Adjusted ADM systems and their expected stability properties: Constraint propagation analysis in Schwarzschild spacetime

Hisa Aki Shinkai, Gen Yoneda

    Research output: Contribution to journalArticle

    17 Citations (Scopus)

    Abstract

    In order to find a way to have a better formulation for numerical evolution of the Einstein equations, we study the propagation equations of the constraints based on the Arnowitt-Deser-Misner formulation. By adjusting constraint terms in the evolution equations, we try to construct an 'asymptotically constrained system' which is expected to be robust against violation of the constraints, and to enable a long-term stable and accurate numerical simulation. We first provide useful expressions for analysing constraint propagation in a general spacetime, then apply it to Schwarzschild spacetime. We search when and where the negative real or non-zero imaginary eigenvalues of the homogenized constraint propagation matrix appear, and how they depend on the choice of coordinate system and adjustments. Our analysis includes the proposal of Detweiler (1987 Phys. Rev. D 35 1095), which is still the best one according to our conjecture but has a growing mode of error near the horizon. Some examples are snapshots of a maximally sliced Schwarzschild black hole. The predictions here may help the community to make further improvements.

    Original languageEnglish
    Pages (from-to)1027-1049
    Number of pages23
    JournalClassical and Quantum Gravity
    Volume19
    Issue number6
    DOIs
    Publication statusPublished - 2002 Mar 21

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    propagation
    adjusting
    formulations
    Einstein equations
    horizon
    proposals
    eigenvalues
    matrices
    predictions
    simulation

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Adjusted ADM systems and their expected stability properties : Constraint propagation analysis in Schwarzschild spacetime. / Shinkai, Hisa Aki; Yoneda, Gen.

    In: Classical and Quantum Gravity, Vol. 19, No. 6, 21.03.2002, p. 1027-1049.

    Research output: Contribution to journalArticle

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