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

TL;DR

This paper introduces a refined method to calculate light deflection in rotating spacetimes with a cosmological constant, providing more accurate predictions that could be tested with future high-precision astronomical observations.

Contribution

The study develops a new approach to derive the light deflection angle in Kerr-de Sitter spacetime, considering finite source and observer positions and solving the EOM directly, advancing previous work.

Findings

Derived a second-order accurate expression for light deflection in Kerr-de Sitter spacetime.

Explicitly included finite source and observer distances in the calculations.

Predicted observable corrections in gravitational lensing by the Sun and Sgr A*.

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 -- the Randers optical space is employed to resolve the staticity constraint. 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 discuss the discrepancies between our results and previous expressions. 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.