International Journal of Geometric Methods in Modern Physics

The principal aim of this paper is to find the expression of *-Bach tensors on ${(\kappa ,\mu )}^{\prime }$-almost-Kenmotsu manifolds. It is shown that if the metric of a ${(\kappa ,\mu )}^{\prime }$-almost-Kenmotsu manifold admits a generalized closed *-Bach soliton, then the metric is *-Bach flat under certain restrictions. We also prove that the metric of a generalized gradient *-Bach soliton on a ${(\kappa ,\mu )}^{\prime }$-almost-Kenmotsu manifold is *-Bach flat, for a soliton function which is invariant under the Reeb vector field. Further, we characterize generalized *-Bach solitons with trace-free *-Bach tensors on ${(\kappa ,\mu )}^{\prime }$-almost-Kenmotsu manifolds and results are verified by an example. As an application of these solitons, we study generalized almost-Bach solitons whose metrics are associated with the Lorentzian metric of the perfect fluid spacetimes.

The set of maximally fermion–boson entangled Bell super-coherent states is introduced. A superposition of these states with separable bosonic coherent states, represented by points on the super-Bloch sphere, we call the Bell-based super-coherent states. Entanglement of bosonic and fermionic degrees of freedom in these states is studied by using displacement bosonic operator. It acts on the super-qubit reference state, representing superposition of the zero and the one super-number states, forming computational basis super-states. We show that the states are completely characterized by displaced Fock states, as a superposition with non-classical, the photon added coherent states, and the entanglement is independent of coherent state parameter $\alpha$ and of the time evolution. In contrast to never orthogonal Glauber coherent states, our entangled super-coherent states can be orthogonal. The uncertainty relation in the states is monotonically growing function of the concurrence and for entangled states we get non-classical quadrature squeezing and representation of uncertainty by ratio of two Fibonacci numbers. The sequence of concurrences, and corresponding uncertainties $\hslash F_n/F_{n+1}$, in the limit $n\to \infty$, convergent to the Golden ratio uncertainty $\hslash /\phi$, where $\phi =\frac{1+\sqrt{5}}{2}$ is found.

Buckyballs are closed spherical carbon cages which are beneficial in several industries. Their chemical graphs provide structural invariants called topological invariants. This study is devoted to investigating the relation between degree-based topological index called Sombor index and physical properties of buckyballs. The sample contains buckyballs consisting of 54, 58, 60, 70, 74, 76, 78, 80, 82, 84, 86 and 90 carbon atoms.

The topological indices with degree bases can be used to display the physical characteristics of buckyballs. The numerical values of topological indices describe the topological structure of a molecule. The physical properties include binding energy, Ramsauer–Townsend effect (RT-1, RT-2), shape resonances (SR-1, SR-2), and heat of formation of buckyballs.

The generalization of the virial theorem, introduced by Clausius in statistical mechanics, has recently been carried out in the framework of geometric approaches to Hamiltonian and Lagrangian theories and it has been formulated in an intrinsic way. It is here revisited not only in its more general situation of a generic vector field but mainly from the perspective of contact and cosymplectic geometry. The previous generalizations allowing virial like relations from one-parameter groups of non-strictly canonical transformations and the rôle of Killing and conformal Killing vector fields for Lagrangians of a mechanical type are here completed with the theory for contact Hamiltonian, as well as gradient and evolution, vector fields. The corresponding theories in the framework of cosymplectic geometry and the particular case of time-dependent vector fields are also developed.

In recent decades, there has been significant research on the role of torsion in gravity, with a focus on aligning gravity with its gauge formulation and including spin into a geometric description. In order to account for the present phenomenon of the universe’s accelerated expansion, recent developments have introduced $f(T)$ theories that rely on the disparities found in teleparallel gravity. Torsion, rather than curvature, is the fundamental geometric property that describes gravity in these theories. When compared to theories involving $f(R)$ functions, the field equations are consistently of second order and surprisingly simple. We consider a specific type of function called torsion, which is defined as $f(T)=T-\alpha T_0[{\{1+{(\frac{T}{T_0})}^2\}}^{-n}-1]$. The expression consists of two free parameters, $n$ and $\alpha$, and the current value of the torsion scalar, $T_0$. In order to solve the modified torsion field equations (MTFEs), we can utilize the parametrization of the deceleration parameter (DP) in terms of redshift, denoted as $q(z)=q_0+q_1(z)$. Here, $q_0$ and $q_1$ represent the model parameters. The model parameters are determined by utilizing observable constraints, including as 57 Hubble data points, 1048 Pantheon supernovae type Ia data, and Baryon Acoustic Oscillations (BAO) datasets. In addition, we utilize Markov Chain Monte Carlo (MCMC) methods for statistical analysis.

