We study the motion of test particles in the gravitational field of a rotating and deformed object within the framework of the adiabatic theory. For this purpose, the Hartle-Thorne metric written in harmonic coordinates is employed in the post-Newtonian approximation where the adiabatic theory is valid. As a result, we obtain the perihelion shift formula for test particles orbiting on the equatorial plane of a rotating and deformed object. Based on the perihelion shift expression, we show that the principle of superposition is valid for the individual effects of the gravitational source mass, angular momentum and quadrupole moment. The resulting formula was applied to the inner planets of the Solar system. The outcomes are in a good agreement with observational data. It was also shown that the corrections related to the Sun's angular moment and quadrupole moment have little impact on the perihelion shift. On the whole, it was demonstrated that the adiabatic theory, along with its simplicity, leads to correct results, which in the limiting cases correspond to the ones reported in the literature.

We compute the weak bending angle of light within generalised Born–Infeld electrodynamics as it passes through the equatorial plane of a magnetic dipole. We start by considering the refractive index associated with the dipole within generalised Born–Infeld electrodynamics. Then, we calculate the Gaussian optical curvature based on these refractive indices. Using the Gauss–Bonnet theorem, we derive a formula to quantify the deflection angle in the presence of a strong magnetic field from a dipole. Our results align with results obtained through traditional geometric optics techniques, underscoring the importance of the Gauss–Bonnet theorem as a versatile tool for solving intricate problems in modern theoretical research. We apply our theoretical deflection angle formula to estimate the light bending in magnetars listed in the McGill catalogue, providing insights into the behaviour of light in environments with strong magnetic fields.

The distribution of dark matter in the low surface brightness spiral galaxies U5750, U11454, U11819, and U11648 is analyzed by utilizing well-established density profiles from existing literature. These profiles include the Beta, Brownstein, Burkert, exponential sphere, pseudo-isothermal, and Persic profiles. For simplicity, we assume spherically symmetric distribution of dark matter in the considered galaxies, without accounting for their intricate structural complexities. For each density profile, we fit the rotation curve data to the aforementioned galaxies. Employing Markov Chain Monte Carlo statistical analyses, we infer model-free parameters from the rotation curves, namely the characteristic (central) density and scale radius. This enables us to estimate the total dark matter mass within the galactic halos. To identify the best-fit profile, we employ the Bayesian Information Criterion. Additionally, we adopt the Levenberg-Marquardt nonlinear least squares approach for the purpose of comparison and completeness. Through our statistical analysis, we offer a physical interpretation behind the selection of specific profiles. This interpretation is based on the insights obtained from the analyses.

We investigate the motion of stars at the central region of the Milky Way Galaxy. We consider two possible scenarios: 1) there is a supermassive black hole without dark matter distribution and 2) there is a dark matter core without any black hole in the galactic center. We remark that, with current observations, one cannot distinguish the two separate cases from each other at distances larger than 100 astronomical units. Here, we present improved analyses regarding the motion of stars and show that differences between these two cases appear at distances smaller than 30 astronomical units. We adopt here the so-called exponential density profile for dark matter distribution which is usually used to explain the rotation curve data points in the bulge of galaxies. We underline our outcomes are model-dependent, i.e. they depend on the choice of the particular dark matter model employed for the analysis.

High-mass X-ray binaries (HMXBs) are commonly divided into persistent sources, which emit X-rays steadily over long periods, and transient sources, which remain mostly in a quiescent state and exhibit episodic X-ray outbursts. The aim of this work is to statistically compare the X-ray luminosity properties of these two classes, focusing on the maximum luminosity and the luminosity variability range . For this purpose, catalog data for Galactic HMXB pulsars were used, including 18 persistent and 64 transient systems. The distributions of and were analyzed using histograms, box plots, cumulative distribution functions (CDFs), and the non-parametric Mann–Whitney test. It is shown that both classes reach similar values of on the order of – erg/s), with no statistically significant difference between their distributions. However, transient systems exhibit a much wider luminosity variability range, reaching increases of 4–5 orders of magnitude (up to ), whereas persistent sources typically show lower variability. This difference is statistically confirmed, with transients demonstrating significantly higher variability p ≈ 0.05). Thus, the main distinction between persistent and transient HMXBs lies not in their peak X-ray luminosity, but in their accretion regime. In persistent systems, the compact object continuously accretes matter from a relatively stable stellar wind of an OB supergiant, resulting in steady X-ray emission. In contrast, transient systems are characterized by intermittent accretion (for example, episodic mass capture from a Be-star circumstellar disc), which leads to their extreme luminosity variability.

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.