  The kinetic description of relativistic plasmas in the presence of
time-varying and spatially non-uniform electromagnetic fields is a fundamental
theoretical issue both in astrophysics and plasma physics. This refers, in
particular, to the treatment of collisionless and strongly-magnetized plasmas
in the presence of intense radiation sources. In this paper the problem is
investigated in the framework of a covariant gyrokinetic treatment for
Vlasov-Maxwell equilibria. The existence of a new class of kinetic equilibria
is pointed out, which occur for spatially-symmetric systems. These equilibria
are shown to exist in the presence of non-uniform background EM fields and
curved space-time. In the non-relativistic limit this feature permits the
determination of kinetic equilibria even for plasmas in which particle energy
is not conserved due to the occurrence of explicitly time-dependent EM fields.
Finally, absolute stability criteria are established which apply in the case of
infinitesimal symmetric perturbations that can be either externally or
internally produced.
