  We propose a new numerical technique for following the evolution of a
self-gravitating collisionless system in general relativity. Matter is modeled
as a scalar field obeying the coupled Klein-Gordon and Einstein equations. A
phase space distribution function, constructed using covariant coherent states,
obeys the relativistic Vlasov equation provided the de Broglie wavelength for
the field is very much smaller than the scales of interest. We illustrate the
method by solving for the evolution of a system of particles in a static,
plane-symmetric, background spacetime.
