Search

The purpose of the paper is to characterize gradient (m , ρ) -quasi Einstein solitons within the framework of two classes of almost Kenmotsu Manifolds. Finally, we consider an example to justify a result of our paper. [ABSTRACT FROM AUTHOR]

In this paper, spin polarized domain walls in Einstein–Cartan (EC) gravity have been recently investigated [L. C. Garcia de Andrade, Einstein–Cartan non-supersymmetric dynamo walls, Ann. Phys. 432 (2021).], where the spin polarizes along the direction orthogonal to planar domain wall. In this case, dynamo effects may appear on the wall. Moreover, dilatonic domain walls (DDWs) have shown to be responsible for inflating DWs in EC gravity, where DWs were non-magnetized [L. Garcia de Andrade, Axial and chiral anomalies in Riemann–Cartan spacetime black holes and electrodynamics, Class. Quantum Grav. 16 (1999) 2097–2103.]. In this paper, our goal is to show that when we consider a magnetized DW in the EC–Maxwell cosmology, the dilaton potential in the form of a DDW potential expressed in terms of torsion and the magnetic energy density may drive dynamo effects. Analytical solution of the dynamo equation shows that depending on the handness of DDW metric, the magnetic fields are amplified by dynamo action. From the coupled system of ECM and dilaton field equations, we find a relation between the magnetic energy density of 1 0 − 3 8 G 2 and the DDW torsion of 1 0 − 1 7 cm − 1 = 1 0 − 3 1 GeV which leads to a thin DDW thickness of 1 fm. For a galactic magnetic field, energy density of 1 0 − 1 2 G 2 leads to a thickness of 1 0 1 8 fm , a much thinner DDW. For galactic dynamo amplification, the ratio r between the magnetic energy density and photon energy density is around 1 0 − 3 4 . From this ratio, a relation between photon mass density and torsion is obtained. Chiral Magnetic effect (CME), torsion and magnetic discontinuities along the wall are investigated. Magnetic field discontinuity across the wall allows us to understand why the magnetic fields at DDW must be located along the wall since the orthogonal magnetic field may vanish. [ABSTRACT FROM AUTHOR]

The limited velocity in a geometry of Lorentzian signature seem to prevent the universe to reach thermodynamic equilibrium as suggested by the cosmic microwave background. Thus it was suggested that the universe which was initially minuscule has reached a more considerable radius in a short duration by a process known as cosmic inflation. However, to drive such a process have led to the suggestion of an ad-hoc scalar field the inflaton, which has no purpose in nature other than driving the cosmic inflation field and then stopping it once the universe reached the right size. In a recent paper it was shown that rapid expansion can occur without postulating an inflation by following Hawking’s suggestion and assuming that primordially the metric of the universe had an Euclidean signature, in which case velocity is not limited and thermalization and rapid expansion are derived without the need to assume an ad-hoc field. However, while in the previous work emphasis was put on the dynamics and physical statistics of the particles in a Euclidean space versus Lorentzian space in which both spaces were given. No mathematical model was given regarding the development of current Lorentzian space-time from the early Euclidean space-time, and how fundamental problems such as the space-time singularity and the homogeneity of the CMB can be solved in the hybrid Euclidean–Lorentzian picture. This lacuna is to be rectified in this paper. [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]

In this paper, we aim to derive new soliton solutions of (1+1)- and (2+1)-dimensional generalized Sasa–Satsuma equations via the new Kudryashov method. In optical fiber transmission systems, the Sasa–Satsuma equation describes the effects of third-order dispersion, self-steepening and stimulated Raman scattering in the propagation of ultrafast pulses. The considered equations are encountered in various physical applications such as ultra-short and femto-second pulse propagation in optical fibers and dynamics of deep water waves. So, investigation of the novel solutions of the equations is one of the important topics. We have successfully extracted some soliton solutions for the considered equation. The various graphs of the obtained solutions have been depicted in the figures by selecting appropriate parameters. The singular and bright soliton solutions have been revealed in the figures. All acquired solutions have been confirmed to satisfy the considered equations. The results show that the approach may be used to find exact solutions to various nonlinear evolution equations. The new solutions and the paper results may enrich the understanding of the wave propagation in the optical fibers and may shed light on new studies. [ABSTRACT FROM AUTHOR]

In this paper, we reconstruct a f (R , T) model where R and T are the curvature scalar and the trace of the stress-tensor, respectively, and confront it with Λ CDM model through the cosmographic parameters. The reconstructed f (R , T) model is fundamentally characterized by a input parameter β for which some suitable values are chosen. Our results show that for some values of these parameters the reconstructed f (R , T) fits very well with the Λ CDM regarding the evolution of the cosmographic parameters. [ABSTRACT FROM AUTHOR]

