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This research paper explores the properties of quasi-Einstein manifolds with a unit concircular generator vector field within doubly warped product structures. The paper begins by investigating the characteristics of quasi-Einstein manifolds that possess a unit concircular generator vector field. Subsequently, it analyzes the behavior of the Hessian, Riemann, and Ricci vector fields in the context of a doubly warped product. Moreover, the impact of the quasi-Einstein condition on both the doubly warped product and its factor manifolds is studied. Finally, conditions are derived to determine whether a doubly warped product satisfying the quasi-Einstein condition can be classified as a warped or a direct product. By presenting these findings, this study contributes to the comprehension of quasi-Einstein manifolds and their interactions within doubly warped product structures. [ABSTRACT FROM AUTHOR]

In this paper, we aim to characterize the sequential warped product κ -almost gradient conformal Ricci–Bourguignon soliton. We derive applications of some vector fields like conformal vector field, torse-forming vector field, torqued vector field on κ -almost conformal Ricci–Bourguignon soliton. The inheritance properties of the Einstein-like sequential warped product κ -almost gradient conformal Ricci–Bourguignon solitons of class types ℙ , , are investigated in this paper. Later we show that if M ̄ = (M 1 × f I M 2 ) × f ̄ I M 3 is a sequential warped product of a complete connected (n − 2) -dimensional Riemannian manifold M 1 and one-dimensional Riemannian manifolds I M 2 and I M 3 admitting κ -almost conformal Ricci–Bourguignon soliton, then (M 1 , g 1) becomes a (n − 2) -dimensional sphere of radius ρ = n − 2 r 1 + (μ − 1 2 (p + 2 n) + ρ R) (4 − n) . We have discovered that for a κ -almost gradient conformal Ricci–Bourguignon soliton sequential warped product, the warping functions are constants under certain conditions. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the existence of Ricci solitons and the nature of curvature inheritance as well as collineations on the Robinson–Trautman (briefly, RT) spacetime. It is shown that under certain conditions RT spacetime admits almost-Ricci soliton, almost- η -Ricci soliton, almost-gradient η -Ricci soliton. As a generalization of curvature inheritance [K. L. Duggal, Curvature inheritance symmetry in Riemannian spaces with applications to fluid space times, J. Math. Phys. 33(9) (1992) 2989–2997] and curvature collineation [G. H. Katzin, J. Livine and W. R. Davis, Curvature collineations: A fundamental symmetry property of the space-times of general relativity defined by the vanishing Lie derivative of the Riemann curvature tensor, J. Math. Phys. 10(4) (1969) 617–629], in this paper, we introduce the notion of generalized curvature inheritance and examine if RT spacetime admits such a notion. It is shown that RT spacetime also realizes the generalized curvature (resp., Ricci, Weyl conformal, concircular, conharmonic, Weyl projective) inheritance. Finally, several conditions are obtained, under which RT spacetime possesses curvature (resp., Ricci, conharmonic, Weyl projective) inheritance as well as curvature (resp., Ricci, Weyl conformal, concircular, conharmonic, Weyl projective) collineation, and we have also introduced the concept of generalized Lie inheritance and showed that RT spacetime realizes such a notion. [ABSTRACT FROM AUTHOR]

Analytical methods provide crucial mathematical insights into the stable solitary waves hidden in nonlinear phenomena. The nonlinear Schrödinger (NLS) equation is one of the most important typical integrable soliton models. From a mathematical perspective, the essence of the celebrated derivative NLS (DNLS) equation’s difference from the classical NLS equation lies in its cubic potential being differentiated once by the spatial variable and multiplied by the imaginary unit, which leads to the former having some characteristics that the latter cannot have. This paper extends the DNLS equation to the fractional integrable case with conformable derivative operators, and uses Darboux transformations (DTs) and generalized DT (GDT) to solve it exactly. Specifically, Lax pairs generating the fractional DNLS equation are first given. Based on the given Lax pairs, then the n-fold DTs and GDT for the fractional DNLS equation are derived. Some special exact solutions of the fractional DNLS equation are further obtained by employing the derived n-fold DTs and GDT. Finally, several novel space–time structures and dynamical evolutions of the obtained exact solutions are analyzed. This paper reveals through the DT and GDT methods that the double power-law fractional orders in the exact solutions of the fractional DNLS equation can be used to dominate the variable velocity propagation and anomalous diffusion in fractional dimensional media at different geometric scales. [ABSTRACT FROM AUTHOR]

