LAUSR

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.