Post-Newtonian approximation of the Vlasov-Nordstr\"om system

We study the Nordstr\"om-Vlasov system which describes the dynamics of a self-gravitating ensemble of collisionless particles in the framework of the Nordstr\"om scalar theory of gravitation. If the speed of light $c$ is considered as a parameter, it is known that in the Newtonian limit $c\to\infty$ the Vlasov-Poisson system is obtained. In this paper we determine a higher approximation and establish a pointwise error estimate of order $O(c^{-4})$. Such an approximation is usually called a 1.5 post-Newtonian approximation.