The influence of cosmological constant on light deflection in rotating spacetimes via the generalized Gibbons-Werner method

Abstract: Recently, we proposed a generalized Gibbons-Werner (GW) method for analyzing particle trajectories in rotating spacetimes, regardless of their asymptotic behavior [Huang \textit{et al.}, \href{https://iopscience.iop.org/article/10.1088/1475-7516/2024/01/013}{J. Cosmol. Astropart. Phys. 01(2024), 013}]. Using this method, we examine the impact of the cosmological constant ($\Lambda$) on the light deflection in rotating spacetimes within the framework of Kerr-de Sitter (KdS) geometry. Although Sultana previously calculated the deflection angle of light in KdS spacetime, our study advances this research in three aspects: (i) Orbit solution -- the light trajectory is derived by directly solving the original equation of motion (EOM) without intermediate processes. (ii) Positions of the source and observer -- the finite distances of the source and observer from the lens are explicitly considered, avoiding approximations. (iii) Staticity of the source and observer -- their comoving nature is incorporated by employing the Randers optical space. Through these refined considerations, we obtain a novel expression for the deflection angle of light in KdS spacetime, accurate to second-order in $\Lambda$, as well as in the mass (M) and spin parameter (a) of the central body. Furthermore, we engage in a detailed discussion of the discrepancies between our results and previous expressions, highlighting the reasons behind them. Finally, we evaluate the observational implications of our corrections relative to Sultana's work in the lensing systems of the Sun and Sgr A*, and show that they may become observable with forthcoming high-precision astronomical measurements.