论文标题
Gödel时空，平面地球学和Möbius地图
Gödel spacetime, planar geodesics and the Möbius map
论文作者
论文摘要
如果使用自然适应圆柱形对称性的标准坐标，则在与gödel时空的对称轴的超平孔上的平时大地测量似乎是椭圆形的。然后，可以通过偏心性 - 拉托直肠参数化适当地描述轨道，这是两体系统的牛顿动力学所熟悉的。然而，正如昆特（Kundt）的戈德尔度量标准（GödelMetric）的形式所展示的那样，改变坐标的这种平面大地测量学都变得明确地循环。我们在这里得出了沿着这些大地测量学的运动常数以及椭圆形与圆形测量学的参数空间之间的一对一对应关系。我们还展示了如何通过在2平面正交中引入一对复杂的坐标来连接两个等效的粒子运动描述，该坐标与对称轴正交，该轴将指标变成了一个形式，该形式是在Möbius变换下不变的形式，从而保留了轨道的对称性，即以圆形的圆圈为单位，以圆圈为圆圈。
Timelike geodesics on a hyperplane orthogonal to the symmetry axis of the Gödel spacetime appear to be elliptic-like if standard coordinates naturally adapted to the cylindrical symmetry are used. The orbit can then be suitably described through an eccentricity-semi-latus rectum parametrization, familiar from the Newtonian dynamics of a two-body system. However, changing coordinates such planar geodesics all become explicitly circular, as exhibited by Kundt's form of the Gödel metric. We derive here a one-to-one correspondence between the constants of the motion along these geodesics as well as between the parameter spaces of elliptic-like versus circular geodesics. We also show how to connect the two equivalent descriptions of particle motion by introducing a pair of complex coordinates in the 2-planes orthogonal to the symmetry axis, which brings the metric into a form which is invariant under Möbius transformations preserving the symmetries of the orbit, i.e., taking circles to circles.
