Kerr几何中光子偏振的精确表达式
An Exact Expression for Photon Polarization in Kerr Geometry
摘要：
在克尔几何中，我们分析了光子沿任意零测地线传播时的偏振变换。其动机来自于一个观测者试图通过传输偏振光子将量子信息传递给克尔时空中的另一个观测者的问题。重要的是，观察者要理解他们的参照系之间的关系，也要知道光子在克尔时空中传播时的偏振是如何转变的。现有的方法来计算光子偏振的旋转（法拉第旋转）依赖于坐标系的选择，是代数复杂的，并且仅在弱场极限下产生结果。利用Killing-Yano理论，给出了沿任意零测地线平行传播的标架的封闭表达式，从而解决了偏振矢量在一个内在的、几何驱动的方式下的平行传输问题.利用克尔几何的对称性，得到了光子偏振的几何诱导相位的一个非常简洁的表达式。我们表明，这个阶段消失的赤道平面和对称轴。
英文摘要：
We analyze the transformation of the polarization of a photon propagating along an arbitrary null geodesic in Kerr geometry. The motivation comes from the problem of an observer trying to communicate quantum information to another observer in Kerr spacetime by transmitting polarized photons. It is essential that the observers understand the relationship between their frames of reference and also know how the photon's polarization transforms as it travels through Kerr spacetime. Existing methods to calculate the rotation of the photon polarization (Faraday rotation) depend on choices of coordinate systems, are algebraically complex and yield results only in the weak-field limit. We give a closed-form expression for a parallel propagated frame along an arbitrary null geodesic using Killing-Yano theory, and thereby solve the problem of parallel transport of the polarization vector in an intrinsic, geometrically-motivated fashion. The symmetries of Kerr geometry are utilized to obtain a remarkably compact expression for the geometrically induced phase of the photon's polarization. We show that this phase vanishes on the equatorial plane and the axis of symmetry.
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