Lm. Widrow, MODELING COLLISIONLESS MATTER IN GENERAL-RELATIVITY - A NEW NUMERICALTECHNIQUE, Physical review. D. Particles and fields, 55(10), 1997, pp. 5997-6001
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.