We introduce the concept of shape operator and rotating blade (also known in the theory of embedded Riemannian manifolds as the second fundamental form and the Gauss map) in the realm of Yang–Mills theories. Hence we arrive at new gauge-invariant variables, which can serve as an alternative to the usual gauge potentials.

In this paper, we present a novel curvature tensor called the ${𝒦}$-curvature tensor, which is formed by combining the Weyl tensor and the ${{𝒲}}_2$-curvature tensor. It is proved that a semi-Riemannian manifold with traceless ${𝒦}$-curvature tensor is Einstein, while a ${𝒦}$-curvature flat semi-Riemannian manifold exhibits constant sectional curvature. We show that a space-time with traceless ${𝒦}$-curvature tensor or ${𝒦}$-curvature flat represents dark energy era. A semi-Riemannian manifold with divergence-free ${𝒦}$-curvature tensor is Weyl harmonic. In a space-time where the ${𝒦}$-curvature tensor is of divergence-free, both the isotropic pressure and energy density are constants. Under certain conditions, it is shown that a pseudo-${𝒦}$-symmetric semi-Riemannian manifold reduces to a pseudo-Riemannian manifold. It is demonstrated that pseudo-${𝒦}$-symmetric space-times can be regarded as generalized Robertson–Walker (GRW) space-times. Finally, a concrete example of pseudo-${𝒦}$-symmetric semi-Riemannian manifolds is presented.

In this paper, we introduce the dual magnetic trajectories traced by the dual Frenet vectors of any dual curves in dual space via the dual Lorentz force, and then we give the characterizations of dual magnetic curves. Moreover, we define the dual flux ruled surfaces corresponding to the Killing vectors on the dual unit sphere and identify the conditions for these surfaces to be minimal or developable. Additionally, we present certain characterizations related to these surfaces. We demonstrate the visual representations of some dual flux ruled surfaces in some examples.

We study the thermodynamic geometry of two types of asymptotically anti-de Sitter black holes in four-dimensional Einsteinian cubic gravity, including the uncharged rotating and charged non-rotating black holes, applying the Ruppeiner thermodynamic geometry method. The divergence of the scalar curvature of the Ruppeiner metric ($R^R$) is found to be related to the vanishing of the heat capacity. The stability of the solutions is shown to be affected by the Einsteinian cubic gravity coupling constant $\lambda$. In the unstable phase of the rotating black hole, the $R^R$ appeared to possess additional diverging points, where the number of these points and the behavior of $R^R$ are controlled by the angular momentum parameter. Also, for the charged non-rotating black hole case, we show that depending on the values of $\lambda$, the solution may enjoy two types of phase transition and $R^R$ behaviors. The characteristic behavior of $R^R$ of these two types of black holes enabled us to recognize the types of interactions between microscopic degrees of freedom.

By taking into account the Einstein–Gauss–Bonnet dilaton-coupled interaction in the background of the Robertson–Walker metric, we provide some bouncing solutions of the early universe from analytic solutions of the field equations for vanishing three space curvature. For a few potentials, the solutions involving the slow-roll-type approximation produce results that are very same to those of the early era’s bouncing solutions. Considering a different approach of slow-roll approximation, the universe goes through much faster initially than standard inflation, but at a later stage, the universe enters into standard exponential inflation.

