Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-03-17
Phys.Rev.D62:044034,2000
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
17 pages, 15 figures. Small changes in the text, and a change in the list of authors. One new reference added
Scientific paper
10.1103/PhysRevD.62.044034
We study the stability of three-dimensional numerical evolutions of the Einstein 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 strong gravitational fields, and for both vacuum and spacetimes with active coupling to matter sources. Cases studied include weak and strong gravitational wave packets, black holes, boson stars and neutron stars. We show under what conditions the CT approach gives better results in 3D numerical evolutions compared to the ADM formulation. In particular, we show that our implementation 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 range of resolutions used in our 3D simulations.
Alcubierre Miguel
Bruegmann Bernd
Dramlitsch Thomas
Font José A.
Papadopoulos Philippos
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