论文标题

对重力镜头的几何和潜在时间延迟的检查

An Examination of Geometrical and Potential Time Delays in Gravitational Lensing

论文作者

Tsupko, Oleg Yu., Bisnovatyi-Kogan, Gennady S., Rogers, Adam, Er, Xinzhong

论文摘要

在本文中,我们研究了重力镜头中电势和几何时间延迟之间的关系。在Shapiro(1964)的原始论文中,与在没有任何质量的情况下相比,地球和金星之间的雷达信号在巨大的物体(太阳)附近(太阳)附近有时间延迟。该延迟的原因与重力对重力电势中光线坐标速度的影响有关。路径长度的变化的贡献恰好是二阶,被认为可以忽略不计。然而,在重力镜头理论中,与潜在项一起通常考虑与路径长度变化有关的几何延迟。在这项工作中,我们解释了这一明显的差异。我们解决了不同情况下时间延迟的几何部分的贡献,并引入了统一的治疗方法,并具有两个限制性镜头方案。这些限制之一对应于在太阳附近的时间延迟实验,该实验表明几何延迟可忽略不计。第二个对应于典型的引力透镜场景,其中多个成像表明几何延迟被证明是显着的。我们基于源和爱因斯坦半径的角度位置之间的关系引入了一个紧凑,分析和定量标准。该标准允许在需要考虑几何延迟时轻松找出。特别是,在源,镜头和观察者之间良好对齐的情况下,几何延迟是不可忽略的,因为在这种情况下,它成为一阶数量(与潜在项相同的阶数)。

In this paper we investigate the relation between the potential and geometric time delays in gravitational lensing. In the original paper of Shapiro (1964), it is stated that there is a time delay in the radar signals between Earth and Venus that pass near a massive object (the Sun), compared to the path taken in the absence of any mass. The reason for this delay is connected with the influence of gravity on the coordinate velocity of a light ray in a gravitational potential. The contribution from the change of the path length, which happens to be of second order, is considered as negligible. Nevertheless, in the gravitational lens theory the geometrical delay, related to the change of path length, is routinely taken into account along with the potential term. In this work we explain this apparent discrepancy. We address the contribution of the geometric part of the time delay in different situations, and introduce a unified treatment with two limiting regimes of lensing. One of these limits corresponds to the time delay experiments near the Sun where the geometrical delay is shown to be negligible. The second corresponds to the typical gravitational lens scenario with multiple imaging where the geometrical delay is shown to be significant. We introduce a compact, analytical, and quantitative criteria based on relation between the angular position of source and the Einstein radius. This criterion allows one to find out easily when it is necessary to take the geometrical delay into account. In particular, it is shown that the geometrical delay is non-negligible in the case of good alignment between source, lens and observer, because in such a case it becomes a first order quantity (the same order as the potential term).

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