The Einstein gravity as an attractor in higher-dimensional theories

In higher-dimensional theories with a suitable potential, the 4-dim Einstein gravity is always realized as an attractor in the dynamical system if the 3-space is expanding. The space-time approaches (the 4-dim Friedmann universe) x (a static internal space). On the other hand, if the 3-space is contracting (e.g. the future of the closed universe or the inside of a collapsing relativistic star), the potential minimum is no longer attractor. The space-time leaves it, finding the blowing up of the internal space and/or the Jordan-Brans-Dicke gravity. Astrophysical consequences of the extra-dimensions might be found. (author)