Smooth and discontinuous (SD) oscillators are the nonlinear models that will exhibit SD dynamics due to continuous variation of the smooth parameter. Kosambi–Cartan–Chern (KCC) theory is a differential geometric theory that describes the deviations from the entire trajectory of the variational equation to the nearby trajectory. This paper presents a completely new dynamical analysis of a type of SD oscillators with nonlinear damping based on the KCC theory. First, the paper gives five KCC geometrical invariants of SD oscillators in the smooth and non-smooth cases, respectively. The results show that the geometric quantities in the non-smooth case cannot be derived directly from the geometric quantities in the smooth case. Second, from these geometric quantities, KCC stability of SD oscillators trajectory at any point except x = 0 is analyzed. Lastly, numerical results show that in some regions that deviate from the equilibrium point of system, the system will exhibit complex and variable dynamical behavior due to small changes in parameters. This paper shows that the KCC theory is also a useful tool in the dynamical analysis of non-smooth systems. [ABSTRACT FROM AUTHOR]

This paper presents a methodical dynamical analysis of the Big Bang model, taking into account dark matter and an arbitrary form of dark energy. Nevertheless, why dynamic analysis? The primary advantage of the dynamical analysis approach is that it obviates the necessity to precisely solve the system for every individual dependent variable. Instead, it enables the prediction of the overall evolutions. In this regard, there are some powerful tools of non-dynamical systems (theorems, perturbation, etc.) which can help us a lot. The model under consideration is a nonlinear system with two dimensions (2D). In order to investigate this, we employ a sophisticated form of nonlinear dynamical systems theory in our research. We have delved into the full potential of nonlinear dynamical system theory known until now in our work. This analysis has produced very interesting solutions, which are in quite a contrast with the linear analysis approach. The stability of the system is considered at length, and the corresponding evolutions of the universe are also discussed consequently. A handful number of figures are given to visualize the behavior of the evolutions. The plots that are presented here are vector field plots and a new plotting technique initiated by us and used in our earlier papers. Interestingly, our work indicates the universe might resemble “phantom” evolution. Also, among the fixed points of our model, one is able to escape the singular situation called “Big Rip”. [ABSTRACT FROM AUTHOR]

In this paper, we investigate in this paper the Type IV singular bouncing in the framework of f (R ,) theory of gravity where R and mean the curvature scalar and the Gauss–Bonnet invariant, respectively. Cosmological f (R ,) models constrained by the slow-roll evolution is reconstructed and their explicit forms are provided near the bounce and far away from it. One obtains finally two models whose stability is numerically analyzed in this work. Our results show that the stability of the reconstructed models is very affected by their parameters. The model far from the singularity recovers stability quickly than the model near the singularity. [ABSTRACT FROM AUTHOR]

This paper presents an analytical study of the behavior of radial free-geodesics in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime within the Lambda Cold Dark Matter (Λ CDM) model. Using the radial free motion solutions, we provide two methods for characterizing the geodesics and defines a general formula that encapsulates all possible solutions, determined by two initial conditions. We show that the past light cone, event horizon, and particle horizon, can be considered as special cases of this overarching formula. Furthermore, the paper explores the free geodesics within the currently accepted cosmological model based on the recent Planck results, thoroughly examining the various possible geodesic scenarios. [ABSTRACT FROM AUTHOR]

In previous works, we have proven that there are local tetrads in four-dimensional curved Lorentzian spacetimes that can be written in terms of two kinds of local structures, the skeletons and the gauge vectors. These tetrads diagonalize locally and covariantly the stress–energy tensors for systems of differential equations of the Einstein–Maxwell kind in the Abelian electromagnetic case, or of the Einstein–Maxwell–Yang-Mills kind when non-Abelian Yang–Mills fields are included, along with suitable Yang–Mills stress–energy tensors. Under local Lorentz transformations, these new tetrads conserve their skeleton-gauge vector structure. In this short paper, we will prove that given any general unit orthogonal tetrad in spacetime, we will be able to construct a new tetrad in the skeleton-gauge vector form. We will prove a theorem stating that the original orthonormal tetrad can be constructed or reexpressed with this same local tetrad skeleton-gauge vector structures. The theorems proved in this paper will enable the demonstration of new results in group isomorphism theorems in the future. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of conformal metric deformations in the quasi-radial coordinate parametrizing the three-sphere in the conformally compactified Minkowski spacetime S1 × S3. Prior to reduction of the associated Laplace–Beltrami operators to a Schrödinger form, a corresponding class of exactly solvable potentials (each one containing a scalar and a gradient term) is found. In particular, the scalar piece of these potentials can be exactly or quasi-exactly solvable, and among them we find the finite range confining trigonometric potentials of Pöschl–Teller, Scarf and Rosen–Morse. As an application of the results developed in the paper, the large compactification radius limit of the interaction described by some of these potentials is studied, and this regime is shown to be relevant to a quantum mechanical quark deconfinement mechanism. [ABSTRACT FROM AUTHOR]

