Ma. Scheel et al., SCALAR GRAVITATION - A LABORATORY FOR NUMERICAL RELATIVITY .3. AXISYMMETRY, Physical review. D. Particles and fields, 49(4), 1994, pp. 1894-1905
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.