arXiv subjects

Ratbay Myrzakulov

Publications and source records attributed to Ratbay Myrzakulov.

At least 19 recordsLinked to original sources

arXiv2025

Wald Entropy in Extended Modified Myrzakulov Gravity Theories: $f(R, T, Q, R_{μν}T^{μν}, R_{μν}Q^{μν}, \dots)$

We investigate black hole entropy in a broad class of modified Myrzakulov gravity theories defined by generalized Lagrangians of the form $ \mathcal{L} = αR + F(T, Q, R_{μν}T^{μν}, R_{μν}Q^{μν}, \dots) $, where $ R $, $ T $, and $ Q $ represent curvature, torsion, and non-metricity scalars. Using the vielbein formalism, we derive the Wald entropy for various subclasses of these models, extending the classical entropy formula to accommodate non-Riemannian geometry. Our focus is on how the additional geometric degrees of freedom modify the entropy expression. The analysis shows that such corrections arise systematically from the extended structure of the action and preserve diffeomorphism invariance. These results refine the theoretical framework for gravitational thermodynamics in extended geometry settings.

gr-qc↗

arXiv2025

Cosmological Reconstructions in Einstein--Cartan--Myrzakulov Gravity with Torsion and Non-Metricity in the Weitzenböck Geometrical Sector

The universe is a vast and complex system, and our understanding of its fundamental workings is constantly evolving. In this work, we present a novel modification to the standard theory of gravity by incorporating curvature, torsion, non-metricity, and the geometric structure of Weitzenböck spacetime. This modified framework, referred to as the Einstein--Cartan--Myrzakulov (ECM) model, enriched by Weitzenböck geometry, offers new insights into cosmological phenomena, including the accelerated expansion of the universe, the nature of dark energy and dark matter, and the formation of cosmic structures. Our model not only reproduces observed cosmic histories but also provides testable predictions that can be compared with current and future observational data. By addressing some of the most profound questions in modern cosmology, this work paves the way for a deeper understanding of the universe's evolution and the fundamental forces that govern it. The ECM model, extended through Weitzenböck spacetime, invites further exploration, offering the potential to revolutionize our conception of gravity and the cosmos.

gr-qc↗

arXiv2025

Dark Matter Constraints in Myrzakulov $F(R,T)$ Gravity: A Vielbein Approach in Weitzenböck Spacetime with Observational Data

We explore dark matter phenomenology in Myrzakulov $F(R,T)$ gravity, formulated via the vielbein approach in Weitzenböck spacetime. In this torsion-based extension of gravity, dark matter emerges as a geometric effect rather than a particle species, with curvature and torsion contributing dynamically to the field equations. Using recent data -- including SPARC galaxy rotation curves, Planck CMB observations, and weak lensing from DES and KiDS -- we constrain the model through MCMC analysis. Our results show that, under specific parameter choices, the theory replicates key cosmological features without introducing additional dark sector matter. This framework offers a testable alternative to $Λ$CDM, providing new insight into structure formation, gravitational lensing, and cosmic acceleration -- all rooted in the geometry of spacetime.

gr-qc↗

arXiv2025

Inflation in Myrzakulov $F(R,T)$ Gravity: A Comparative Study in Metric, Symmetric Teleparallel, and Weitzenböck Formalisms

We present a unified treatment of cosmic inflation within the framework of Myrzakulov Gravity, exploring its realization in three different formalisms: metric (curvature-based), teleparallel (torsion-based), and symmetric teleparallel (non-metricity-based). For each case, we derive the corresponding field equations in a flat FLRW background, study inflationary solutions driven by a scalar field, and compute observable quantities such as the scalar spectral index $ n_s $ and the tensor-to-scalar ratio $ r $. In addition to these geometric sectors, we extend our analysis to the more general and dynamically richer Myrzakulov $ F(R,T) $ gravity, which incorporates both curvature $ R $ and torsion $ T $ in a unified action. We derive the inflationary dynamics in this hybrid model and investigate how it interpolates between pure $ f(R) $ and $ f(T) $ behaviors. The resulting framework allows for enhanced flexibility in matching Planck and BICEP/Keck observational constraints. We present analytic estimates and schematic predictions in the $ n_s $--$ r $ plane, demonstrating that appropriately chosen parameters in $ F(R,T) $ models can produce viable and distinguishable inflationary signatures. This comparative and extended study highlights the potential of Myrzakulov Gravity and its generalizations to provide a consistent and geometrically motivated description of the early universe, with predictive power across different formulations of spacetime geometry.