This paper considers the possibility that abstract thinking and advanced synthesis skills might encourage extraterrestrial civilizations to accept communication with mankind on Earth. For this purpose, a notation not relying upon the use of alphabet and numbers is proposed, in order to denote just some basic geometric structures of current physical theories: vector fields, 1-form fields, and tensor fields of arbitrary order. An advanced civilization might appreciate the way here proposed to achieve a concise description of electromagnetism and general relativity, and hence it might accept the challenge of responding to our signals. The abstract symbols introduced in this paper to describe the basic structures of physical theories are encoded into black and white bitmap images that can be easily converted into short bit sequences and modulated on a carrier wave for radio transmission. [ABSTRACT FROM AUTHOR]

This paper investigates discrete symmetries for dyon and the invariance of Maxwell's field equations in the macroscopic media (material medium). Using advanced mathematical approaches, the paper derived electromagnetic duality and a unique form of Poynting theorem for dyon in macroscopic media. Here, we demonstrate that the combination of parity (P) , charge conjugation (C) , and time reversal (T) symmetry: CPT , is an exact symmetry for dyon in macroscopic media. Furthermore, a comprehensive analysis of the electromagnetic wave equation for dyons in conducting media is also derived. These findings contribute significantly to the understanding of dyon behavior in electromagnetic fields. [ABSTRACT FROM AUTHOR]

The finding of new integrable coupling systems has become an important area of research in mathematical physics and their study will aid in the classification of multi-component integrable systems. A basic method for generating integrable coupling systems is algebraic expansion, for example, the Frobenius algebra, the Lie algebra, the superalgebra, and so on. In this paper, we introduce a Frobenius Boussinesq equation based on the Frobenius algebra, and then we present a Lax pair of it. It follows that we give a Bäcklund transformation of the Frobenius Boussinesq equation. Furthermore, the lattice equation of the Frobenius Boussinesq equation is presented by using three Bäcklund transformations, and then obtain the exact solutions. Additionally, we obtain the conservation laws of the Frobenius Boussinesq equation via the Bäcklund transformation. Strongly coupled and weakly coupled systems physically represent strong and weak interactions, respectively. In this paper, we introduce a weakly coupled Degasperis–Procesi (DP) equation, and construct a Lax pair of it. In addition, the Bäcklund transformation and superposition principle are applied to investigate the weakly coupled DP equation. We also obtain the conservation laws of the weakly coupled DP equation. Then, we introduce a strongly coupled DP equation, and use the same method to study the strongly coupled DP equation. The exact solutions of these two equations are obtained. Moreover, we introduce a Z n -DP equation. Considering the superposition principle, we obtain the solution of an associated Z n -DP equation by using Bäcklund transformations. These new multi-component integrable systems can enrich the existing integrable models and possibly describe new nonlinear phenomena. [ABSTRACT FROM AUTHOR]

In this paper, it has been proven that locally the inertial frames and gauge states of the electromagnetic field are equivalent. This proof is valid for Einstein–Maxwell theories in four-dimensional Lorentzian spacetimes. Theorems proved in a previous paper will be used. These theorems state that locally the group of electromagnetic gauge transformations is isomorphic to the local group of Lorentz transformations of a special set of tetrad vectors. The tetrad that locally and covariantly diagonalizes any non-null electromagnetic stress–energy tensor. There are in total two isomorphisms, one for each orthogonal plane of stress–energy eigenvectors. We discuss the opposite problem in this paper. What happens with local electromagnetic gauge when the test object under study is boosted by any mechanical means? We will prove that boosting matter is indistinguishable from introducing an appropriate local electromagnetic gauge transformation. [ABSTRACT FROM AUTHOR]

A graph G is a fractional (a,b,m)-deleted graph if deleting any m edges from G, the resulting subgraph still admits a fractional [a,b]-factor. As an exclusive graph-based parameter, isolated toughness and its variant are utilized to measure the vulnerability of networks which are modelled by graph topology structures. Early studies have shown the inherent connection between isolated toughness and the existence of fractional factors in specific settings. This paper provides a theoretical perspective on the sufficient conditions for fractional (a,b,m)-deleted graphs with respect to isolated toughness and its variant. The sharpness of the given isolated toughness bounds is explained by counterexamples. [ABSTRACT FROM AUTHOR]

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 Ψ(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(αℛ) −ln(βℛ) in which α and β are positive constants. [ABSTRACT FROM AUTHOR]