The objective of this paper is to explore the unexplored algebraic representations of the constraint manifolds associated with $4C$ and $6C$ spatial closed chains in Lorentzian space. Initially, we establish the structure equations of spatial closed chains by utilizing the structure equations for spatial open chains in Lorentzian space. Subsequently, we employ these structure equations to derive the algebraic expressions defining the constraint manifolds of $4C$ and $6C$ spatial closed chains in Lorentzian space, considering factors such as the causal character of the first link and the rotational axis of the cylindrical joint. This study will finalize all algebraic representations of constraint manifolds for spacelike and timelike mechanisms in Lorentzian space.

We present the proof for the source of exchange flying ring of the biological bosonic state in homochirality of L-amino acids. It is a source of knot in parallel transport of Yang–Mills field in genetic code evolved from natural selection. It serves as a source of protein folding structure in L-amino acids over all the protein structure of a living organism. In the proof, we modified Frank’s model for homochirality and added more properties of nonlinearity and supersymmetry. The mirror symmetries transform their left and right homochiral hidden states of reversed reaction over Frank’s equation for spontaneous autocatalysis. We also change the rate of reaction in the model from the Euclidean norm to Minkowski metric with Lorentz invariant in special relativity theory. The speed of light in Minkowski space in this model is an analogy with a source of all species of all living organisms with common 20 L-amino acids as their constituents. The result of the proof agrees with the existence of L-amino acids in nature. By long-term of evolution, the number of concentration of left homochirality is more than the concentration of right homochirality in amino acids propositional to the Chern–Simons current.

This paper focuses on the examination of stable and unstable geometrical structures of thin-shell wormholes constructed from Henneaux–Martinez–Troncoso–Zanelli black holes through the Visser cut-and-paste approach. We use the Israel thin-shell formalism for evaluating the stress–energy tensor components of the matter distribution near the wormhole throat. Equations of state, specifically the phantom-like and generalized Chaplygin gas model for exotic matter, are used to conduct an extensive investigation into the stability of the thin-shell. The radial perturbation around the equilibrium throat radius is also considered to explore the stable configuration for specific values of physical parameters. Our results show that the stable zones of these thin-shell wormholes increase as the scalar field parameter ${ℰ}$ approaches −1. This study gives light on the behavior and dynamics of these wormholes throw light on their potential stability and lead the way for additional theoretical physics research.

This paper delivers the characterization of a pseudo $B$-symmetric spacetimes and we illustrate that a pseudo $B$-symmetric spacetime admitting Codazzi type of $B$-tensor represents a perfect fluid spacetime and if this spacetime admits the time-like convergence criterion, then the pseudo $B$-symmetric spacetime fulfills cosmic strong energy criterion and contains pure matter. Besides, we find in a pseudo $B$-symmetric spacetime with Codazzi type of $B$-tensor the electric part of the Weyl tensor vanishes and has Riemann and Weyl compatible vector fields. Furthermore, it is established that the chosen spacetime with Codazzi type of $B$-tensor is conformally flat and represents a Robertson–Walker spacetime. Also, we calculate the scale factor $\mathrm{\Psi }(t)$ for these spacetimes in a spatially flat Robertson–Walker spacetime. Finally, we study the impact of this spacetime under $f(R)$ gravity scenario and deduce several energy conditions by considering a new model $f({ℛ})=e^{(\alpha {ℛ})}-\mathrm{\text{ln}}(\beta {ℛ})$ in which $\alpha$ and $\beta$ are positive constants.

This paper investigates the impact of the semiconformal curvature tensor’s symmetry on the base and fiber manifolds of a warped product manifold. It establishes that the fiber manifold of a warped product manifold has a constant sectional curvature, whereas the base manifold is semiconformally symmetric. Furthermore, the paper derives the specific forms of the semiconformal curvature tensor for both the base and fiber manifolds. Also, it is demonstrated that a semiconformally symmetric (flat) GRW space-time is a perfect fluid space-time and exhibits an irrotational velocity vector field.

