Rigorous approach to gravitational lensing

We revisit a weak gravitational lensing problem by constructing a setup which describes the actual system as accurately as possible and solving the null geodesic equations. Details are given for the case of a universe driven only by a cosmological constant, $\Lambda$, which confirm the conventional results: The conventional lensing analysis is correct as it is, without any need for correction of $\mathcal{O}(\Lambda )$. We also treat the cases of the lensing in generic Friedmann-Robertson-Walker backgrounds.

Figure 1

Lensing schematics.

Figure 2

Lensing schematics in conventional analysis.