In Newtonian gravity the final states of cold dissipationless collapses are characterized by several structural and dynamical properties remarkably similar to those of observed elliptical galaxies .
Are these properties a peculiarity of the Newtonian force or a more general feature of long-range forces ?
We study this problem by means of N - body simulations of dissipationless collapse of systems of particles interacting via additive r ^ { - \alpha } forces .
We find that most of the results holding in Newtonian gravity are also valid for \alpha \neq 2 .
In particular the end products are triaxial and never flatter than an E7 system , their surface density profiles are well described by the Sérsic law , the global density slope-anisotropy inequality is obeyed , the differential energy distribution is an exponential over a large range of energies ( for \alpha \geq 1 ) , and the pseudo phase-space density is a power law of radius .
In addition , we show that the process of virialization takes longer ( in units of the system ’ s dynamical time ) for decreasing values of \alpha , and becomes infinite for \alpha = -1 ( the harmonic oscillator ) .
This is in agreement with the results of deep-MOND collapses ( qualitatively corresponding to \alpha = 1 ) and it is due to the fact the force becomes more and more similar to the \alpha = -1 case , where as well known no relaxation can happen and the system oscillates forever .