In this paper, we have developed a class of new solutions for relativistic compact stars in higher-dimensional (D ≥ 4) space-time assuming pseudo-spheroidal geometry of the grr metric component. To study the physical properties, we consider equation of state of interior strange matter p = 1 3(ρ − 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 (α) in the interior, and at the stellar surface, B attains a constant value independent of α. At the interior, B increases with the increase of α. We also note that the value of B approaches a constant value with increasing spheroidal parameter λ. B(ρ) also depends on space-time dimensions and it is interesting to note that B(ρ) 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 (EB). Strange quark matter will be stable if energy per baryon EB < 930.4MeV/fm3. It is noted that the maximum mass obtainable in this model is 1.99M⊙ 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). [ABSTRACT FROM AUTHOR]

In this paper, we give Weierstrass-type representation formulas for the null curves and for the minimal Lorentz surfaces in the Minkowski 3-space ℝ13 using real-valued functions. Applying the Weierstrass-type representations for the null curves, we find a correspondence between the null curves in ℝ24 and the pairs of null curves in ℝ13. Based on this correspondence, we obtain a relation between the minimal Lorentz surfaces in ℝ24 and the pairs of minimal Lorentz surfaces in ℝ13. As an application, we give examples showing how we can obtain a minimal Lorentz surface in ℝ24 using a pair of minimal Lorentz surfaces in ℝ13. [ABSTRACT FROM AUTHOR]

In Liu et al. [On the generalized time fractional diffusion equation: Symmetry analysis, conservation laws, optimal system and exact solutions, Int. J. Geom. Methods Mod. Phys. 17(01) (2020) 2050013], the generalized time-fractional diffusion equation Dtαu = aupu xx + buqu x2 is studied by the symmetry analysis method. Liu et al. obtained two group generators X1 = ∂ ∂x, X2 = 2t α ∂ ∂t + x ∂ ∂x and only one trivial solution u(t,x) = f(t) = C0 Γ(α)tα−1 for the equation. In this paper, we classify the Lie symmetry group admitted by the equation, and for the case p = q + 1, we obtain a richer set of group generators and some nontrivial solutions, including unprecedented exact solutions and power series solutions. In addition, we construct the one-dimensional optimal system of the Lie symmetry group admitted by the time-fractional diffusion-type equation by Olver’s method, and obtain the conservation laws for all the obtained Lie symmetries using the general method developed by Ibragimov. For the novel exact solutions and power series solutions, we analyze their dynamic behavior graphically. [ABSTRACT FROM AUTHOR]

In this paper, we have provided a discussion regarding the structural properties of a spherical compact stellar object within the background of f (R , G) modified gravity. We have considered that the interior region of the compact stellar body is filled by a composition of anisotropic dark energy and isotropic normal matter which are assumed to be non-interacting. To relate the two stated fluids, we have considered the dark energy density directly proportional to the matter density. In particular, Krori–Barua (K–B) matric potentials are used to explore the solutions of modified field equations corresponding to f (R , G) = R + β R 2 + G m . Next, we have delivered a detailed 3-dimensional graphical analysis to design physically well-behavior and stability of different parameters like energy density, individual pressure components for both dark energy and normal matter and anisotropy. Also, we have explored the stability and physical acceptability criterion by causality conditions, adiabatic index, TOV equation, and Harrison–Zeldovich–Novikov criteria. Consequently, we have discussed the violation of energy conditions for dark energy and hold the same for the normal matter. Here is an important note we have taken for three compact objects like, SAX JI808.4-3658, PSR J1614-2230, and 4U1820-30, for graphical analysis. Furthermore, we have calculated the predicted values of central density, central pressure, and surface pressure for both dark and normal matter. Finally, we concluded that our proposed dark energy stellar configuration maintains all required stability and physical acceptability criteria. [ABSTRACT FROM AUTHOR]

In this paper, we explore a set of geometric properties of Mixed Super Quasi-Einstein (MSQE) manifolds and provide examples of both Riemannian and Lorentzian MSQE manifolds to demonstrate their existence. Furthermore, we examine MSQE spacetimes in the context of the space-matter tensor, discussing several related properties. Finally, we establish the existence of an MSQE spacetime through a nontrivial example. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a Lichnerowicz-type formula for J -Witten deformation and give the proof of the Kastler–Kalau–Walze-type theorems associated with J -Witten deformation on four-dimensional and six-dimensional almost product Riemannian manifold with (respectively, without) boundary. We give an explanation of the Einstein–Hilbert action for J -Witten deformation on four-dimensional manifold with boundary. [ABSTRACT FROM AUTHOR]

