the desired parallel between DSR and gravity this association of variables is plausible in the following extrapolation: The unbounded pseudo-variables describe the situation with a repulsive potential, that goes to infinity at zero distance, in the absence of gravity: To reach smaller and smaller distances from each other, the particles must have arbitrarily high asymptotic energies. In most cases the same is true in the presence of Newtonian gravity, but the asymptotic energy necessary to bring particles close together, is lower. This actual energy is described by the physical variables, which are smaller. Moreover, being bounded, they predict distance zero at a finite asymptotic energy, thus mimicking a gravitational collapse, when the exchange particle’s energy reaches the Planck region. By this fact DSR is closer to GR than to Newtonian theory.

Here, of course, we are going to compare only the leading corrections stemming from the inclusion of classical gravity, as well as from DSR, both based on the ratio $p/m_P$ ($=E/m_P$ in our assumption). Whereas in DSR the power of these ratio is a matter of an ad hoc definition, classical gravity in three space dimensions fixes the lowest order to be two, due to the simple fact that 