General Relativity and Gravitation

, Volume 38, Issue 4, pp 625–632 | Cite as

Why solve the Hamiltonian constraint in numerical relativity?

Research Article

Abstract

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.

Keywords

Cauchy problem Cosmology 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.National Science Foundation, Physics DivisionArlingtonUSA

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