Қазақ ұлттық қыздар педагогикалық университеті / Казахский национальный женский педагогический университет

Постоянный URI для этого сообществаhttps://cris.qyzpu.edu.kz/handle/123456789/1

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2023 - 20264

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Автор: search.filters.author.Ayazhan Orazymbet

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    A shadows from the static black hole mimickers
    (Al-Farabi Kazakh National University, 2023-01-10)
    Aray Muratkhan
    ;
    Ayazhan Orazymbet
    ;
    Madina Zhakipova
    ;
    M. Assylbek
    ;
    Saken Toktarbay
    In this work, we study shadows from the naked singularity spacetime. The most analytical solutions of black hole shadows only investigated the case that the geodesic equations for photons can separate variables. We review the spherical null naked singularity metric and this spherically symmetric naked singularity spacetime metric is the solution of Einstein equations with an anisotropic fluid source which has no photon sphere. We also review a static, axially-symmetric singular solution of the vacuum Einstein’s equations without an event horizon which is can be used to describe the exterior gravitational field of a mass distribution with quadrupole moment. Moreover, the corresponding spacetime is characterized by the presence of naked singularities. It is theoretically known that not only a black hole can cast shadow, but other compact objects such as naked singularities, gravastar or boson stars can also cast shadows. We present the analytical calculation of shadows for both naked singularities spacetime and compare with the shadow of Schwarzschild static black hole, we show that this can serve as a black hole mimicker. Keywords: compact object, naked singularity, shadow.
    Цитирования (OpenAlex) 5
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    Application of GBT theorem for Gravitational deflection of light by Compact Objects
    (Al-Farabi Kazakh National University, 2023-03-13)
    Nurzada Beissen
    ;
    Daniya Utepova
    ;
    Aray Muratkhan
    ;
    Ayazhan Orazymbet
    ;
    Manas Khassanov
    One of the most renowned classical experiments that verifies the curved nature of space-time geometry is the bending of light. This phenomenon is extensively discussed in most textbooks on general relativity, with a clear and comprehensive explanation provided. In this study, we employ the material medium approach to determine the refractive index associated with the gravitational field of a compact object with a quadrupole moment. Our research presents a method for calculating the gravitational deflection angle for compact objects by utilizing the refractive index and the GBT theorem for an isotropic metric. This method is particularly important because it allows for the calculation of the deflection angle for both light and relativistic particles. The material medium approach enables us to consider the compact object's gravitational field as a medium with a refractive index. By applying this approach, we establish a relationship between the refractive index and the quadrupole moment of the compact object. We then utilize this relationship to calculate the deflection angle of light and relativistic particles.
    Цитирования (OpenAlex) 6Цитирования (OpenCitations) 3
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    NUMERICAL STUDY OF ORBITAL STABILITY IN THE RELATIVISTIC RESTRICTED THREE-BODY PROBLEM
    (2026-03-29)
    Ayazhan Orazymbet
    ;
    Aliya Taukenova
    ;
    Daniya Utepova
    ;
    Nurzada Beissen
    ;
    N. Sandibayeva
    This paper presents a numerical study of the relativistic restricted three-body problem within the framework of General Relativity. Using the Lagrangian and Hamiltonian formalisms, the equations of motion with relativistic corrections up to the order of 1/c2 were derived and solved numerically in Wolfram Mathematica. The developed model allows one to analyze orbital stability under small relativistic perturbations. Numerical simulations were performed using the Runge–Kutta integration method for three systems: “Earth–Sun–Moon,” “Earth–Sun– Mercury,” and an equal-mass configuration. The results confirm the stability of circular orbits and reproduce the observed relativistic precession of Mercury’s perihelion. For the equal-mass system, the calculations reveal a transition from quasi-periodic to chaotic motion, depending on the initial conditions. The study demonstrates the reliability and efficiency of the Mathematica environment for modeling nonlinear relativistic dynamics and shows that the proposed approach can be useful for further research in celestial mechanics and gravitational physics.
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    Vertical epicyclic stability and dissipative settling in a weakly deformed q-metric spacetime
    (L. N. Gumilyov Eurasian National University, 2026-09-30)
    Ayazhan Orazymbet
    ;
    Aray Muratkhan
    ;
    Aliya Taukenova
    ;
    A. Dalelkhankyzy
    We investigate the motion of massive test particles close to the equatorial plane of a weakly deformed q-metric spacetime. Working to first order in the dimensionless quadrupole parameter q, we derive the orbital angular velocity and the vertical epicyclic frequency for equatorial circular orbits while keeping the physical monopole mass fixed. The Schwarzschild limit is recovered at q = 0, whereas a nonzero quadrupole removes the degeneracy between the vertical and azimuthal frequencies already at O(q). A small phenomenological damping term is then introduced into the linearized vertical equation to describe the gradual approach of a perturbed orbit toward the equatorial plane. In the conservative case, the particle continues to oscillate about this plane without any decrease in amplitude. With damping, the amplitude decays exponentially. The quadrupolar deformation changes the vertical oscillation frequency and, consequently, the number of cycles completed before a specified settling threshold is reached. It does not, however, set the decay timescale, which follows from the adopted damping prescription. Since the coordinate-time damping coefficient is kept fixed in our numerical examples, the trajectories share the same exponential envelope but oscillate at different frequencies. The comparison with the exact q-metric also provides a direct check of the firstorder approximation. Over the sampled domain |q| ≤ 0.1 and 6 ≤ r/M ≤ 20, the relative error in the vertical frequency remains below 0.34%, while the corresponding frequency ratio is reproduced to better than 0.10%. These results show explicitly how the quadrupolar geometry modifies vertical orbital dynamics within a model in which dissipative settling is introduced independently.