gr-qc↗

arXiv2025

Einstein-Gauss-Bonnet-Myrzakulov Gravity from $R + F(T, G)$: Numerical Insights and Torsion-Gauss-Bonnet Dynamics in Weitzenböck Spacetime

The study of modified gravity models has garnered significant attention because of their potential to provide alternative explanations for cosmological phenomena, such as the accelerated expansion of the universe and the nature of dark energy. One such model, the Einstein-Gauss-Bonnet-Myrzakulov $R + F(T, G)$ gravity (EGBMG), which incorporates the curvature $R$, torsion $T$, and the Gauss-Bonnet term $G$, offers a promising framework to explore the dynamics of the universe and its evolution. This paper delves into the theoretical and observational implications of the EGBMG model, focusing on its ability to address long-standing challenges in cosmology, including the evolution of dark energy and the transition from early-time inflationary behavior to late-time acceleration. We review recent advancements in the model, including its compatibility with observational data and its ability to provide new insights into cosmic acceleration. Through a combination of theoretical models, dynamical systems analysis, and cosmological diagnostics, we demonstrate the robustness of the EGBMG framework in explaining the large-scale structure of the universe and its accelerated expansion. This paper serves as a step toward further exploring the potential of this model to understand the fundamental forces driving Weitzenb$ö$ck spacetime.

gr-qc↗

arXiv2025

Metric-Affine Myrzakulov Gravity Theories: Models, Applications and Theoretical Developments

This review presents a comprehensive overview of Myrzakulov gravity, highlighting key developments and significant results shaping the theory. It examines the foundational principles, field equations, and the role of non-metricity and torsion in gravitational interactions. The theory's implications extend to cosmology, astrophysics, and strong gravitational fields, offering alternatives to dark matter and dark energy. A focus is placed on the modified Einstein-Hilbert action, its impact on cosmic expansion, and astrophysical applications such as black holes and gravitational waves. Observational constraints from cosmology and gravitational wave tests are discussed to refine the model. By situating Myrzakulov gravity within the broader context of modified gravity, this review explores its potential to reshape fundamental physics.

gr-qc↗

arXiv2024

Myrzakulov Gravity in Vielbein Formalism: A Study in Weitzenböck Spacetime

The quest to understand gravity's role in shaping the universe has led to the exploration of modified gravity theories. One such theory is Myrzakulov gravity, which incorporates both curvature and torsion. In this work, we investigate the effects of torsion within the framework of $f(R,T)$-gravity, a modification of General Relativity that includes both curvature and torsion. We present this theory in the Vielbein formalism, which offers a more flexible, geometric perspective on gravity. This formalism is particularly useful in Weitzenb"ock spacetime, where torsion significantly influences gravitational interactions. Our study aims to extend Myrzakulov's theory and explore its cosmological and astrophysical implications. We examine the effects of torsion on phenomena like black holes, gravitational waves, and neutron stars. These modifications could lead to observable deviations in black hole thermodynamics, gravitational wave propagation, and dense matter structure. This work provides new insights into the nature of spacetime and gravity, offering a fresh perspective on the fundamental forces governing the cosmos. It paves the way for future studies, both observational and theoretical, that could reveal new physics beyond General Relativity.

gr-qc↗

arXiv2024

Corrected Thermodynamics and Stability of Magnetic charged AdS Black Holes surrounded by Quintessence

