  In this article, we present a vector field method for the study of solutions
to massless relativistic transport equations. Compared to the methodologie
developped by Fajman-Joudioux-Smulevici, we remove the Lorentz boosts of the
commutation vector fields, which makes our method more suitable for the study
of systems coupling a massless Vlasov equation with an equation which has a
different speed of propagation. We also believe that our approach can be
adapted more easily to the context of curved backgrounds.
  In a second time, we apply our method in order to derive sharp decay
estimates on the spherically symmetric small data solutions of the relativistic
massless Vlasov-Poisson system. No compact support assumption is required on
the data and, in particular, the initial decay in the velocity variable is
optimal. In order to compensate the slow decay rate of the particle density
near the light cone, we take advantage of the null structure of the equations.
