MODELING COLLISIONLESS MATTER IN GENERAL-RELATIVITY - A NEW NUMERICALTECHNIQUE

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 Einste in equations. A phase-space distribution function, constructed using c ovariant coherent states, obeys the relativistic Vlasov equation provi ded the de Broglie wavelength for the field is very much smaller than the scales of interest. We illustrate the method by solving for the ev olution of a system of particles in a static, plane symmetric, backgro und spacetime.