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Constraint propagation in N+1-dimensional space-time

Hisa-aki Shinkai·Gen Yoneda
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Abstract

Higher dimensional space-time models provide us an alternative interpretation of nature, and give us different dynamical aspects than the traditional four-dimensional space-time models. Motivated by such recent interests, especially for future numerical research of higher-dimensional space-time, we study the dimensional dependence of constraint propagation behavior. The $N+1$ Arnowitt-Deser-Misner evolution equation has matter terms which depend on $N$, but the constraints and constraint propagation equations remain the same. This indicates that there would be problems with accuracy and stability when we directly apply the $N+1$ ADM formulation to numerical simulations as we have experienced in four-dimensional cases. However, we also conclude that previous efforts in re-formulating the Einstein equations can be applied if they are based on constraint propagation analysis.

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Hisa-aki Shinkai, Gen Yoneda. 2004-02-24. Constraint propagation in N+1-dimensional space-time. https://doi.org/10.1023/b%3Agerg.0000036050.58858.e5

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