Constructing hyperbolic systems in the Ashtekar formulation of general relativity

Gen Yoneda*, Hisa Aki Shinkai

*この研究の対応する著者

研究成果: Article査読

11 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)13-34
ページ数22
ジャーナルInternational Journal of Modern Physics D
9
1
DOI
出版ステータスPublished - 2000 2月

ASJC Scopus subject areas

  • 数理物理学
  • 天文学と天体物理学
  • 宇宙惑星科学

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