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Keywords = McVittie metric

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18 pages, 1219 KiB  
Article
Elliptical Space with the McVittie Metrics
by Vladimir N. Yershov
Universe 2024, 10(4), 165; https://doi.org/10.3390/universe10040165 - 31 Mar 2024
Viewed by 1867
Abstract
The main feature of elliptical space—the topological identification of its antipodal points—could be fundamental for understanding the nature of the cosmological redshift. The physical interpretation of the mathematical (topological) structure of elliptical space is made by using physical connections in the form of [...] Read more.
The main feature of elliptical space—the topological identification of its antipodal points—could be fundamental for understanding the nature of the cosmological redshift. The physical interpretation of the mathematical (topological) structure of elliptical space is made by using physical connections in the form of Einstein-Rosen bridges (also called “wormholes”). The Schwarzschild metric of these structures embedded into a dynamic (expanding) spacetime corresponds to McVittie’s solution of Einstein’s field equations. The cosmological redshift of spectral lines of remote sources in this metric is a combination of gravitational redshift and the time-dependent scale factor of the Friedmann-Lemaitre-Robertson-Walker metric. I compare calculated distance moduli of type-Ia supernovae, which are commonly regarded as “standard candles” in cosmology, with the observational data published in the catalogue “Pantheon+”. The constraint based on these accurate data gives a much smaller expansion rate of the Universe than is currently assumed by modern cosmology, the major part of the cosmological redshift being gravitational by its nature. The estimated age of the Universe within the discussed model is 1.48·1012 yr, which is more than two orders of magnitude larger than the age assumed by using the standard cosmological model parameters. Full article
(This article belongs to the Section Cosmology)
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16 pages, 278 KiB  
Article
On the Effect of the Cosmological Expansion on the Gravitational Lensing by a Point Mass
by Oliver F. Piattella
Universe 2016, 2(4), 25; https://doi.org/10.3390/universe2040025 - 18 Oct 2016
Cited by 15 | Viewed by 3997
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)
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