  We discuss the relativistic kinetic theory for a simple, collisionless,
charged gas propagating on an arbitrary curved spacetime geometry. Our general
relativistic treatment is formulated on the tangent bundle of the spacetime
manifold and takes advantage of its rich geometric structure. In particular, we
point out the existence of a natural metric on the tangent bundle and
illustrate its role for the development of the relativistic kinetic theory.
This metric, combined with the electromagnetic field of the spacetime, yields
an appropriate symplectic form on the tangent bundle. The Liouville vector
field arises as the Hamiltonian vector field of a natural Hamiltonian. The
latter also defines natural energy surfaces, called mass shells, which turn out
to be smooth Lorentzian submanifolds.
  A simple, collisionless, charged gas is described by a distribution function
which is defined on the mass shell and satisfies the Liouville equation.
Suitable fibre integrals of the distribution function define observable fields
on the spacetime manifold, such as the current density and stress-energy
tensor. Finally, the geometric setting of this work allows us to discuss the
relationship between the symmetries of the electromagnetic field, those of the
spacetime metric, and the symmetries of the distribution function. Taking
advantage of these symmetries, we construct the most general solution of the
Liouville equation an a Kerr-Newman black hole background.
