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

Hisa Aki Shinkai*, Gen Yoneda

*この研究の対応する著者

研究成果: Article査読

18 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1027-1049
ページ数23
ジャーナルClassical and Quantum Gravity
19
6
DOI
出版ステータスPublished - 2002 3 21

ASJC Scopus subject areas

  • 物理学および天文学(その他)

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