Towards a stable numerical evolution of strongly gravitating systems in general relativity: The conformal treatments - art. no. 044034

We study the stability of three-dimensional numerical evolutions of the Ein stein equations, comparing the standard ADM formulation to variations on a family of formulations that separate out the conformal and traceless parts of the system. We develop an implementation of the conformal-traceless (CT) approach that has improved stability properties in evolving weak and stron g gravitational fields, and for both vacuum and spacetimes with active coup ling to matter sources. Cases studied include weak and strong gravitational wave packets, black holes, boson stars and neutron stars. We show under wh at conditions the CT approach fives better results in 3D numerical evolutio ns compared to the ADM formulation. In particular, we show that our impleme ntation of the CT approach gives more long term stable evolutions than ADM in all the cases studied, but is less accurate in the short term for the ra nge of resolutions used in our 3D simulations.