球对称中的广义调和公式
Generalized harmonic formulation in spherical symmetry
摘要：
在这篇教学结构的文章中，我们描述了一个广义的谐波制定的爱因斯坦方程的球对称，这是经常在原点。在过去的几年中，广义调和方法在数值相对论中引起了极大的关注，特别是在应用于双星的螺旋和合并问题时。使用该技术时的一个关键问题是仪表源函数的选择，最近的工作提供了几个处方的仪表驱动程序，旨在以受控的方式发展这些功能。我们在真实无质量标量场完全非线性坍缩的背景下数值研究了其中一些驱动因素的参数空间，并确定了特定情况下几乎最佳的参数设置。令人惊讶的是，我们发现许多在使用笛卡尔坐标的3+1计算中表现良好的驱动程序在球对称中的效率要低得多，其中一些实际上是不稳定的。
英文摘要：
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention in numerical relativity over the past few years, especially as applied to the problem of binary inspiral and merger. A key issue when using the technique is the choice of the gauge source functions, and recent work has provided several prescriptions for gauge drivers designed to evolve these functions in a controlled way. We numerically investigate the parameter spaces of some of these drivers in the context of fully non-linear collapse of a real, massless scalar field, and determine nearly optimal parameter settings for specific situations. Surprisingly, we find that many of the drivers that perform well in 3+1 calculations that use Cartesian coordinates, are considerably less effective in spherical symmetry, where some of them are, in fact, unstable.
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