is constant, the kinetic energy increases and compensates the negative potential energy. As it is only the kinetic energy, which plays a role in the interaction process, we can replace gravity by an effective growth of energy and momentum. On the other hand, after the collision the particles are slightly slowed down by gravity and their asymptotic outgoing energy is smaller than the energy immediately after the interaction, so that asymptotic energy conservation is guaranteed. (We do not assume graviton production, so that gravity is conservative.)

So, instead of speaking about gravity, it is possible to ascribe an effective energy $E_{\rm eff}$ to the particles, enlarged by $-\Delta E_1$ and $-\Delta E_2$ in comparison with the asymptotic values, $$\label{eps}
E_{\rm eff}=E-\Delta E_1-\Delta
E_2=E\left(1+\alpha\,\frac{mE}{m_P^2}+\beta\,\frac{E^2}{m_P^2}\right)$$ with factors $\alpha$ and $\beta$ of the order of magnitude around 1 to 10.

Having ascribed an effective energy to the incoming particles, we can also ascribe an effective momentum to them, simply by using the free high-energy-momentum relation $E\approx p$, $$\label{pp}
p_{\rm
eff}=p\left(1+\alpha\,\frac{mp}{m_P^2}+\beta\,\frac{p^2}{m_P^2}\right).$$ In some analogy to DSR, gravity is now hidden in effective variables. (One might wonder whether a calculation involving a Newtonian potential can be applicable to relativistic particles. Relations (\[eps\]) and (\[pp\]) are 