Hyperbolic formulations and numerical relativity: II. Asymptotically constrained systems of Einstein equations

Gen Yoneda, Hisa Aki Shinkai

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

We study asymptotically constrained systems for numerical integration of the Einstein equations, which are intended to be robust against perturbative errors for the free evolution of the initial data. First, we examine the previously proposed 'λ system', which introduces artificial flows to constraint surfaces based on the symmetric hyperbolic formulation. We show that this system works as expected for the wave propagation problem in the Maxwell system and in general relativity using Ashtekar's connection formulation. Second, we propose a new mechanism to control the stability, which we call the 'adjusted system'. This is simply obtained by adding constraint terms in the dynamical equations and adjusting their multipliers. We explain why a particular choice of multiplier reduces the numerical errors from non-positive or pure-imaginary eigenvalues of the adjusted constraint propagation equations. This 'adjusted system' is also tested in the Maxwell system and in the Ashtekar system. This mechanism affects more than the system's symmetric hyperbolicity.

Original languageEnglish
Pages (from-to)441-462
Number of pages22
JournalClassical and Quantum Gravity
Volume18
Issue number3
DOIs
Publication statusPublished - 2001 Feb 7

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Fingerprint Dive into the research topics of 'Hyperbolic formulations and numerical relativity: II. Asymptotically constrained systems of Einstein equations'. Together they form a unique fingerprint.

Cite this