The non-relativistic limit of the Nordström-Vlasov system

Abstract

The Nordström-Vlasov system provides an interesting relativistic generalization of the Vlasov-Poisson system in the gravitational case, even though there is no direct physical application. The study of this model will probably lead to a better mathematical understanding of the class of non-linear systems consisting of hyperbolic and transport equations. In this paper it is shown that solutions of the Nordström-Vlasov system converge to solutions of the Vlasov-Poisson system in a pointwise sense as the speed of light tends to infinity, providing a further and rigorous justification of this model as a \textit{genuine} relativistic generalization of the Vlasov-Poisson system.

arXiv comment19 pages

References in corpus (2)

• Spherically symmetric steady states of galactic dynamics in scalar gravity
• Global weak solutions to the Nordström-Vlasov system

Cited by in corpus (6)

• Global classical solutions to the 3D Nordström-Vlasov system
• Multipole radiation in a collisonless gas coupled to electromagnetism or scalar gravitation
• Global Small Solutions of the Vlasov-Norstrom System
• Global existence of solutions of the Nordström-Vlasov system in two space dimensions
• Post-Newtonian dynamics at order 1.5 in the Vlasov-Maxwell system
• Post-Newtonian approximation of the Vlasov-Nordström system