Difficulties in the Interpretation of the Einstein's Relativity Theory

From obtained structure equations, restrictions on a space-time geometry for possible solutions of relativistic continua are studied. Bases of simplest NRF are constructed: 1.Relativistic globally uniformly accelerated Born-rigid NRF. 2. Relativistic Born rigid uniformly rotating reference frame (RF) without a horizon. 3. Rigid irrotational spherically symmetrical quasi-Einstein's NRF. One can't describe bases of these systems in the Minkowski space, the Riemannian space-time is needed. The space-time of these RF is not directly connected with the general relativity theory (GRT), though it imposes conditions on some solutions of the Einstein equations. A solution of the Sagnac's, Erenfest's and Bell's paradoxes is proposed. It can be shown that the Schwarzschild and Reissner-Nordström solutions have no physical meaning. The last solution permits a physical meaning if one constructs a reference frame outside the charged sphere, which massive charged particles represent. The Newtonattractive forces are balanced by the Coulomb repulsion forces. If the test particle charge is equal to the electron charge, then their mass corresponds to masses of elementary black holes (maximons).