论文标题
将零无穷大的双框架通用谐波量规和正规化
Regularizing Dual-Frame Generalized Harmonic Gauge at Null Infinity
论文作者
论文摘要
双框架形式主义导致一种方法，以将数值相对论模拟在通用谐波计（GHG）中一直延伸至无效无穷大。一个重大的挫折是，在不小心的情况下，即使是简单的初始数据选择也会产生对数发散的术语，这将导致不规则变量和压缩域上的方程，这反过来又可以防止准确的数值近似。但是，已经表明，可以使用适当的量规和约束选择来防止其外观。目前，我们在压缩的倍曲面切片上给出了一阶对称性双曲线降低，从而利用了这些知识并消除了这些对数字的主要命令。由于它们对渐近解决方案空间的影响，因此系统地选择了特定的正式奇异项。这种形式上的奇异术语已在玩具模型中成功地进行了数值处理，并带来了所需特性的表述，即无穷大附近的非物理辐射含量被抑制。
The dual-frame formalism leads to an approach to extend numerical relativity simulations in generalized harmonic gauge (GHG) all the way to null infinity. A major setback is that without care, even simple choices of initial data give rise to logarithmically divergent terms that would result in irregular variables and equations on the compactified domain, which would in turn prevent accurate numerical approximation. It has been shown, however, that a suitable choice of gauge and constraint addition can be used to prevent their appearance. Presently we give a first order symmetric hyperbolic reduction of general relativity in GHG on compactified hyperboloidal slices that exploits this knowledge and eradicates these log-terms at leading orders. Because of their effect on the asymptotic solution space, specific formally singular terms are systematically chosen to remain. Such formally singular terms have been successfully treated numerically in toy models and result in a formulation with the desirable property that unphysical radiation content near infinity is suppressed.
