SCALAR GRAVITATION - A LABORATORY FOR NUMERICAL RELATIVITY .3. AXISYMMETRY

We construct a two-dimensional axisymmetric mean-field particle simula tion scheme that solves the equations of relativistic scalar gravitati on coupled to collisionless matter. Although scalar gravitation theory disagrees with experiment, it is useful as a testing ground for numer ical methods used to solve the equations of general relativity, partic ularly in the generation of gravitational waves. We discuss methods fo r extracting the gravitational wave amplitude from the field variables , as well as methods for imposing an accurate outgoing-wave boundary c ondition on the scalar field at a finite radius. We find that for cont inuous matter distributions, our code is able to calculate smooth and accurate gravitational wave forms, despite the stochastic representati on of the matter source terms caused by sampling with a finite number of particles. A similar scheme should provide accurate wave forms in g eneral relativity, provided sufficient computer resources are used.