In this study, we explore the corrected thermodynamics of non-linear magnetic charged anti-de Sitter (AdS) black holes surrounded by quintessence, incorporating thermal fluctuations and deriving the corrected thermodynamic potentials. We analyze the effects of corrections due to thermal fluctuations on various thermodynamic potentials, including enthalpy, Helmholtz free energy, and Gibbs free energy. Our results show significant impacts on smaller black holes, with first-order corrections destabilizing them, while second-order corrections enhance stability with increasing parameter values. The specific heat analysis further elucidates the stability criteria, indicating that the large black holes ensure stability against phase transitions. However, the thermal fluctuations do not affect the physical limitation points as well as the second-order phase transition points of the black hole. Our findings highlight the intricate role of thermal fluctuations in black hole thermodynamics and their influence on stability, providing deeper insights into the behaviour of black holes under corrected thermodynamic conditions.

gr-qc↗

arXiv2024

Four $\mathbb{S}\mathbb{T}\mathbb{U}$ Black Holes Shadows

In this work, we examine the optical behaviors and thermodynamic phase structures using shadow analysis for four $\mathbb{S}\mathbb{T}\mathbb{U}$ black holes. The study is conducted for four cases of charge configurations on the parameter space $\mathcal{M}\left(q_1,q_2,q_3,q_4\right)$. As a matter of fact, both the electric charge as a parameter and the parameter space $\mathcal{M}\left(q_1,q_2,q_3,q_4\right)$ affect the geometry of the black hole shadow, particularly the size of the shadow. We also introduce a constraint on the charge of the black hole from the observational results of the M87$^\star$ {\color{black}and Sgr A$^\star$} shadow. Furthermore, we show that the electric charge and the parameter space $\mathcal{M}\left(q_1,q_2,q_3,q_4\right)$ have a non-trivial impact on the variation of the energy emission rate. Interestingly enough, we find novel scenarios in which the evaporation is slower, which causes the lifetime of the black holes to be considerably elongated. On the other side, the phase structure of four $\mathbb{S}\mathbb{T}\mathbb{U}$ black holes is explored for two cases of electric charge configuration. The findings show a perfect correlation between the shadow and event horizon radii. This correlation is, in fact, helpful in discovering the phase transition in terms of the shadow radius. In addition, the microstructure is being analyzed in terms of shadow analysis, providing similar behavior to the ordinary situation of the Ruppeiner formalism.

gr-qc↗

arXiv2024

Metric-affine Myrzakulov gravity and its generalizations

Since the discovery of cosmic acceleration, modified gravity theories play an important role in the modern cosmology. In particular, the well-known F(R) - theories reached great popularity motivated by the easier formalism and by the prospect to find a final theories of gravity for the dark scenarios. In the present work, we study some generalizations of F(R), F(T) and F(Q) gravity theories, where $R, T, Q$ are the Ricci, torsion and nonmetricity scalars. At the beginning, we briefly review the formalism of such theories. Then, we will consider one of their generalizations, the so-called Myrzakulov F(R,T) gravity theory or the MG-I theory. The point-like Lagrangian is explicitly presented. Based on this Lagrangian, the field equations of MG-I are found. For the specific model $F(R,T)=μR+νT,$ the corresponding exact solutions are derived. Furthermore, we will consider the physical quantities associated to such solutions and we will find how for some values of the parameters the expansion of our universe can be accelerated without introducing any dark component. Finally, some metric-affine Myrzakulov gravity theories with and without boundary term scalars are presented.

physics.gen-ph↗

arXiv2024

Stability analysis of a dark energy model in Rastall gravity

We study a cosmological model in Rastall's theory of gravity in the framework of the flat FLRW metric. We formulate the value of the Hubble parameter, which contains two model parameters, $ α$ and $ j $. Employing the Markov Chain Monte Carlo (MCMC) sampling technique, we determine the values of these model parameters along with their uncertainties. Moreover, we derive the equation of state (EoS) parameter, which converges around the quintessence region. We perform a dynamical system analysis using the linearization technique to validate the results independently. Also, we discuss various physical attributes of the model, highlighting the transition to acceleration and the violation of the strong energy condition (SEC) in the late stages of evolution. In conclusion, our model mimics the behavior of a dark matter fluid during the past epoch and transitions into a quintessence dark energy model in the future epoch.

