On the effect of angular momentum on the prompt cusp formation via the gravitational collapse

In this work, we extend the model proposed by White concerning the post-collapse evolution of density peaks while considering the role of angular momentum. On a timescale smaller than the peak collapse, $t_{0}$, the inner regions of the peak reach the equilibrium forming a cuspy profile, as in White's paper, but the power-law density profile is flatter, namely $\rho \propto r^{-1.52}$, using the specific angular momentum $J$ obtained in theoretical models of how it evolves in CDM universes, namely $J \propto M^{2/3}$. The previous result shows how angular momentum influences the slope of the density profile, and how a slightly flatter profile obtained in high-resolution numerical simulations, namely $\rho \propto r^{\alpha}$, $(\alpha \simeq -1.5)$ can be reobtained. Similarly to simulations, in our model adiabatic contraction was not taken into account. This means that more comprehensive simulations could give different values for the slope of the density profile, similar to an improvement of our model.