Evolution of self-gravitating spherical dark-matter halos with and without new physics

We present an efficient numerical algorithm for evolving self-gravitating systems of dark-matter particles that leverages the assumption of spherical symmetry to reduce the nominally six-dimensional phase space to three dimensions. It can be used to quickly determine numerically the evolution of an initially static stable self-consistent self-gravitating system if there is some additional or new physics. We illustrate here with four examples: (1) the effects of the growth of a supermassive black hole at the center; (2) the effects of stripping of the outer layers of the halo (a toy model for the effects of tidal stripping of galaxies); (3) the response of a self-gravitating system to dark matter that decays to a slightly less massive state; and (4) the effects of a slow change to Newton's constant. The approach can be extended to study dark matter with elastic and inelastic self-interactions and to study the process of virialization in spherical collapse. We describe some aspects of a code NSphere that implements this approach which we are making available.