Constructing hyperbolic systems in the Ashtekar formulation of general relativity

Gen Yoneda, Hisa Aki Shinkai

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    13 Citations (Scopus)

    Abstract

    Hyperbolic formulations of the equations of motion are essential technique for proving the well-posedness of the Cauchy problem of a system, and are also helpful for implementing stable long time evolution in numerical applications. We, here, present three kinds of hyperbolic systems in the Ashtekar formulation of general relativity for Lorentzian vacuum spacetime. We exhibit several (I) weakly hyperbolic, (II) diagonalizable hyperbolic, and (III) symmetric hyperbolic systems, with each their eigenvalues. We demonstrate that Ashtekar's original equations form a weakly hyperbolic system. We discuss how gauge conditions and reality conditions are constrained during each step toward constructing a symmetric hyperbolic system.

    Original languageEnglish
    Pages (from-to)13-34
    Number of pages22
    JournalInternational Journal of Modern Physics D
    Volume9
    Issue number1
    Publication statusPublished - 2000 Feb

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    ASJC Scopus subject areas

    • Space and Planetary Science
    • Mathematical Physics
    • Astronomy and Astrophysics

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