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arXiv 0810.1790gr-qc
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Einstein-Gauss-Bonnet引力的$N+1$形式

$N+1$ formalism in Einstein-Gauss-Bonnet gravity

Takashi Torii, Hisa-aki Shinkai

摘要:

为了研究高维和/或弦引力模型中的全动力学,我们给出了Einstein-Gauss-Bonnet引力理论的基本方程。我们显示$(N+1)$维版本的ADM分解,包括高斯-邦纳条款,这将是标准的方法来处理的时空作为一个柯西问题。由于Gauss-Bonnet引力的准线性性质,我们发现演化方程可以用数值方法处理。我们还展示了构造初始数据的保形变换约束方程。我们讨论了如何通过调整共形因子的幂来简化约束。我们的方程既可用于类时叶理,也可用于类空叶理。

英文摘要:

Towards the investigation of the full dynamics in higher-dimensional and/or stringy gravitational model, we present the basic equations of the Einstein-Gauss-Bonnet gravity theory. We show $(N+1)$-dimensional version of the ADM decomposition including Gauss-Bonnet terms, which shall be the standard approach to treat the space-time as a Cauchy problem. Due to the quasi-linear property of the Gauss-Bonnet gravity, we find that the evolution equations can be in a treatable form in numerics. We also show the conformally-transformed constraint equations for constructing an initial data. We discuss how the constraints can be simplified by tuning the powers of conformal factors. Our equations can be used both for timelike and spacelike foliations.

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