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- Title
Elimination method for construction of images for N-point gravitational lenses for a circular source.
- Authors
Kotvytskiy, Albert; Parimucha, Štefan
- Abstract
This study aims to enhance precise analytical methods for image construction from circular sources in gravitational lenses. We begin by formulating the lens equations, using the bending angle formula for a light ray in a single-point lens with weak deflection and the thin lens approximation. We delve into the mathematical concepts of the resultant and Sylvester matrix, which help eliminate variables and find common polynomial roots. These concepts aid in parameter elimination within the lens equations to determine image coordinates. We showcase our method's application in one-point and binary lenses. In both cases, we derive implicit analytical expressions that entirely define the images of a circular source at any given position. By advancing analytical techniques, we reduce the reliance on numerical simulations, which can be computationally intensive and may not guarantee the discovery of all solutions. This work contributes to the understanding and characterization of gravitational lenses and provides a foundation for further developments in the field.
- Subjects
GRAVITATIONAL lenses; SYLVESTER matrix equations; COMPUTER simulation
- Publication
Astrophysics & Space Science, 2023, Vol 368, Issue 11, p1
- ISSN
0004-640X
- Publication type
Article
- DOI
10.1007/s10509-023-04257-4