In this paper, we have developed a class of new solutions for relativistic compact stars in higher-dimensional $(D\ge 4)$ space-time assuming pseudo-spheroidal geometry of the $g_{rr}$ metric component. To study the physical properties, we consider equation of state of interior strange matter $p=\frac{1}{3}(\rho -4B)$, as proposed in MIT bag model in the presence of a density-dependent $B$ parameter. The interior matter of a quark star may consist of three flavor quarks. We observe some interesting results. The parameter $B$ depends on the anisotropy $(\alpha )$ in the interior, and at the stellar surface, $B$ attains a constant value independent of $\alpha$. At the interior, $B$ increases with the increase of $\alpha$. We also note that the value of B approaches a constant value with increasing spheroidal parameter $\lambda$. $B(\rho )$ also depends on space-time dimensions and it is interesting to note that $B(\rho )$ picks up negative values near core region which limits the number of space-time dimensions available for a stellar model. All the stability criterion and energy conditions hold good for a physically realistic stellar configuration. It is observed that strange quark matter may be stable or metastable or unstable depending upon the value of energy per baryon $(E_B)$. Strange quark matter will be stable if energy per baryon $E_B<930.4{\mathrm{\text{MeV/fm}}}^3$. It is noted that the maximum mass obtainable in this model is $1.99M_{\odot }$ considering stable strange quark matter when dimension $D=4$. In addition, we observe that the dimensions have some effect on the gross properties of strange stars (SS).

In this study, we investigate a scalar field cosmological model with Lyra’s geometry to explain the present cosmic expansion in a homogeneous and isotropic flat FRW universe. In Einstein’s field equations, we presupposed a variable displacement vector as an element of Lyra’s geometry. In the context of the conventional theory of gravity, we suggest a suitable parametrization of the scalar field’s dark energy density in the hybrid function of redshift $z$, confirming the essential transition behavior of the universe from a decelerating era to the present accelerated scenario. We present constraints on model parameters using the most recent observational datasets from OHD, BAO/CMB and Pantheon, taking Markov Chain Monte Carlo (MCMC) analysis into account. For the proposed model, the best estimated values of parameters for the combined dataset (OHD, BAO/CMB and Pantheon) are $H_0=71.15\pm 0.26$km/s/Mpc, ${\mathrm{\Omega }}_{m0}=0.2625\pm 0.0024$, ${\mathrm{\Omega }}_{\varphi 0}=0.676\pm 0.038$, $\alpha =-0.22\pm 0.13$, $n=0.096\pm 0.079$ and $k=0.38\pm 0.32$. The model exhibits a flipping nature, and the redshift transition occurs at $z_t=0.756_{-0.015}^{+0.005}$. The current value of the decelerated parameter for the proposed model is calculated as $q_0=-0.625_{-0.085}^{+0.067}$ for the combined dataset. Some dynamical properties of the model like energy density (${\rho }_{\varphi }$), scalar field pressure ($p_{\varphi }$), EoS parameter of scalar field (${\omega }_{\varphi }$), and effective EoS parameter (${\omega }_{\mathrm{\text{eff}}}$) are analyzed and presented. Further, we have also examined the statefinder diagnosis and jerk parameters of the derived model. The total density parameter for the derived model is found to be unity which is in nice agreement with recent standard findings.

Energy storage systems are crucial for the advancement of modern technology, yet achieving optimal efficiency in these systems remains a significant challenge. This study investigates how spatial distribution impacts energy diffusion within battery electrodes using Gaussian peak models. We explore two distinct configurations of Gaussian peaks separate and overlapping to understand their effects on diffusion patterns. Separate Gaussian peaks produce simpler diffusion profiles with well-defined influence regions, while overlapping peaks create complex diffusion patterns with intricate contours reflecting the combined effects of multiple sources. To enhance the accuracy and efficiency of our simulations, we leverage machine learning (ML) optimization techniques. An ML-based optimizer is employed to refine the parameters of the diffusion model, resulting in more precise and efficient simulations. This approach allows us to better understand and predict how different peak arrangements affect diffusion dynamics. By simulating these scenarios in rectangular and square electrode geometries, we reveal how the spatial arrangement of energy sources influences diffusion behavior. Our findings provide valuable insights for optimizing battery designs, suggesting that tailored diffusion profiles can significantly improve energy storage efficiency and reliability. This research not only advances the theoretical understanding of energy diffusion processes but also demonstrates how ML optimization can be used to enhance the performance of lithium-ion batteries and other energy storage systems.