Galactic dynamics in MOND -- Existence of equilibria with finite mass and compact support

We consider a self-gravitating collisionless gas where the gravitational interaction is modeled according to MOND (modified Newtonian dynamics). For the resulting modified Vlasov-Poisson system we establish the existence of spherically symmetric equilibria with compact support and finite mass. In the standard situation where gravity is modeled by Newton’s law the latter properties only hold under suitable restrictions on the prescribed microscopic equation of state. Under the MOND regime no such restrictions are needed.