gr-qc↗

arXiv2024

Phase structures and critical behaviour of rational non-linear electrodynamics AdS black holes in Rastall gravity

This research paper presents a black hole solution with a rational non-linear electrodynamics source in the Rastall gravity framework. The paper analyzes the thermodynamic properties of the solution in normal phase space and explores its critical behavior. The phase structure is examined using the extended first law of thermodynamics, with the cosmological constant $Λ$ serving as pressure $P$. The isotherms exhibit van der Waals behavior at small values of horizon $r_+$. The paper also investigates the Gibbs free energy behavior and finds two critical points with two pressures where the reentrant phase transition occurs and disappears. On the other hand, we explore the prevalent microstructure of black holes in Ruppeiner geometry, uncovering significant deviations in the nature of particle interactions from conventional practice. Moreover, the thermodynamic geometry is analyzed using the Ruppeiner formalism, with the normalized Ricci scalar indicating possible point-phase transitions of the heat capacity, and the normalized extrinsic curvature having the same sign as the normalized Ricci scalar. The three-phase transitions of the heat capacity are those that we find for the normalized Ruppeiner curvatures. Thus, there is an absolute correspondence.

gr-qc↗

arXiv2024

Transit cosmological models in Myrzakulov F(R,T) gravity theory

In the present paper, we investigate some exact cosmological models in Myrzakulov $F(R,T)$ gravity theory. We have considered the arbitrary function $F(R, T)=R+λT$ where $λ$ is an arbitrary constant, $R, T$ are respectively, the Ricci-scalar curvature and the torsion. We have solved the field equations in a flat FLRW spacetime manifold for Hubble parameter and using the MCMC analysis, we have estimated the best fit values of model parameters with $1-σ, 2-σ, 3-σ$ regions, for two observational datasets like $H(z)$ and Pantheon SNe Ia datasets. Using these best fit values of model parameters, we have done the result analysis and discussion of the model. We have found a transit phase decelerating-accelerating universe model with transition redshifts $z_{t}=0.4438_{-0.790}^{+0.1008}, 0.3651_{-0.0904}^{+0.1644}$. The effective dark energy equation of state varies as $-1\leω_{de}\le-0.5176$ and the present age of the universe is found as $t_{0}=13.8486_{-0.0640}^{+0.1005}, 12.0135_{-0.2743}^{+0.6206}$ Gyrs, respectively for two datasets.

gr-qc↗

arXiv2024

Dark matter effects of a black hole with nonsingular Yukawa-modified potential in Einstein-Gauss-Bonnet Gravity

This paper investigates the contribution of the nonsingular Yukawa-modified potential in the context of four-dimensional Einstein-Gauss-Bonnet (EGB) gravity modeling by a static and spherically symmetric black hole solution. These Yukawa-type corrections are essentially described along two parameters, $β$ and $λ$, affecting Newton's law of gravity at large distances, and a deformation parameter $\ell_0$, which is essential at short distances. Primarily, the strongest effect is encoded in $β$, which alters the total mass of the black hole with additional mass proportional to $β\mathcal{M}$, imitating the effects of dark matter at large distances from the black hole. In contrast, the effect due to $λ$ is small for astrophysical values. On the other hand, the EGB gravity is ruled by the Gauss-Bonnet (GB) coupling constant $α$, a fundamental parameter of the theory. We pay particular attention to thermodynamic stability, critical orbits, geodesics and quasinormal modes. The results demonstrate stability of the black hole solution for a range of values of the GB coupling constant $α$. Furthermore, this study investigates the null geodesic motion, namely the shadow behavior, providing intriguing results in relation to the size of the black hole shadow.

