We present a symmetric hyperbolic formulation of the Einstein equations in affine-null coordinates. Giannakopoulos et al. [Phys. Rev. D 102, 064035 (2020)] recently showed that the most commonly numerically implemented formulations of the Einstein equations in affine-null coordinates (and other single-null coordinate systems) are only weakly—not strongly—hyperbolic. By making use of the tetrad-based Newman–Penrose formalism, our formulation avoids the hyperbolicity problems of the formulations investigated by Giannakopoulos et al. [Phys. Rev. D 102, 064035 (2020)]. We discuss a potential application of our formulation for studying gravitational wave scattering.

中文翻译：

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仿射零坐标下真空爱因斯坦方程的对称双曲公式

我们在仿射零坐标中提出了爱因斯坦方程的对称双曲公式。詹纳科普洛斯等人。[物理。Rev. D 102 , 064035 (2020)] 最近表明，在仿射零坐标（和其他单零坐标系）中最常用的爱因斯坦方程的数值实现公式只是弱双曲，而不是强双曲。通过利用基于四分体的 Newman-Penrose 形式主义，我们的公式避免了 Giannakopoulos等人研究的公式的双曲线问题。[物理。修订版 D 102 , 064035 (2020)]。我们讨论了我们的公式在研究引力波散射方面的潜在应用。