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Revista de Matemática: Teoría y Aplicaciones
Article . 2025 . Peer-reviewed
License: CC BY NC SA
Data sources: Crossref
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https://dx.doi.org/10.48550/ar...
Article . 2024
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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Transparent spheres as gravitational lenses

Authors: Santiago-Leandro, Edwin; Mora-Chaverri, Alexander; Frutos-Alfaro, Francisco;

Transparent spheres as gravitational lenses

Abstract

In this work, we present a concise and educational study of gravitational lensing by transparent matter distributions. We focus on the calculation of image properties for several idealized mass profiles, including the uniform transparent sphere, the isothermal gas sphere, the non singular isothermal sphere, and the transparent King profile. Using numerical techniques and the XFGLenses software, we compute and visualize the resulting lensed images, along with the associated critical curves and caustics. The results are consistent with established theoretical predictions for transparent lenses, for example, the occurrence of an odd number of images, and the reduction of two images as the source crosses a caustic. The caustic geometries observed include diamond-shaped, elliptical, and lemniscate-like structures. Among the critical curves, ellipses were most commonly observed, while lemniscatelike forms emerged specifically in the transparent non-singular isothermal sphere case, in agreement with known behaviors in gravitational lensing by smooth matter distributions.

Keywords

Cosmology and Nongalactic Astrophysics (astro-ph.CO), FOS: Physical sciences, Astrophysics - Cosmology and Nongalactic Astrophysics

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green