In this paper, we will discuss an alternative theory for the origin of dark matter and dark energy based on the new concept of tetrad gauge states of spacetime. The new tetrads already introduced new physics since it has been proved that local electromagnetic gauge transformations can boost the local tetrad fields in a four-dimensional curved Lorentz spacetime. It is within this context that we will present a different qualitative explanation for the so-called dark matter and dark energy and new possible topological solutions of a galactic nature for Einstein–Maxwell spacetimes in its relation to dark matter and new possible topological solutions of a cosmological nature for Einstein–Maxwell spacetimes in its relation to dark energy. [ABSTRACT FROM AUTHOR]

In this paper, our aim is to research the change in the magnetic field using the curvature theory of ruled surfaces. For this, we examine magnetic curves of the curve whose existence is guaranteed from the derivative formulas of the rotation frame. The Killing vector fields and Lorentz forces of these magnetic curves are calculated. Additionally, correlations between curvatures are obtained. Flux ruled surfaces are obtained and the conditions for developable are achieved. Finally, examples of the magnetic flux developable ruled surfaces are given. [ABSTRACT FROM AUTHOR]

In this paper, we analyze energy density inhomogeneities for charged fluid configuration in the background of f (T) theory and recognize its prime features as computed in GR. The dynamical equations are composed employing Bianchi identities for the standard, f (T) extra terms, and energy-momentum tensor for the electromagnetic field. We evaluate various mathematical models of dissipative and anisotropic fluid distributions in-plane symmetry under f (T) gravity. To proceed with the investigation, we design the f (T) field equations, kinematical quantities, and mass function. We analyzed dynamical variables and Ellis equations in terms of our considered theory. To examine the associated inhomogeneity factors, specific scenarios are illustrated alongside and without dissipation. Within a non-radiating situation, we analyze dust and isotropic and anisotropic matter in the state of electric charge. We examine the inhomogeneity factor of a dissipative fluid via a charged dust haze. We derive that the electromagnetic field fosters matter inhomogeneity, but additional curvature factors make the entire structure more homogenous as time passes. [ABSTRACT FROM AUTHOR]

The center of this paper is to establish the generalized variational structure (GVS) of the (3 + 1) -dimensional Zakharov–Kuznetsov–Burgers equation (ZKBe) by taking advantage of the Semi-inverse method (SIM). Two different GVSs are extracted and the derivation process is presented in detail. The extracted GVSs reveal the energy conservation law and can offer some new insights on the study of the variational method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the bouncing universe in a modified gravity model f (Q , T). The bouncing universe theory posits that the universe goes through periodic expansions and contractions, with a "bounce" occurring at the end of each contraction that leads to a new expansion. This theory suggests that our universe didn't emerge on its own out of nothing, but is instead the latest in a series of universes that have been expanding and contracting for eternity. It has gained renewed interest in recent years as a potential alternative to the Big Bang theory, which suggests that our universe began with a massive expansion from a singularity. According to the above explanations, first, we review of f (Q , T) gravity model, then the bouncing universe scenario according to the f (Q , T) gravity model in some special functions is analyzed in detail. We find that in which condition of parameters space, bouncing occurs. [ABSTRACT FROM AUTHOR]

In this paper, we employ parametrization techniques within the framework of f (T) gravity to investigate the deceleration parameter (DP), a key quantity characterizing the universe's expansion dynamics. By analyzing the DP, we gain valuable insights into the nature of cosmic constituents and their impact on the universe's evolution. We utilize a combination of observational data, including 31 Cosmic Chronometers (CC) measurements, 1048 Type Ia Supernovae (SNIa), 17 Baryon Acoustic Oscillation (BAO) measurements, Cosmic Microwave Background (CMB), 162 Gamma Ray Bursts (GRB), and 24 observations of compact radio quasars (Q). We employ the Markov chain Monte Carlo (MCMC) sampling technique to estimate the best-fit range of model parameters. Cosmological and cosmographic parameters are investigated, and their implications in the context of cosmology have been discussed. We also analyze the statefinder and Om diagnostic to gain deeper insights into the universe's behavior. Furthermore, we conduct statistical analyses to compare our model with the standard Λ CDM model. Our investigation also includes the study of physical parameters, providing comprehensive insights into the cosmological behavior within the f (T) gravity framework. The results and comparisons presented in this work contribute to a deeper understanding of the universe's dynamics and provide valuable implications for the cosmological model under consideration. [ABSTRACT FROM AUTHOR]