gr-qc↗

arXiv2024

Exact Cosmology in Myrzakulov Gravity

In this paper, we have investigated some exact cosmological models in Myrzakulov gravity using a flat Friedmann-Lematre-Robertson-Walker (FLRW) spacetime metric. We have considered the modified Lagrangian function as $F(R,T)=R+λT$, where $R, T$ are respectively the Ricci curvature scalar and the torsion scalar with respect to non-special connection, and $λ$ is a model parameter. We have obtained two exact solutions in two different situations for the scale factor $a(t)$. Using this scale factor, we have obtained various geometrical parameters to investigate cosmological properties of the universe. We have obtained the best fit values of model parameters through the MCMC analysis of two types latest observational datasets like $H(z)$ and Pantheon SNe Ia samples, with $1-σ, 2-σ$ \& $3-σ$ regions. We have performed a comparative and relativistic study of geometrical and cosmological parameters. In model-I, we have found that the effective equation of state (EoS) parameter $ω_{eff}$ varies in the range $-1\leω_{eff}\le0$ while in the model-II, it varies as $-1.031\leω_{eff}\le0$. We have found that both models are transit phase (decelerating to accelerating) universe with transition redshift in the range $0.6<z_{t}<0.8$ and present age of the universe $t_{0}\approx13.5$ Gyrs.

gr-qc↗

arXiv2022

Cosmology of Metric-Affine $R + βR^2$ Gravity with Pure Shear Hypermomentum

In this paper we study the cosmological aspects of metric-affine $f(R)$ gravity with hyperfluid. The equations of motion of the theory are obtained by varying the action with respect to the metric and the independent connection. Subsequently, considering a Friedmann-Lemaître-Robertson-Walker background, we derive the modified Friedmann equations in the presence of a perfect cosmological hyperfluid. Especially, we focus on the particular case in which $f(R)=R+βR^2$, considering purely shear hypermomentum and finding exact solutions in the weak coupling limit.

gr-qc↗

arXiv2022

A constrained cosmological model in $f(R,L_m)$ gravity

In this article, we study the expanding nature of universe in the contest of $f(R,L_m)$ gravity theory, here $ R $ represents the Ricci scalar and $ L_m $ is the matter Lagrangian density. With a specific form of $ f(R,L_m) $, we obtain the field equations for flat FLRW metric. We parametrize the deceleration parameter in terms of the Hubble parameter and from here we find four free parameters, which are constraints and estimated by using $H(z)$, $Pantheon$, and their joint data sets. Further, we investigate the evolution of the deceleration parameter which depicts a transition from the deceleration to acceleration phases of the universe. The evolution behaviour of energy density, pressure, and EoS parameters shows that the present model is an accelerated quintessence dark energy model. To compare our model with the $ Λ$CDM model we use some of the diagnostic techniques. Thus, we find that our model in $ f(R,L_m) $ gravity supports the recent standard observational studies and delineates the late-time cosmic acceleration.

gr-qc↗

arXiv2022

Integrable generalized Heisenberg ferromagnet equations with self-consistent potentials and related Yajima-Oikawa type equations

We consider some nonlinear models describing interactions of long and short (LS) waves. Such LS models have been derived and proposed with various motivations, which mainly come from fluid and plasma physics. In this paper, we study some of integrable LS models, namely, the Yajima-Oikawa equation, the Newell equation, the Ma equation, the Geng-Li equation and etc. In particular, the gauge equivalent counterparts of these integrable LS models (equations) are found. In fact, these gauge equivalents of the LS equations are integrable generalized Heisenberg ferromagnet equations (HFE) with self-consistent potentials (HFESCP). The associated Lax representations of these HFESCP are given. We also presented several spin-phonon equations which describe nonlinear interactions of spin and lattice subsystems in ferromagnetic materials.

nlin.SI↗