论文标题
Painleve-Gullstrand坐标与Kerr时空几何形状
Painleve-Gullstrand coordinates versus Kerr spacetime geometry
论文作者
论文摘要
我们讨论了Painleve-Gullstrand坐标系统的可能存在与Kerr时空的显式几何特征之间的张力；在他意外死亡之前的几周里，塔努·帕德曼汉（Thanu Padmanabhan）教授的感兴趣主题。我们将仔细区分强大和弱的painleve-gullstrand坐标系，以及其共形变体，分类我们所知道的可以和不能做的事情 - 有时我们可以做出明确的全球陈述，有时我们必须诉诸于隐性的本地陈述。对于Kerr时空，似乎可以实现的最好的是将衰减函数设置为统一性，并用3级分解的单峰形式表示空间切片。这是由于考虑到笛卡尔坐标中的Kerr Spacetime的Doran版本而引起的。我们通过探索这种构建可能导致实施适用于Kerr Spacetime实验室模拟的“模拟时空”模型的（有限）范围来结束。
We discuss the tension between the possible existence of Painleve-Gullstrand coordinate systems versus the explicit geometrical features of the Kerr spacetime; a subject of interest to Professor Thanu Padmanabhan in the weeks immediately preceding his unexpected death. We shall carefully distinguish strong and weak Painleve-Gullstrand coordinate systems, and conformal variants thereof, cataloguing what we know can and cannot be done -- sometimes we can make explicit global statements, sometimes we must resort to implicit local statements. For the Kerr spacetime the best that seems to be achievable is to set the lapse function to unity and represent the spatial slices with a 3-metric in factorized unimodular form; this arises from considering the Doran version of Kerr spacetime in Cartesian coordinates. We finish by exploring the (limited) extent to which this construction might possibly lead to implementing an "analogue spacetime" model suitable for laboratory simulations of the Kerr spacetime.
