arXiv subjects

Aliya Taukenova

Publications and source records attributed to Aliya Taukenova.

6 recordsLinked to original sources

arXiv2026

Thin accretion-disc transfer functions in the q-metric spacetime: quadrupolar lensing signatures

We study geometrically thin equatorial disc images in the static, axisymmetric q-metric spacetime using backward ray tracing. The Schwarzschild solution is recovered at $q=0$; for the nonzero deformations considered here, $r=2M$ is a curvature singularity rather than an event horizon. For a distant nearly face-on observer, we construct the first three equatorial transfer functions $r_m(b;q)$. In the {Schwarzschild} limit, the resolved third-crossing interval contains the critical impact parameter $b=3\sqrt{3}M$. As $q$ increases from $-0.3$ to $0.3$, the branch center shifts from $b_{3,c}/M\simeq3.716$ to $6.702$. In units of the physical monopole mass $\mathcal M=(1+q)M$, it instead decreases from $b_{3,c}/\mathcal M\simeq5.309$ to $5.156$. Much of the displacement in metric-parameter units therefore reflects the changing monopole scale. At fixed $\mathcal M$, the inclined first-intersection maps show that the contour dimensions increase with $q$, with larger relative changes near the inner disc. A prescribed power-law emissivity and relativistic frequency-shift weighting yield direct images whose integrated flux differs from the Schwarzschild value by at most $2.4\%$. Between the endpoint models, the horizontal median-flux position increases by $8.8\%$ and the interquartile width by $14.5\%$. Within this emission prescription, the residual deformation dependence appears mainly as a displacement and broadening of the brightness distribution. Higher-order radiative contributions are not included.

gr-qc↗

arXiv2026

Rotation-Induced Effective Anisotropy in White Dwarfs as a Newtonian Benchmark with Relativistic Scale Assessment

We develop a one-dimensional Newtonian reduction for uniformly rotating cold white dwarfs in which the angle-averaged centrifugal support is represented by an effective anisotropic term. From the stationary Euler equation, using $\langle\sin^2θ\rangle=2/3$, the rotational contribution becomes $ Δ_{\rm rot}(r)=\frac{1}{3}ρ(r)Ω^2 r^2 . $ The mapping keeps the spin frequency explicit while preserving a one-dimensional hydrostatic system. With the Chandrasekhar degenerate-electron equation of state, we compute sequences over $ρ_c\in[10^6,10^{11}]~{\rm g\,cm^{-3}}$ for rotation proxies $f=Ω/Ω_{K,0}(ρ_c)\leq0.35$. The high-density readout shows monotonic increases of mass and radius with $f$, with a percent-level mass shift for the largest retained proxy. Applicability is checked on the rotating configurations through sub-Keplerian diagnostics and the bulk-interior measure $\mathcal{A}_{10^{-2}}$. We further compare the reduced rotational correction with an auxiliary quasi-two-dimensional reconstruction and a static isotropic Tolman--Oppenheimer--Volkoff reference sequence. These scale checks show that the reduced model remains useful for controlled trend-level surveys in the slow-rotation regime, while rotational and static relativistic corrections can both become percent-level effects at high central density. The construction provides a transparent Newtonian benchmark for future axisymmetric and relativistic rotating white-dwarf calculations.

gr-qc↗

arXiv2024

Gravitational capture cross-section in Zipoy-Voorhees spacetimes

We consider geodesics of massive and massless test particles in the gravitational field of a static and axisymmetric compact object described by the quadrupolar metric ($q$-metric), which is the simplest generalization of the Schwarzschild metric, containing an independent quadrupole parameter $q$. We analyze the effective potential profile and calculate the orbital parameters and capture cross-sections of test particles in this spacetime. Moreover, we derive the explicit expression for the escape angle of photons as a function of the quadrupole parameter. All the results reduce in the corresponding limit of vanishing quadrupole to the well-known case of the Schwarzschild spacetime. We argue that our results could be used to investigate realistic compact objects such as white dwarfs and neutron stars.

gr-qc↗

arXiv2023

Luminosity of accretion disks around rotating regular black holes

We consider thin accretion disks in the field of a class of rotating regular black holes. For this purpose, we obtain the radius of the innermost stable circular orbit, $r_{ISCO}$ and efficiency of accretion disk in converting matter into radiation $η$ with the aim of modeling the disk's emission spectrum. We consider a simple model for the disk's radiative flux, differential and spectral luminosity and compare the results with those expected from accretion disks around Kerr black holes. As a remarkable result, from our computations we find that both the luminosity of the accretion disk and the efficiency are larger in the geometry of rotating regular black holes for fixed and small values of the spin parameter $j$ with respect to those predicted with the Kerr metric for a black hole of the same mass. These results may have interesting implications for astrophysical black holes.

gr-qc↗

arXiv2023

Adiabatic theory in Kerr spacetimes

We present the main aspects of the adiabatic theory and show that it can be used to study the motion of test particles in general relativity. The theory is based upon the use of vector elements of the orbits and adiabatic invariants. To prove the applicability of the adiabatic theory in Einstein's gravity, we derive a particular representation of the Kerr metric in harmonic coordinates, which allows us to obtain a general formula for the perihelion shift of test particles orbiting on the non-equatorial plane of a rotating central object. We show that the principle of superposition is fulfilled for the individual effects of the gravitational source mass and angular momentum up to the second order. We demonstrate 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.

gr-qc↗

arXiv2022

Adiabatic theory of motion of bodies in the Hartle-Thorne spacetime

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.

gr-qc↗