Chaos in relativity and cosmology
The chaos is studied in two cases of interest in Relativity and Cosmology: (i) the Mixmaster Universe model; (ii) the motion around two fixed black holes. In the first case, it is shown that the Mixmaster equations have two solutions: one general, depending on 6 arbitrary constants, which is of Painlevé type and another which is not Painlevé. Therefore, the Mixmaster model cannot be integrable. However, in this paper it is shown that in the Belinskii-Khalatnikov time \(\tau\), the Mixmaster model has the basic characteristics of a chaotic scattering problem, i.e. the two views can be made compatible. In the case of two fixed black holes, the orbits of photons separate into three types and it is shown that the chaos appears because between any two orbits of different types there are orbits of the third type. The transition from order to chaos is made through an infinite sequence of period doubling bifurcations. It is shown that the bifurcation ratio is the same in relativity as in classical dynamics.
scientific article; zbMATH DE number 1442246