  We consider the relativistic Vlasov--Maxwell (RVM) equations in the limit
when the light velocity $c$ goes to infinity. In this regime, the RVM system
converges towards the Vlasov--Poisson system and the aim of this paper is to
construct asymptotic preserving numerical schemes that are robust with respect
to this limit. Our approach relies on a time splitting approach for the RVM
system employing an implicit time integrator for Maxwell's equations in order
to damp the higher and higher frequencies present in the numerical solution. A
number of numerical simulations are conducted in order to investigate the
performances of our numerical scheme both in the relativistic as well as in the
classical limit regime. In addition, we derive the dispersion relation of the
Weibel instability for the continuous and the discretized problem.
