Saken Toktarbay

Mass inflation is conventionally understood as an instability of black-hole interiors driven by the exponential amplification of counter-streaming perturbations near a non-degenerate inner horizon. In this work, we investigate how this picture is modified when the inner-horizon surface gravity vanishes. Focusing on static, spherically symmetric black-hole geometries with degenerate inner horizons, we formulate the interior problem in a double-null framework and analyze the near-horizon asymptotics for weak ingoing and outgoing null perturbations in the case κ in = 0 . We show that inner-horizon degeneracy replaces the standard exponential horizon scaling by an algebraic one and, correspondingly, removes the conventional exponential amplification factor from the transport equations of the Misner–Sharp mass. Within the weak asymptotic regime considered here, the effective mass exhibits at most algebraic or logarithmic growth, depending on the decay rates of the perturbing tails, rather than the usual exponentially amplified behavior of the non-degenerate Cauchy-horizon case. We further examine the associated invariant curvature sector and show that, although the unperturbed degenerate inner horizon is curvature-regular, the perturbed interior may still admit a weaker residual singular response. Our results therefore indicate that vanishing inner-horizon surface gravity suppresses the conventional exponential mass-inflation mechanism without, by itself, implying full regularization of the spacetime interior.

This study explores the cosmological implications of holographic dark energy model within the framework of [Formula: see text] gravity ([Formula: see text] represents the non-metricity scalar). We formulate the field equations for spatially flat, homogeneous and isotropic spacetime with perfect fluid matter distribution. To reconstruct the [Formula: see text] models, we consider the Chevalier–Polarski–Linder, Jassal–Bagla–Padmanabhan and Wetterich parameterizations for the holographic dark energy density profile in conjunction with power-law and exponential models of scale factors. The evolutionary cosmology is examined graphically through the equation of state parameter and stability analysis via squared speed of sound. Furthermore, we investigate the null and strong energy conditions to understand the nature of gravity and cosmic acceleration. Our graphical analysis reveals that the reconstructed models undergo a transition from quintessence to phantom era, exhibit cosmological viability as well as stability at present and near-future times for suitable choices of model parameters.

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.

Mass inflation is a phenomenon occurring in the vicinity of the inner horizon in a spacetime with two horizons. It is shown that the mass of initially small perturbations grows exponentially as they approach the inner horizon. This implies that the inner horizon of a black hole is unstable under perturbations. Since mass inflation is determined by the surface gravities of the inner horizons, Carballo-Rubio et al. showed that if one makes the surface gravities of the inner horizons vanish, then the exponential growth associated with mass inflation is not present. Based on this conclusion, we look for the black hole solutions of multiple horizons in the presence of a nonlinear Maxwell field. We then make the inner horizons coincide with each other such that the surface gravities of all inner horizons vanish. In this way, black holes with multiple horizons without mass inflation are constructed.

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.