Towards a stable numerical evolution of strongly gravitating systems in general relativity: The conformal treatments
By M. Alcubierre, B. Bruegmann, Thomas Dramlitsch, J. Font, P. Papadopoulos, E. Seidel, Nikolaos Stergioulas, Ryoji Takahashi. 2000
142 citations recorded by the source corpus.
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.
Subfields: Astronomy and Astrophysics, Oceanography
View Paper: https://www.semanticscholar.org/paper/b0d1580c0b1476157e8d9ff5e22def36522f74ca
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In Astronomy and Astrophysics
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In Oceanography
Citations in the corpus
- The Einstein Toolkit: a community computational infrastructure for relativistic astrophysics (2011, methodology): “For this, the BSSN conformal-tracefree reformulation [9, 10, 149] of the original ADM formalism [129] is employed.”
- Turduckening black holes: An Analytical and computational study (2008, methodology): “One of them is McLachlan, a three-dimensional adaptive mesh refinement code, which uses the BSSN system of equations, as described in [15, 31], with the gauge conditions described in section II above.”