Multidimensional cosmology, constants and transition to new SI units

Main current problems of physics, gravitation and cosmology in particular are analyzed. Special attention is paid to results of the theory with extra dimensions and variations of fundamental physical constants. As an example the family of spherically symmetric solutions with horizon with multi-component anisotropic fluid is presented. The metrics of solutions are defined on a manifold that contains a product of n-1 Ricci-flat "internal" spaces. A simulation of black brane solutions is considered. For the solution with the fluid matter the post-Newtonian parameters β and γ corresponding to the 4-dimensional section of the metric are found. © 2011 World Scientific Publishing Company.