Energy Norms and the Stability of the Einstein Evolution Equations

Details Energy Norms and the Stability of the Einstein Evolution Equations Energy Norms and the Stability of the Einstein Evolution Equations

2002-06-12

arxiv.org/abs/gr-qc/0206035v3

Phys.Rev. D66 (2002) 084014

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Corrected typos; to appear in Physical Review D

Scientific paper

10.1103/PhysRevD.66.084014

The Einstein evolution equations may be written in a variety of equivalent analytical forms, but numerical solutions of these different formulations display a wide range of growth rates for constraint violations. For symmetric hyperbolic formulations of the equations, an exact expression for the growth rate is derived using an energy norm. This expression agrees with the growth rate determined by numerical solution of the equations. An approximate method for estimating the growth rate is also derived. This estimate can be evaluated algebraically from the initial data, and is shown to exhibit qualitatively the same dependence as the numerically-determined rate on the parameters that specify the formulation of the equations. This simple rate estimate therefore provides a useful tool for finding the most well-behaved forms of the evolution equations.

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