Constructing hyperbolic systems in the Ashtekar formulation of general relativity

Gen Yoneda, Hisa Aki Shinkai

Research output: Contribution to journalArticlepeer-review

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
DOIs
Publication statusPublished - 2000 Feb

ASJC Scopus subject areas

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

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