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Journal Article

Towards an understanding of the stability properties of the 3+1 evolution equations in general relativity.

MPS-Authors

Alcubierre,  Miguel
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Allen,  Gabrielle
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Brügmann,  Bernd
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Seidel,  Edward
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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9908079v2.pdf
(Preprint), 470KB

Phy.Rev.D.62.124011.pdf
(Publisher version), 308KB

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Citation

Alcubierre, M., Allen, G., Brügmann, B., Seidel, E., & Suen, W.-M. (2000). Towards an understanding of the stability properties of the 3+1 evolution equations in general relativity. Physical Review D, 62(12): 124011, pp. 1-15. doi:10.1103/PhysRevD.62.124011.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-56DC-0
Abstract
We study the stability properties of the standard ADM formulation of the 3+1 evolution equations of general relativity through linear perturbations of flat spacetime. We focus attention on modes with zero speed of propagation and conjecture that they are responsible for instabilities encountered in numerical evolutions of the ADM formulation. These zero speed modes are of two kinds: pure gauge modes and constraint violating modes. We show how the decoupling of the gauge by a conformal rescaling can eliminate the problem with the gauge modes. The zero speed constraint violating modes can be dealt with by using the momentum constraints to give them a finite speed of propagation. This analysis sheds some light on the question of why some recent reformulations of the 3+1 evolution equations have better stability properties than the standard ADM formulation.