  The existence and the properties of isolated solutions to the relativistic
Vlasov-Maxwell system with initial data on the backward hyperboloid
$t=-\sqrt{1+|x|^2}$ are investigated. Isolated solutions of Vlasov-Maxwell can
be defined by the condition that the particle density is compactly supported on
the initial hyperboloid and by imposing the absence of incoming radiation on
the electromagnetic field. Various consequences of the mass-energy conservation
laws are derived by assuming the existence of smooth isolated solutions which
match the inital data. In particular, it is shown that the mass-energy of
isolated solutions on the backward hyperboloids and on the surfaces of constant
proper time are preserved and equal, while the mass-energy on the forward
hyperboloids is non-increasing and uniformly bounded by the mass-energy on the
initial hyperboloid. Moreover the global existence and uniqueness of classical
solutions in the future of the initial surface is established for the one
dimensional version of the system.
