Vortices of a spatially flat spacetime

In this paper, we study the dynamics of a spatially flat spacetime in which the direction of the velocity of a spatially moving particle is fixed by the physical state of the space. It is shown that the theory is a model of gravitation based on the advent of a spatially flat spacetime. In this theory, the corresponding velocity is given by the Cartan's velocity, and the Boltzmann's law is satisfied.