Gravitational deflection angle of light: Definition by an observer and its application to an asymptotically nonflat spacetime
Gravitational deflection angle of light: Definition by an observer and its application to an asymptotically nonflat spacetime
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DOI：
10.1103/physrevd.101.104032
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发表时间：
2020-01
影响因子：
5
通讯作者：
Kei Takizawa;T. Ono;H. Asada
中科院分区：
文献类型：
--
作者：
Kei Takizawa;T. Ono;H. Asada
Ishihara 等人研究了距透镜物体有限距离处的观察者和光源的光的重力偏转角。 [物理。 Rev. D, 94, 084015 (2016)]，基于高斯-邦尼定理并使用光学度量。他们处理有限距离情况的方法仅限于渐近平坦时空。通过做出几个假设，我们从观察者的角度给出了它们的定义的解释：观察者假设观察者位置处假设的光发射方向，并将基准发射方向与沿真实光线的方向进行比较。 Ishihara 等人可以将观察者位置处两个方向之间的角度解释为偏转角。目前的解释不需要渐进平坦性。受此启发，我们避免了这样的渐近区域，讨论光偏转角的另一种积分形式。这种形式清楚地表明，所提出的偏转角不仅可用于渐近平坦时空，而且还可用于渐近非平坦时空。对于后一种情况，我们在两个模型中检查了所提出的偏转角；广义相对论中的科特勒（史瓦西-德西特）解和外尔共形引力中的球形解。外尔共形引力中有限距离对光偏转的影响导致偏转角中出现一个额外的项，这在一定的参数区域中可能是勉强可观察到的。另一方面，科特勒时空中的那些是当前技术无法企及的。
The gravitational deflection angle of light for an observer and source at finite distance from a lens object has been studied by Ishihara et al. [Phys. Rev. D, 94, 084015 (2016)], based on the Gauss-Bonnet theorem with using the optical metric. Their approach to finite-distance cases is limited within an asymptotically flat spacetime. By making several assumptions, we give an interpretation of their definition from the observer's viewpoint: The observer assumes the direction of a hypothetical light emission at the observer position and makes a comparison between the fiducial emission direction and the direction along the real light ray. The angle between the two directions at the observer location can be interpreted as the deflection angle by Ishihara et al. The present interpretation does not require the asymptotic flatness. Motivated by this, we avoid such asymptotic regions to discuss another integral form of the deflection angle of light. This form makes it clear that the proposed deflection angle can be used not only for asymptotically flat spacetimes but also for asymptotically nonflat ones. We examine the proposed deflection angle in two models for the latter case; Kottler (Schwarzschild-de Sitter) solution in general relativity and a spherical solution in Weyl conformal gravity. Effects of finite distance on the light deflection in Weyl conformal gravity result in an extra term in the deflection angle, which may be marginally observable in a certain parameter region. On the other hand, those in Kottler spacetime are beyond reach of the current technology.