expansion. The author's conclusions are: chaos is highly correlated with gravitational radiation emitted by unstables smooth regions of the universe, some regions which expands faster than the rest of the universe exhibit chaos and chaos is a physical consequence of the space time singularities or (more interesting) vice versa.
scientific article; zbMATH DE number 4161313