Abstract

The purpose of this paper is to investigate if the weak field lensing (WFL) observables can distinguish between three physically distinct lenses, mathematically connected by a combination of real and complex transformations. All three kinds of lenses have been discussed in the literature in the strong field limit, but since the weak field light deflection does not follow as a PPN expansion from the strong field deflection due to a logarithmic divergence at the photon sphere, the WFL requires a separate investigation that has not yet been done adequately. This paper attempts to fill this gap by calculating the WFL observables such as the position, magnification and differential time delay of the images using the Keeton-Petters method. We shall, for illustration, assume the lens to be the compact object SgrA* and compare the WFL signatures with those of the Schwarzschild black hole. It is shown that, while the zeroth-order observables for the three classes of lenses are indistinguishable from those of the Schwarzschild black hole, higher-order correction terms are theoretically distinguishable for different lenses, and future accurate measurements might constrain the parameter \(\gamma\) of the solutions.

中文翻译：

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弱场透镜能否在裸奇点，Ellis-Bronnikov常规虫眼和黑洞之间区分开？

摘要

本文的目的是研究可观察到的弱视场透镜（WFL）是否可以区分三个物理上不同的透镜，这些透镜通过实数和复数变换的组合在数学上相连。文献中已经讨论了这三种透镜的强场极限，但是由于弱场光偏转没有由于光子球上的对数发散所引起的强场偏转导致PPN扩展，因此WFL需要进行单独的研究，而这项研究尚未充分进行。本文试图通过使用Keeton-Petters方法计算WFL观测值（例如图像的位置，放大率和微分时间延迟）来填补这一空白。为了说明起见，我们假设镜头是紧凑型物体SgrA *，并将WFL签名与Schwarzschild黑洞的签名进行比较。结果表明，虽然三类透镜的零阶可观测值与Schwarzschild黑洞的零阶可观测值没有区别，但理论上可区分不同透镜的高阶校正项，未来的精确测量可能会限制该参数。\（\ gamma \）解决方案。