On the effect of the cosmological expansion on the gravitational lensing by a point mass

Abstract

We analyze the effect of the cosmological expansion on the deflection of light caused by a point mass, adopting the McVittie metric as the geometrical description of a pointlike lens embedded in an expanding universe. In the case of a generic, non-constant Hubble parameter $H$ we derive and approximately solve the null geodesic equations, finding an expression for the bending angle $\delta$, which we expand in powers of the mass-to-closest approach distance ratio and of the impact parameter-to-lens distance ratio. It turns out that the leading order of the aforementioned expansion is the same as the one calculated for the Schawarzschild metric and that cosmological corrections contribute to $\delta$ only at sub-dominant orders. We explicitly calculate these cosmological corrections for the case of $H$ constant and find that they provide a correction of order $10^{-11}$ on the lens mass estimate.

10 pages, 7 figures (created with tikz)

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Cited by in corpus (8)

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• Calculating black hole shadows: Review of analytical studies
• First analytical calculation of black hole shadow in McVittie metric
• Light bending by the cosmological constant
• Gravitational lensing in a universe with matter and a cosmological constant
• Deflection of light in time-periodic spherically symmetric gravitational fields
• Probing dark fluids and modified gravity with gravitational lensing
• McVittie-Plummer Spacetime: Plummer Sphere Immersed in the FLRW Universe