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arXiv 1105.5629gr-qcastro-ph.SR
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定态时空中的自旋光学

Spinoptics in a stationary spacetime

Valeri P. Frolov, Andrey A. Shoom

摘要:

本文的主要目的是研究光子在旋转的大质量致密天体产生的引力场中的偏振对光子运动的影响。研究了圆偏振光束在静止引力场中的传播。本文利用麦克斯韦方程组的(3+1)形式导出了频率为$ω$的单色电磁波在给定螺旋度下传播的主方程。我们首先用“标准”几何光学方法在高频近似下分析了它的解。在此之后,我们演示了如何可以修改这个“标准”的方法,以包括光子的螺旋度对它们的运动的影响。这种改进的方法在短距离内再现了几何光学的标准结果。然而,它修改的渐近行为的圆偏振光束在晚时间制度。我们证明,相应的方程的圆偏振光束可以有效地获得通过修改的背景几何形状,包括一个小的因子成比例的$ω^{-1}$,其符号对应于光子螺旋度。我们利用这种“重整化”方法得到了圆偏振光的修正方程,并计算了克尔几何中相应的重整化项。

英文摘要:

The main goal of the present paper is to study how polarization of photons affects their motion in a gravitational field created by a rotating massive compact object. We study propagation of the circularly polarized beams of light in a stationary gravitational field. We use (3+1)-form of the Maxwell equations to derive a master equation for the propagation of monochromatic electromagnetic waves of the frequency $ω$ with a given helicity. We first analize its solutions in the high frequency approximation using the `standard' geometrical optics approach. After that we demonstrate how this `standard' approach can be modified in order to include the effect of the helicity of photons on their motion. Such an improved method reproduces the standard results of the geometrical optics at short distances. However, it modifies the asymptotic behavior of the circularly polarized beams in the late-time regime. We demonstrate that the corresponding equations for the circularly polarized beam can be effectively obtained by modification of the background geometry by including a small factor proportional to $ω^{-1}$ whose sign corresponds to photon helicity. We obtain the modified equations for circularly polarized rays by using such a `renormalization' procedure, and calculate the corresponding renormalization term for the Kerr geometry.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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