Жарияланымдар / Публикации

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Gravitational field of slightly deformed naked singularities
(Springer Science+Business Media, 2022-04-01)
Saken Toktarbay
;
Hernando Quevedo
;
Medeu Abishev
;
Aray Muratkhan
Abstract We derive a particular approximate solution of Einstein equations, describing the gravitational field of a mass distribution that slightly deviates from spherical symmetry. The deviation is described by means of a quadrupole parameter that is responsible for the appearance of a curvature singularity, which is not covered by a horizon. We investigate the motion of test particles in the gravitational field of this naked singularity and show that the quadrupole parameter affects the properties of Schwarzschild trajectories. By investigating radial geodesics, we find that no effects of repulsive gravity are present. We interpreted this result as indicating that repulsive gravity is non-linear effect.
Цитирования (OpenAlex) 12Цитирования (OpenCitations) 9
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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.
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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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Analytical constraints on generalized β -velocity laws in X-ray-illuminated HMXBs
(Oxford University Press, 2026-03-20)
Saken Toktarbay
;
Aray Muratkhan
;
N. Myrzakulov
;
Zhantay Muratkhan
ABSTRACT We derive analytic constraints on the parameters of the generalized $\beta$-velocity law used to describe radiation-driven winds from OB (O- and B-type) supergiants in wind-fed X-ray binaries. Starting from the radial equation of motion with Castor–Abbott–Klein (CAK) line driving, gas pressure, and X-ray irradiation, we perform an asymptotic analysis of the near-base region and show that a monotonic CAK-type acceleration requires the exponent of the velocity law to satisfy a robust lower bound $\beta _{\min }=1/2$. A separate condition follows from requiring the $\beta$-law to connect smoothly to the subsonic layers: the wind speed at the stellar surface must be at least comparable to the isothermal sound speed, which yields a conservative upper limit on the onset parameter, $b \lesssim 1-\left(a_{\rm s}/v_\infty \right)^{1/\beta }$,and implies $b_{\max } \approx 0.95$–0.99 for typical OB-star parameters. We include the effects of X-ray photoionization and attenuation in an approximate way by introducing an effective force-multiplier slope $\alpha _{\rm eff}$ and an optical-depth parameter controlling the weakening of X-ray inhibition. A scaling analysis shows that strong irradiation favours larger $\beta$ and can lead to the loss of monotonic acceleration, providing an effective system-dependent upper limit on the acceleration index. To assess the consistency of these bounds, we integrate a simplified momentum equation and fit the resulting accelerating solutions with a generalized $\beta$-law. The best-fitting pairs $(b,\beta)$ lie within the analytically allowed domain and occupy the range $\beta \approx 0.6$–1.2, in good agreement with empirical determinations for several persistent high-mass X-ray binaries. Our results provide physically motivated constraints on velocity-law parameters that can guide wind modelling and the interpretation of spectroscopic diagnostics in irradiated massive-star winds.
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Correlation analysis of the wind acceleration parameter in high-mass X-ray binaries
(Al-Farabi Kazakh National University, 2026-06-19)
Zhantay Muratkhan
;
Saken Toktarbay
;
Aray Muratkhan
;
Aliya Taukenova
;
Nadeem Azhar
This work presents a correlation analysis of the wind acceleration parameter β in high-mass X-ray binaries (HMXBs). The aim of the study is to determine how β depends on the geometric and dynamical characteristics of the system, primarily on the ratio of the orbital radius to the stellar radius, a⁄R_* and on the terminal wind velocity v_∞. For this purpose, published values of R_*, a and v_∞ together with measured wind velocities in the vicinity of the neutron star, were used. Based on these data, the parameters of the β-velocity law were determined numerically. The resulting β values were then approximated using a linear regression, β≈k a⁄R_* +c, yielding a simple empirical relation. The results show that the linear correlation between β and the orbital-to-stellar radius ratio is weak (with a Pearson correlation coefficient r ≈ 0.22) and is accompanied by substantial scatter, indicating the influence of additional physical factors. The linear regression yields a small positive slope (k ≈ 0.14), which suggests only a weak tendency for β to increase with the orbital ratio. Because of the small sample size, this trend should be regarded as tentative. The proposed linear model allows β to be estimated without detailed spectroscopic analysis and may be useful as a rough empirical indicator of wind-accretion properties in HMXBs. The originality of this study lies in providing a simple empirical first-order assessment of the β parameter in HMXBs based on observed orbital and wind properties in systems where detailed spectroscopic constraints are limited. Key words: high-mass X-ray binaries (HMXBs), β-law (β-velocity profile), wind velocity profile, terminal wind velocity, orbital ratio a⁄R_* , correlation analysis.

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