Transparent spheres as gravitational lenses
DOI:
https://doi.org/10.15517/3fczkg02Keywords:
Gravitational lensing, Numerical simulations, General relativityAbstract
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.
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Copyright (c) 2025 Edwin Santiago-Leandro, Alexander Mora-Chaverri, Francisco Frutos-Alfaro (Autor/a)
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