Eingorn M. Gravitational interaction in multidimensional models.

The thesis is devoted to investigation of gravitational interaction in multidimensional Kaluza-Klein models with toroidal compactification of extra spatial dimensions. These models are widely used for self-consistent construction of modern theories of unification of all known fundamental interactions: the M-theory, the supergravity and the theory of superstrings. In the non-relativistic limit formulas for the multidimensional potential of a point-like particle at rest are found. The relationship between 4-dimensional and multidimensional Planck scales is established. In the case of disposition of interacting particles on the same brane potentials, radial accelerations of test bodies and the self-energy are determined for the fields of infinitely thin and arbitrary spherical shells. Formulas for the potential energy and the absolute value of the force of gravitational interaction of two spheres are found and the corresponding effective gravitational constant is introduced. New restrictions on periods of tori are established on basis of the solution of the hierarchy problem and laboratory tests of the gravitational inverse square law. In the approximation of the weak gravitational field up to terms of the order 1/c^2 the metrics, which describes the field of the system of point-like particles, is determined. Formulas for astrophysical tests (the frequency shift, the perihelion shift and the deflection of light) are obtained. It is shown that the last two of them contradict observations for D>3. In the framework of PPN formalism restrictions on parameters of multidimensional solitons are established. Corresponding post-Newtonian parameters and equations of state of matter in external and internal spaces are found. These equations of state are not dust-like in the general case. A new class of solitons, which are at the same level of agreement with tests, as general relativity, is discovered. They got the name of latent solitons. Black strings and black branes belong to this class.