论文标题
Kerr Spacetime中空间3米的Darboux对角线化
Darboux diagonalization of the spatial 3-metric in Kerr spacetime
论文作者
论文摘要
凯尔时空的天体重要性不能被夸大。在当前已知的爱因斯坦场方程的确切解决方案中，Kerr时空在描述天文学黑洞候选物的直接适用性方面脱颖而出。在对立点上，纯粹是数学上，由于达伯（Darboux），差异几何形状的古老经典结果是，所有3个manifolds都可以将其指标重新铸成对角线形式。在Kerr时空的情况下，Boyer-Lindquist坐标提供了一个明确的对角线空间3米。不幸的是，正如我们在本文中所证明的那样，KERR时空的空间3个线的Darboux对角化是不兼容的，同时将KERR指标放入单位解体形式的同时，同时保留了明显的轴向对称性。这种无关定理有点让人联想到无关定理的效果，即不能选择克尔时空的3个单点是合并平坦的。
The astrophysical importance of the Kerr spacetime cannot be overstated. Of the currently known exact solutions to the Einstein field equations, the Kerr spacetime stands out in terms of its direct applicability to describing astronomical black hole candidates. In counterpoint, purely mathematically, there is an old classical result of differential geometry, due to Darboux, that all 3-manifolds can have their metrics recast into diagonal form. In the case of the Kerr spacetime the Boyer-Lindquist coordinates provide an explicit example of a diagonal spatial 3-metric. Unfortunately, as we demonstrate herein, Darboux diagonalization of the spatial 3-slices of the Kerr spacetime is incompatible with simultaneously putting the Kerr metric into unit-lapse form while retaining manifest axial symmetry. This no-go theorem is somewhat reminiscent of the no-go theorem to the effect that the spatial 3-slices of the Kerr spacetime cannot be chosen to be conformally flat.
