2020/09/11 by Stanislav Komarov, Komarov, Stanislav, A. K. Gorbatsievich +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Relativity and Gravitational Theory #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2009.05663
openalex publication_date 2020/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the time evolution of the redshift of the spectrum of\nelectromagnetic radiation that is emitted by the star that moves in the\nvicinity of supermassive black hole. For the case of Schwarzschild black hole\nwe solve this problem exactly in General Theory of Relativity. Also we\nformulate an approach that gives possibilities to solve the inverse problem:\nreconstruction of motion of a star in the vicinity of black hole using the\nredshift data. This approach consists of two steps. The first step gives\npossibilities to find unique solution for the integrals of motion of the star\nby solution of a system of non-linear equations, rather than the direct\napplication of standard statistical methods. For this purpose we consider\nproperties of congruences of isotropic geodesics that connect of the worldline\nof the source and the worldline of the observer. The second step is the\napplication of standard least squares method in order to obtain more accurate\nsolution. This approach is used on the numerical model of the star in the\nvicinity of the Center of our Galaxy.\n