Dabrowski et al. [Spectral metric and Einstein functionals for Hodge–Dirac operator, preprint (2023), arXiv:2307.14877] gave spectral Einstein bilinear functionals of differential forms for the Hodge–Dirac operator d + δ on an oriented even-dimensional Riemannian manifold. In this paper, we generalize the results of Dabrowski et al. to the cases of 4-dimensional oriented Riemannian manifolds with boundary. Furthermore, we give the proof of Dabrowski–Sitarz–Zalecki-type theorems associated with the Hodge–Dirac operator for manifolds with boundary. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamical stability analysis by considering the torsion field ϕ which is proportional to the Hubble parameter and barotropic equation-of-state parameter in the framework of the homogenous and isotropic FLRW metric with non-zero torsion in the scenario of dark matter and dark energy interacting terms. We discuss the stability of the critical points corresponding to the eigenvalues in the presence of dust and radiation at quintessence, ΛCDM and phantom regimes by utilizing the different linear and nonlinear interaction models which depend on the energy density. As a result, we observe that the first linear model shows the stable behavior throughout the universe for dust and radiation phase. The other linear and nonlinear models show the stable critical points, computing with the eigenvalues at phantom and ΛCDM era with the best fit value of interaction strength and coupling constant for dust and radiation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The principal aim of this paper is to find the expression of *-Bach tensors on (κ,μ)′-almost-Kenmotsu manifolds. It is shown that if the metric of a (κ,μ)′-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 (κ,μ)′-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 (κ,μ)′-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. [ABSTRACT FROM AUTHOR]

In this paper, we propose the subtrigonometric series solution for the equation of the scaling-law wave motion to describe the special vibrating string associated with the Mandelbrot scaling law. [ABSTRACT FROM AUTHOR]

In this paper, we use the cosmographic approach to discuss Friedmann space-time in the presence of torsion. For this, we explore equations of motion that explain creation in an isotropic and homogeneous cosmic backdrop with nonzero torsion. Here, we consider the energy density of holographic dark energy model ρd = 3c2(z)M p2L−2 where c2 is a dimensionless parameter depending on redshift parameter z,Mp = 1 κ is the reduced Planck mass and L represents the holographic length scale. We examine this dark energy model with both constant and variable holographic length scales in terms of Hubble parameter to determine the best-fit scale. The interaction between dark sector components is taken to evaluate cosmographic parameters, like Hubble, equation of state, deceleration, jerk, snap, lerk and statefinder parameters. We consider four c(z) parametrizations, which are Chevallier–Polarski–Linder, Jassal–Bagla–Padmanabhan, Wetterich and Ma–Zhang for both cases. We obtain consistent results for specific choices of constant parameters in the underlying scenario. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigating the behavior of charged compact stars in the f(R,ϕ,X) theory of gravity, where R denotes the Ricci Scalar, ϕ is a scalar potential, and X is a kinetic term. For this purpose, we consider spherically symmetric spacetime with Bardeen geometry as exterior spacetime to investigate various properties of compact stars, including energy density and pressure components. Matching conditions are used to find model parameters. We present a detailed analysis, including a discussion of equations of state parameters, and stability criteria. In this analysis, we discuss the energy conditions to check the viability of our model. Furthermore, an equilibrium condition can be visualized through the modified Tolman–Oppenheimer–Volkov equation. It is concluded that Bardeen’s geometry supports the existence of compact stars in the background of the f(R,ϕ,X) theory of gravity. [ABSTRACT FROM AUTHOR]

f(R,Lm) gravity provides an alternative explanation for the late-time acceleration of the universe without introducing the concept of dark energy. In this paper, the non-static Bianchi type-III spacetimes have been derived by considering f(R,Lm) = f1(R) + f2(R)H(Lm). The solutions of field equations of f(R,Lm) theory of gravity and Bianchi type-III metric have been obtained for some special cases by taking particular metric components. Noether symmetries have been discussed for the derived spacetimes and it was observed that all of the discussed spacetimes must have at least five Noether symmetries. [ABSTRACT FROM AUTHOR]

It is known that a simply connected Riemann surface satisfies the isoperimetric equality if and only if it has constant Gaussian curvature. In this paper, we show that the circles centered at origin in the Randers Poincaré disc satisfy the isoperimetric equality with respect to different volume forms however, these Randers metrics do not necessarily have constant (negative) flag curvature. In particular, we show that Osserman’s result [12] of the Riemannian case cannot be extended to the Finsler geometry as such. [ABSTRACT FROM AUTHOR]

