The central cusps in dark matter halos: fact or fiction?

We investigate the reliability of standard N-body simulations by modelling of the well-known Hernquist halo with the help of \texttt{GADGET-2} code (which uses the tree algorithm to calculate the gravitational force) and \texttt{ph4} code (which uses the direct summation). Comparing the results, we find that the core formation in the halo center (which is conventionally considered as the first sign of numerical effects, to be specific, of the collisional relaxation) has nothing to do with the collisional relaxation, being defined by the properties of the tree algorithm. This result casts doubts on the universally adopted criteria of the simulation reliability in the halo center. Though we use a halo model, which is theoretically proved to be stationary and stable, a sort of numerical 'violent relaxation' occurs. Its properties suggest that this effect is highly likely responsible for the central cusp formation in cosmological modelling of the large-scale structure, and then the 'core-cusp problem' is no more than a technical problem of N-body simulations.