Spatial Curvature's Impact on Light Bending and Time Delay in Einstein-Straus--de Sitter Spacetime

A recent paper by Mourad Guenouche titled "Effect of the spatial curvature on light bending and time delay in curved Einstein-Straus--de Sitter spacetime" explores how spatial curvature affects light behavior in the context of general relativity. The research focuses on integrating the null geodesic equations of the Einstein-Straus-de Sitter metric, aiming to provide a generalized method for calculating light deflection and time delay caused by spherical mass distributions.

The study assumes a flat Universe while incorporating the latest measurements of the Hubble constant and the cosmological constant. It forecasts five time delays between the four bright images of the lensed quasar SDSS J1004+4112, comparing these predictions with existing data in the field.

One significant finding is that the contribution of a positive cosmological constant to light bending is too small to be noticeable on cosmological scales. Similarly, the impact of the expected small curvature density of the current Universe is negligible, suggesting that it can be safely ignored unless the curvature density increases significantly.

The implications of this research are noteworthy for astrophysics, particularly in understanding how light behaves in various cosmological models. The results indicate that while spatial curvature has a theoretical effect on light bending and time delay, it may not be significant enough to influence current observational practices unless future measurements reveal a larger curvature density. This work could help refine models of gravitational lensing and improve our understanding of the Universe's structure.

For further details, the paper can be accessed at arXiv:2406.10436.