The impact of deformation space on the physical characteristics of diverse physics systems has been thoroughly investigated in research papers. In this work, we study the deformed Klein–Gordon equation (DKGE) in the three-dimensional relativistic non-commutative quantum space (3D-RNCQS) regime by using the improved Hua plus modified Eckart potential (IHPMEP) model. For this consideration, the DKGE in the 3D-RNCQS regime is solved using the standard perturbation theory and the well-known Bopp’s shifts method with the Greene–Aldrich approximation to the centrifugal barrier. The new relativistic energy equation and eigenfunction for the IHPMEP in the presence of deformation space-space for the heterogeneous (CO, HF, and NO) and homogeneous (N2, H2, and Li2) diatomic molecules are obtained to be sensitive to the atomic quantum numbers (j,l,s, and m), the mixed potential depths (V0,V1,V2, and V3), the inverse of the screening parameter α, and non-commutativity parameters (Φ, χ, and ζ). Analysis is performed on the non-relativistic limit of new energy spectra. By appropriately adjusting the combined potential parameters, we analyze the obtained new bound state eigenvalues of the DKGE and deformed Schrödinger equation with the IHPMEP in 3D-NCQS symmetries and obtain the new modified Eckart potential, the modified Hua potential, the modified Morse potential, and the modified Pöschl–Teller potential. Within the framework of the 3D-NRNCQS regime, the homogeneous and heterogeneous composite systems under IHPMEP models are examined. A thorough investigation is carried out into the impact of space-space deformation on the thermal parameters of the IHPMEP, including the partition function, mean energy, free energy, specific heat, and entropy. This work is of a fundamental absorbability nature and pedagogical interest in atomic and molecular physics. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel curvature tensor called the 풦-curvature tensor, which is formed by combining the Weyl tensor and the 풲2-curvature tensor. It is proved that a semi-Riemannian manifold with traceless 풦-curvature tensor is Einstein, while a 풦-curvature flat semi-Riemannian manifold exhibits constant sectional curvature. We show that a space-time with traceless 풦-curvature tensor or 풦-curvature flat represents dark energy era. A semi-Riemannian manifold with divergence-free 풦-curvature tensor is Weyl harmonic. In a space-time where the 풦-curvature tensor is of divergence-free, both the isotropic pressure and energy density are constants. Under certain conditions, it is shown that a pseudo-풦-symmetric semi-Riemannian manifold reduces to a pseudo-Riemannian manifold. It is demonstrated that pseudo-풦-symmetric space-times can be regarded as generalized Robertson–Walker (GRW) space-times. Finally, a concrete example of pseudo-풦-symmetric semi-Riemannian manifolds is presented. [ABSTRACT FROM AUTHOR]

Ordinary nonlinear differential equations with classical and fractional derivatives are used to simulate several real-world problems. Nonetheless, numerical approaches are used to acquire their solutions. While various have been proposed, they are susceptible to both disadvantages and advantages. In this paper, we propose a more accurate numerical system for solving nonlinear differential equations with classical and Caputo–Fabrizio derivatives by combining two concepts: the parametrized method and the predictor–corrector method. We gave theoretical analyses to demonstrate the method’s correctness, as well as several illustrated examples for both scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we develop an extended space-time geometry that includes an internal space built with division octonions with realization via Pauli matrices and Zorn (vectorial) matrices. Here, we extend a former field theory that used split octonion algebra to a division octonion algebra on a non-Riemannian manifold. The octonionic algebra is the last possible algebra allowed by the Hurwitz theorem. The interpretation of the “octonionic field” in this division octonionic algebra is not straightforward, however it behaves in a similar way to the quaternionic Yang–Mills fields. Former work suggests that this Yang–Mills-like octonionic field is associated with the field governing quarks within nucleons. In this work, we discover that the inclusion of octonionic fields in the geometry of an internal space necessarily excludes the quaternionic (Yang–Mills) fields in an extended non-Riemannian geometry. This is not what is expected from the standpoint of a “unified” field theory, which leads us to propose a different approach to Einstein’s unified field theory. [ABSTRACT FROM AUTHOR]

In this paper, we define a ruled surface obtained by an infinitesimal bending of a curve in Minkowski 3-space. We also characterize such ruled surfaces according to causal characters of the curve. Furthermore, we find appropriate conditions of ruled surfaces obtained by infinitesimal bendings of curves to be (lightlike) developable, in particular, cylindrical or conical in Minkowski 3-space, with examples presented. [ABSTRACT FROM AUTHOR]

In this paper, we have explored cold dark matter and holographic dark energy cosmological model with big rip singularity. To obtain the solution of the field equation, we supposed that scalar expansion 휃 is proportional to shear scalar σ2, which leads to P1 = (P2)n, where P1, P2 are metric potentials and n is constant. Big bang and big rip singularity are investigated. The state-finder parameter is analyzed. The physical and geometrical parameters of the universe are explained. [ABSTRACT FROM AUTHOR]

