Constraint propagation in the family of ADM systems

Details Constraint propagation in the family of ADM systems Constraint propagation in the family of ADM systems

2001-03-09

arxiv.org/abs/gr-qc/0103032v2

Phys.Rev. D63 (2001) 124019

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, RevTeX, 2 eps figures

Scientific paper

10.1103/PhysRevD.63.124019

The current important issue in numerical relativity is to determine which formulation of the Einstein equations provides us with stable and accurate simulations. Based on our previous work on "asymptotically constrained" systems, we here present constraint propagation equations and their eigenvalues for the Arnowitt-Deser-Misner (ADM) evolution equations with additional constraint terms (adjusted terms) on the right hand side. We conjecture that the system is robust against violation of constraints if the amplification factors (eigenvalues of Fourier-component of the constraint propagation equations) are negative or pure-imaginary. We show such a system can be obtained by choosing multipliers of adjusted terms. Our discussion covers Detweiler's proposal (1987) and Frittelli's analysis (1997), and we also mention the so-called conformal-traceless ADM systems.

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