The author analyses the difficulties in describing accelerated motion trajectories in M4 in the framework of the Special Relativity Theory due to the lack of time as an independent scalar parameter. It is proposed reinstating the Newtonian time in an Integral Relativity Theory (IRT) without detriment to the Lorentz transformations. It is shown that in the frame of IRT it is possible to exceed the speed of light in accelerated motion. The formula is deduced for the composition of relative velocities with acceleration in M4. As an illustrative example the radial velocity is calculated in the course of the cosmic cloud G2 orbiting Sagittarius A* comparing results with the observed data and the author suggests the possibility that in the G2 cloud there is a system of two or three stars. He proposes an explanation of the phenomenon of "black hole" as the passage to the hyperluminic subspace in M4. Further research is suggested towards an IRT capable of handling in M4 the Hamiltonian formulation of classical mechanics and relativistic quantum mechanics.