We introduce the notion of conformal trajectories in three-dimensional Riemannian manifolds M3. Given a conformal vector field V ∈ 픛(M3), a conformal trajectory of V is a regular curve γ in M3 satisfying ∇γ′γ′ = qV × γ′, for some fixed nonzero constant q ∈ ℝ. In this paper, we study the conformal trajectories in the space forms ℝ3, 핊3 and ℍ3. For (non-Killing) conformal vector fields in 핊3 (respectively, in ℍ3), we prove that conformal trajectories have constant curvature and its torsion is a linear combination of trigonometric (respectively, hyperbolic) functions on the arc-length parameter. In the case of Euclidean space ℝ3, we obtain the same result for the radial vector field and characterizing all conformal trajectories. [ABSTRACT FROM AUTHOR]

In this paper, we present comparisons of the deflection angles of massless and massive particles in the Schwarzschild space-time. For the case of photons in a general static space-time, we construct a spatial 3D equation of motion for their path that leads to an implicit formula for the deflection angle. We then compare our results with well-known results of the literature in the Schwarzschild space-time. For the case of massive particles, we calculate the deflection angle only in the Schwarzschild space-time. The end result is that as the velocity of any massive particle diminishes, the deflection angle increases. To show the relevance of these comparisons, we constructed different black hole shadows for massive particles in order to be compared with a shadow made by photons. [ABSTRACT FROM AUTHOR]

The complete title of this paper should be “The geometry of the constant gravitational field or how to switch from the mechanical Lagrangian to a geometric Lagrangian” and in this abstract we sketch why. To begin with, let us say that Einstein managed to integrate the constant gravitational field in the special theory of relativity, obtaining a metric whose geodesics are locally parabolas. The existence of a similar metric deduced from the considerations of Newtonian mechanics is somehow obstructed by the Lagrangian involved in the description of the constant gravitational field. Therefore, we need to explain how the mechanical Lagrangian above which is not suitable for a metric description of the constant gravitational field can be switched into a geometrical Lagrangian having the same geodesics and suitable for the metric description of the constant gravitational field. The geometric method found by us is related to a parabolic type of transformations. A consequence of the previous method can be applied for the study of bending of light rays in a constant gravitational field. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel approach to quantizing the length in noncommutative spaces with positional-dependent noncommutativity. The method involves constructing ladder operators that change the length not only along a plane but also along the third direction due to a noncommutative parameter that is a combination of canonical/Weyl–Moyal-type and Lie algebraic-type. The primary quantization of length in canonical-type noncommutative space takes place only on a plane, while in the present case, it happens in all three directions. We establish an operator algebra that allows for the raising or lowering of eigenvalues of the operator corresponding to the square of the length. We also attempt to determine how the obtained ladder operators act on different states and work out the eigenvalues of the square of the length operator in terms of eigenvalues corresponding to the ladder operators. We conclude by discussing the results obtained. [ABSTRACT FROM AUTHOR]

This paper investigates the evolutionary phases of a collapsing dissipative star cluster in the presence of dark matter. For this purpose, the minimal coupling model of f(R,T) gravity is used as a candidate for exotic matter in star cluster. The collapse equation is derived from generalized dynamical equations which show the total conservation of energy within the cluster. In this context, the approach of Misner and Sharp is applied to study the phenomenon and differentiate between homologous as well as non-homologous gravitational collapse. The generalized dynamical equations are also connected to modified heat transport equations related to heat flux, viscosity and shear, which deals with Israel–Stewart theory (without removing the thermodynamics heat/viscous coupling coefficients). It is found that shear-free and non-dissipative fluid give homologous collapse. The dissipation of collapsing star cluster provides a relation between tidal forces and density inhomogeneity. It is theoretically predicted that the presence of exotic matter controlled the collapsing mechanism. [ABSTRACT FROM AUTHOR]

A type of general fractional calculus with respect to another function is introduced in this paper. The kernel function within the fractional derivative and integral is specified as the Exponential function in a typical way. Based on the excellent property of the newly defined general fractional calculus, we proposed two viscoelastic models in the fractional manner compared with the classical calculus. [ABSTRACT FROM AUTHOR]

This paper presents a numerical technique to solve the generalized fractional Lane–Emden–Fowler equation. We use the Haar wavelet technique to approximate the solution of the generalized fractional Lane–Emden–Fowler equation. In this method, a differential equation transforms into a system of nonlinear equations, and this system is further solved to obtain Haar coefficients. We also showed the convergence of this method by establishing an upper bound. The rate of convergence is also discussed in our algorithm. Many numerical examples have been taken, and the results of those numerical experiments have been written in tabular form. We also documented the experiments graphically to show the efficiency and accuracy of this method. [ABSTRACT FROM AUTHOR]