Testing the approximations in large-scale simulations of systems with gravitational forces

In simulations of galaxies and structures in the universe, the particle-particle-particle-mesh "PPPM" (P3M) or "TreePM" approximations are used. The forces from objects at large distances are replaced by forces localized at meshes, and solving the Poisson equation determines their effect on an object. The particle-mesh approximation (PM) breaks the symmetry of pair interactions between objects and destroys the exact conservation of momentum and angular momentum. Here, the effects of the PM approximations are examined by performing "brute-force" simulations with and without the PM approximation. However, the exact simulations can only be performed for a small "dwarf galaxy" of ≈500 objects. The simulations show that the stability of the galaxy is sensitive to the approximations, which sooner or later lead to the objects being released from their bound rotation. However, the stability of the dwarf galaxy can be ensured by modifying Newton's gravitational long-range attractions from an inverse square attraction to an inverse attraction, a gravity modification often proposed in the f(R) modified general relativity theory.