Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-10-13
Gen.Rel.Grav. 38 (2006) 625-632
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Submitted to a volume in honor of Michael P. Ryan, Jr. Based on talk given at GR17
Scientific paper
The indefinite sign of the Hamiltonian constraint means that solutions to Einstein's equations must achieve a delicate balance--often among numerically large terms that nearly cancel. If numerical errors cause a violation of the Hamiltonian constraint, the failure of the delicate balance could lead to qualitatively wrong behavior rather than just decreased accuracy. This issue is different from instabilities caused by constraint-violating modes. Examples of stable numerical simulations of collapsing cosmological spacetimes exhibiting local mixmaster dynamics with and without Hamiltonian constraint enforcement are presented.
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