Schwarzschild-Tangherlini时空的光学2-度规与Bohlin-Arnold对偶
Optical 2-metrics of Schwarzschild-Tangherlini Spacetimes and the Bohlin-Arnold Duality
摘要：
我们考虑投影零测地线的Schwarzschild-Tangherlini度量在n+1维的静态Killing矢量的轨道空间中的一个给定的光线的运动被认为是躺在一个平面。投影曲线与光学2度规的非参数化测地线相吻合，并且可以同样理解为描述非相对论性粒子在中心力中的运动。我们考虑的投影零曲线的n值对之间的对偶性，并解释其数学意义的光学2-度量。度量不是射影等价的，但对应关系可以用三阶微分方程来表达。我们还探讨了这个概念的二元性Reissner-Nordstrom的情况下的扩展。
英文摘要：
We consider the projection of null geodesics of the Schwarzschild-Tangherlini metric in n+1 dimensions to the space of orbits of the static Killing vector where the motion of a given light ray is seen to lie in a plane. The projected curves coincide with the unparametrised geodesics of optical 2-metrics and can be equally understood as describing the motion of a non-relativistic particle in a central force. We consider a duality between the projected null curves for pairs of values of n and interpret its mathematical meaning in terms of the optical 2-metrics. The metrics are not projectively equivalent but the correspondence can be exposed in terms of a third order differential equation. We also explore the extension of this notion of duality to the Reissner-Nordstrom case.
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