Appearance of coordinate shocks in hyperbolic formalisms of general relativity
Appearance of coordinate shocks in hyperbolic formalisms of general relativity
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广义相对论双曲形式中坐标激波的出现
DOI：
10.1103/physrevd.55.5981
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发表时间：
1996
影响因子：
5
通讯作者：
M. Alcubierre
中科院分区：
文献类型：
--
作者：
M. Alcubierre
我认为在广义相对论的双曲形式主义的冲击的外观。我研究的博纳-马索形式主义与零位移矢量的特殊情况下，并显示如何冲击与两个家庭的特征字段可以发展。这些冲击并不代表时空几何中的不连续性，而是坐标系变得病态的区域。因此，我称之为协调冲击。我展示了如何一个家庭的冲击可以消除限制博纳-马索切片条件的特殊情况。然而，即使在谐波切片的情况下，也不能消除另一族冲击。我还显示的特殊情况下的一个平坦的二维时空，一个平坦的四维时空与球对称切片，和球对称黑洞时空的数值模拟的结果。在所有三种情况下，协调冲击都很容易发展，证实了数学分析的预测。虽然在这里我集中在博纳-马索形式主义中，但坐标激波的现象应该出现在任何其他双曲形式主义中。特别是，由于外观的冲击是由选择的规格，这里提出的结果意味着，在任何形式主义的使用谐波切片可以产生冲击。
I consider the appearance of shocks in hyperbolic formalisms of General Relativity. I study the particular case of the Bona-Masso formalism with zero shift vector and show how shocks associated with two families of characteristic fields can develop. These shocks do not represent discontinuities in the geometry of spacetime, but rather regions where the coordinate system becomes pathological. For this reason I call them coordinate shocks. I show how one family of shocks can be eliminated by restricting the Bona-Masso slicing condition to a special case. The other family of shocks, however, can not be eliminated even in the case of harmonic slicing. I also show the results of numerical simulations in the special cases of a flat two-dimensional spacetime, a flat four-dimensional spacetime with a spherically symmetric slicing, and a spherically symmetric black hole spacetime. In all three cases coordinate shocks readily develop, confirming the predictions of the mathematical analysis. Although here I concentrate in the Bona-Masso formalism, the phenomena of coordinate shocks should arise in any other hyperbolic formalism. In particular, since the appearance of the shocks is determined by the choice of gauge, the results presented here imply that in any formalism the use of a harmonic slicing can generate shocks.