Dynamical Gauge Conditions for the Einstein Evolution Equations
Dynamical Gauge Conditions for the Einstein Evolution Equations
复制标题
爱因斯坦演化方程的动态规范条件
DOI：
10.1103/physrevd.67.124005
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发表时间：
2003
影响因子：
5
通讯作者：
M. Scheel
中科院分区：
文献类型：
--
作者：
L. Lindblom;M. Scheel
以前，当规范场--密化的损耗和位移--被视为坐标的固定函数时，爱因斯坦演化方程已经写成了许多对称双曲线形式。通过将规范自由度添加到动态场集合中，构造了扩展的演化方程组，从而形成了引力场和规范场联合演化的对称双曲组。通过调整这些新系统中的14个自由参数，可以使相关的特征速度成为因果关系(即，小于或等于光速)，并且有21个额外的自由参数可用，例如，以优化数值演化的稳定性。这些系统中的规范演化方程是“K驱动”和“伽玛驱动”条件的推广，这两个条件已经在数值黑洞演化中得到了一些成功的应用。
The Einstein evolution equations have previously been written in a number of symmetric hyperbolic forms when the gauge fields—the densitized lapse and the shift—are taken to be fixed functions of the coordinates. Extended systems of evolution equations are constructed here by adding the gauge degrees of freedom to the set of dynamical fields, thus forming symmetric hyperbolic systems for the combined evolution of the gravitational and the gauge fields. The associated characteristic speeds can be made causal (i.e., less than or equal to the speed of light) by adjusting 14 free parameters in these new systems, and 21 additional free parameters are available, for example, to optimize the stability of numerical evolutions. The gauge evolution equations in these systems are generalizations of the "K-driver" and "Gamma-driver" conditions that have been used with some success in numerical black hole evolutions.