On classical solutions of the Nordstrom-Vlasov system

The Nordstrom-Vlasov system describes the dynamics of a self-gravitating ensemble of collisionless particles in the framework of the Nordstrom scalar theory of gravitation. We prove existence and uniqueness of classical solutions of the Cauchy problem in three dimensions and establish a condition which guarantees that the solution is global in time. Moreover, we show that if one changes the sign of the source term in the field equation, which heuristically corresponds to the case of a repulsive gravitational force, then solutions blow up in finite time for a large class of initial data. Finally, we prove global existence of classical solutions for the one dimensional version of the system with the correct sign in the field equation.