论文标题
重力透镜没有渐近平坦的镜头：其应用于Weyl重力
Gravitational lens without asymptotic flatness: Its application to the Weyl gravity
论文作者
论文摘要
我们在不假设渐近平坦的情况下讨论了与透镜对象有限距离内的观察者和来源的重力透镜。所提出的镜头方程与Takizawa等人的非矩形观察者定义的光的偏转角度一致。 [物理。 Rev. D 101，104032（2020）]基于使用光学指标的高斯定理。该镜头方程，尽管它被证明等同于Bozza镜头方程[Phys。 Rev. D 78，103005（2008）]在偏转角度是线性的。因此，为进行迭代分析而言，提出的方程式更为方便。作为渐近非纤维时空的明确示例，我们考虑了Weyl共形重力中的静态和球面对称解，尤其是Weyl Gravity模型中的$γ$参数是当前哈勃半径的逆阶。对于这种情况，我们检查了有限距离距离镜头方程的迭代解决方案，直至三阶。 Weyl Gravity对镜头图像位置的影响以三阶开始，并且在光的冲击参数中是线性的。镜头图像位置与一般相对论的偏差是$ \ sim 10^{ - 2} $ microarcsecond，用于镜头和源，分离角为$ \ sim 1 $ arcminute，我们考虑了一个带有$ 10^{14} m _ _ {\ odot} $ sim $ 10^{14} $ sim $ sim $ sim $ gpc的星系群。即使分隔角为$ \ sim 10 $ arcminutes，偏差变为$ \ sim 10^{ - 1} $ microarcseconds。因此，在重力镜头的电流和近乎未来的观察结果中，Weyl重力模型的作用可以忽略不计。另一方面，以第三阶$ \ sim 0.1 $ milliarcseconds的一般相对论更正可能与VLBI观察结果相关。
We discuss, without assuming asymptotic flatness, a gravitational lens for an observer and source that are within a finite distance from a lens object. The proposed lens equation is consistent with the deflection angle of light that is defined for nonasymptotic observer and source by Takizawa et al. [Phys. Rev. D 101, 104032 (2020)] based on the Gauss-Bonnet theorem with using the optical metric. This lens equation, though it is shown to be equivalent to the Bozza lens equation[Phys. Rev. D 78, 103005 (2008)], is linear in the deflection angle. Therefore, the proposed equation is more convenient for the purpose of doing an iterative analysis. As an explicit example of an asymptotically nonflat spacetime, we consider a static and spherically symmetric solution in Weyl conformal gravity, especially a case that $γ$ parameter in the Weyl gravity model is of the order of the inverse of the present Hubble radius. For this case, we examine iterative solutions for the finite-distance lens equation up to the third order. The effect of the Weyl gravity on the lensed image position begins at the third order and it is linear in the impact parameter of light. The deviation of the lensed image position from the general relativistic one is $\sim 10^{-2}$ microarcsecond for the lens and source with a separation angle of $\sim 1$ arcminute, where we consider a cluster of galaxies with $10^{14} M_{\odot}$ at $\sim 1$ Gpc for instance. The deviation becomes $\sim 10^{-1}$ microarcseconds, even if the separation angle is $\sim 10$ arcminutes. Therefore, effects of the Weyl gravity model are negligible in current and near-future observations of gravitational lensing. On the other hand, the general relativistic corrections at the third order $\sim 0.1$ milliarcseconds can be relevant with VLBI observations.
