Generalization of Einstein's relativity theory for the anisotropic space-time

A general relativistic theory of the locally anisotropic space-time and gravitation is developed on the basis of the concept of the locally Finslerian space of events and the weak equivalence principle. The Finslerian metric function is explicitly defined by the Riemann metric tensor field g/sub ik/(x), a scalar field tau(x) specifying the magnitude of the local anisotropy and the null vector field v/sub i/(x) indicating the locally preferred direction in space-time. The static centrally-symmetrical solution of the Schwarzschild external problem for the locally anisotropic space has been found. The radial motion of a quantal change in the particle's dynamic variables is revealed. After the occurrence of the effect, the motion towards the centre of force is slowed down and then reversed