Diagonalizability of constraint propagation matrices

Gen Yoneda, Hisa Aki Shinkai

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    In order to obtain stable and accurate general relativistic simulations, reformulations of the Einstein equations are necessary. In a series of our works, we have proposed using eigenvalue analysis of constraint propagation equations for evaluating violation behaviour of constraints. In this letter, we classify asymptotical behaviours of constraint violation into three types (asymptotically constrained, asymptotically bounded and diverge), and give their necessary and sufficient conditions. We find that degeneracy of eigenvalues sometimes leads constraint evolution to diverge (even if its real part is not positive) and conclude that it is quite useful to check the diagonalizability of constraint propagation matrices. The discussion is general and can be applied to any numerical treatments of constrained dynamics.

    Original languageEnglish
    JournalClassical and Quantum Gravity
    Volume20
    Issue number4
    DOIs
    Publication statusPublished - 2003 Feb 21

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    propagation
    matrices
    eigenvalues
    Einstein equations
    simulation

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Diagonalizability of constraint propagation matrices. / Yoneda, Gen; Shinkai, Hisa Aki.

    In: Classical and Quantum Gravity, Vol. 20, No. 4, 21.02.2003.

    Research output: Contribution to journalArticle

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