Light propagation in arbitrary spacetimes and the gravitational lens approximation
Light propagation in arbitrary spacetimes and the gravitational lens approximation
复制标题
任意时空中的光传播和引力透镜近似
DOI：
10.1088/0264-9381/11/9/016
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发表时间：
1994
影响因子：
3.5
通讯作者：
J. Ehlers
中科院分区：
文献类型：
--
作者：
S. Seitz;P. Schneider;J. Ehlers
我们重新表述了决定任意时空中无限小光束的大小、形状和取向的输运方程。研究了这种光束在顶点和共轭点附近的行为，特别注意了光学标量的奇异行为。然后，我们将一般输运方程特化到非均匀宇宙的近似度规的情况，即具有叠加的孤立弱物质非均质性的Friedmann度规。在一系列定义明确的近似中，导出了引力透镜理论的方程。最后，我们导出了一个相对光学聚焦方程，它描述了光束相对于宇宙中不受物质不均匀影响的情况下的聚焦，由此立即得出结论：在光束通过其第一共轭点之前，任何光束都不能比不受物质团块影响的光束聚焦更少。
We reformulate the transport equation which determines the size, shape and orientation of infinitesimal light beams in arbitrary spacetimes. The behaviour of such light beams near vertices and conjugate points is investigated, with special attention to the singular behaviour of the optical scalars. We then specialize the general transport equation to the case of an approximate metric of an inhomogeneous universe, which is a Friedmann metric `on average' with superposed isolated weak matter inhomogeneities. In a series of well defined approximations, the equations of gravitational lens theory are derived. Finally, we derive a relative optical focusing equation which describes the focusing of light beams relative to the case that the beam is unaffected by matter inhomogeneities in the universe, from which it follows immediately that no beam can be focused less than one which is unaffected by matter clumps, before it propagates through its first conjugate point.