Next Article in Journal / Special Issue
A Solution of the Mitra Paradox
Previous Article in Journal
Which Quantum Theory Must be Reconciled with Gravity? (And What Does it Mean for Black Holes?)
Previous Article in Special Issue
General Relativity and Cosmology: Unsolved Questions and Future Directions
Open AccessArticle

On the Effect of the Cosmological Expansion on the Gravitational Lensing by a Point Mass

Physics Department, Universidade Federal do Espírito Santo, Vitória 29075-910, Brazil
Academic Editors: Lorenzo Iorio and Elias C. Vagenas
Universe 2016, 2(4), 25;
Received: 2 September 2016 / Revised: 6 October 2016 / Accepted: 9 October 2016 / Published: 18 October 2016
We analyse 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 point-like 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 δ, 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 Schwarzschild metric and that cosmological corrections contribute to δ only at sub-dominant orders. We explicitly calculate these cosmological corrections for the case of the H constant and find that they provide a correction of order 10−11 on the lens mass estimate. View Full-Text
Keywords: McVittie metric; gravitational lensing; cosmology McVittie metric; gravitational lensing; cosmology
Show Figures

Figure 1

MDPI and ACS Style

Piattella, O.F. On the Effect of the Cosmological Expansion on the Gravitational Lensing by a Point Mass. Universe 2016, 2, 25.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

Back to TopTop