THE ANALYSIS OF IMAGES OF A CIRCULAR SOURCE IN N-POINT GRAVITATIONAL LENSES

Abstract

Currently, in the field of computer processing, there are difficulties. When processing astrophysical experimental data, the difficulties are connected, on the one hand, with a large amount of information that requires processing, and, on the other hand, with the technical capabilities of computers. The use of analytical methods can significantly reduce information processing time. The information that is entered is recorded in an analytical form, more convenient for processing. Information is processed analytically (Kotvytskiy & Bronza, 2016), and not by methods of the Ray Tracing type. Some results were obtained strictly analytically, and they do not need further computer processing (Kotvytskiy et al., 2016). The goal of this paper is to analyze images in N-point gravitational lenses by: - reduction of research of an arbitrary source to the study of a circular source; - reduction of research of a circular source in an N-point gravitational line to its study in the Schwarzschild lens and other few-point lenses; - analytical study of a circular source in the Schwarzschild lens and other few-point gravity lenses; - research of the place of the Schwarzschild lens, in the set of N - point gravitational lenses. Using the methods of algebraic geometry, algebraic topology and the theory of functions, we have prepared a problem for computer modeling: finding images of arbitrary sources in an N-point gravitational lens. We researched the images of a circular source in the Schwarzschild lens and proved that the study of images of any other sources is combinatorial reduced to this case.

Keywords

• gravitational lens, algebraic geometry, phases of images