In Einstein's General Relativity (GR), the gravitational interactions are described by the spacetime curvature. Recently, other alternative geometric formulations and representations of GR have emerged in which the gravitational interactions are described by the so-called torsion or non-metricity. Here, we consider the recently proposed modified symmetric teleparallel theory of gravity or f (Q) gravity, where Q represents the non-metricity scalar. In this paper, motivated by several papers in the literature, we assume the power-law form of the function f (Q) as f (Q) = α Q n + 1 + β , (where α , β , and n are free model parameters) that contains two models: Linear (n = 0) and nonlinear (n ≠ 0). Further, to add constraints to the field equations we assume the deceleration parameter form as a divergence-free parametrization. Then, we discuss the behavior of various cosmographic and cosmological parameters such as the jerk, snap, lerk, O m diagnostic, cosmic energy density, isotropic pressure, and equation of state (EoS) parameter with a check of the violation of the strong energy condition (SEC) to obtain the acceleration phase of the Universe. Hence, we conclude that our cosmological f (Q) models behave like quintessence dark energy (DE). [ABSTRACT FROM AUTHOR]

'Internal spacetime' is a modification of general relativity that was recently introduced as an approximate spacetime geometric model of quantum nonlocality. In an internal spacetime, time is stationary along the worldlines of fundamental (dust) particles. Consequently, the dimensions of tangent spaces at different points of spacetime vary, and spin wavefunction collapse is modeled by the projection from one tangent space to another. In this paper, we develop spinors on an internal spacetime, and construct a new Dirac-like Lagrangian ℒ = ψ ̄ (i ∂ / − ω ̂) ψ whose equations of motion describe their couplings and interactions. Furthermore, we show that hidden within ℒ is the entire standard model: ℒ contains precisely three generations of quarks and leptons, the electroweak gauge bosons, the Higgs boson, and one new massive spin- 2 boson; gluons are considered in a companion paper. Specifically, we are able to derive the correct spin, electric charge, and color charge of each standard model particle, as well as predict the existence of a new boson. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the accelerated expansion of the Universe in the context of f (Q) modified theory of gravity, where Q is a non-metricity scalar which characterizes the gravitational interaction by using parametrization of the deceleration parameter q = α − β H with f (Q) = ξ + λ Q , where ξ and λ are free parameters constrained by the 57 points of H (z) datasets, 1048 points of Pantheon, 10 points from Baryon Acoustic Oscillations (BAO) datasets and the shift parameters from Planck 2018 of Cosmic Microwave Background (CMB). In the purpose of validating our model, we proceed by the Om diagnostic and the energy conditions. Later we discussed how our model statistically supports Λ CDM using AIC c criterion analysis. [ABSTRACT FROM AUTHOR]

Several spacetime metrics in teleparallel geometry of Einstein like unified field theory (UFT) are presented. Cosmic magnetic fields are obtained in terms of the early universe torsion and other stages of the universe. For example, in one of the metrics, integration of the 2-form torsion 0-component is written in terms of magnetic flux, from Faraday's induced equation. These ideas were obtained from a recent paper we published [Class. Quantum Grav. (2015)] on non-stationary teleparallel metrics, where at coherent length of 1 0   kpc a magnetic field of 1 0 − 2 7   Gauss is obtained. At early universe, a torsion of 1   MeV leads us to a magnetic field of the order of 1 0 2 1   Gauss which is weaker than the Bierman battery effect magnetic field of the order of 1 0 3 0   Gauss. Hence this new metric indicates that unifield theory metrics a la Schrödinger may be used to obtain primordial magnetic fields. Other tests of this metric led to the nowadays magnetic field of 1 0 − 3 8   Gauss from the torsion at present universe (at the laboratory using dual maser obtained by Kostelecky et al. [Phys. Rev. Lett.]) of 1 0 − 3 1   GeV. Cartan torsion has been frequently associated to topological defects in crystals or in pseudo-magnetic torsional fields. In this paper, we discuss how from teleparallel gravity one may obtain a theory of electromagnetism from metrics in spacetime. Topological defects given by Letelier [Class. Quantum Grav.12 (1995) 1133] and Tod [Class. Quantum Grav.11(5) (1994)] metrics can also be associated with pseudo-magnetic fields. Electromagnetism is geometrized via a bimetric theory of gravity where one metric is responsible for Ampere's law and the other by the Faraday induction equation which gives rise to dynamo equation. [ABSTRACT FROM AUTHOR]

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]

We introduce in this paper a tomographic analysis of the properties of a Friedmann–Lemaitre–Robertson–Walker (FLRW) universe with a perfect fluid. We first review previous works where the Schutz's parametrization in terms of Clebsch potentials was adopted to describe the perfect fluid. This approach allows to introduce a fiducial time in the Wheeler–De Witt equation. We revisit the properties of the perfect fluid and the introduced Clebsch potentials. In particular, we see that thermasy plays an extremely important role in the definition of fiducial time. The definition of a time and the condition a ≥ 0 for the expansion factor imply that the Hamiltonian operator must be self-adjoint which implies a restriction on the initial conditions for the wave packet. We show that these allow to obtain well-defined tomograms. Tomograms are marginal functions which incorporate all the information contained in the wave function of the universe, but have the properties of classical probability functions. They can be defined for classical distributions on the phase space as well, enabling us to describe quantum and classical states with the same family of functions. The aim of this paper is to compare the difference between classical tomograms where the Hawking and Penrose theorems imply the inevitability of an initial singular state and the well-defined initial quantum states found in literature. Finally the introduction of a time in the Wheeler–DeWitt allows us to consider the evolution of the classical and quantum initial states of the universe which can be accomplished by introducing a transition probability function for tomograms. [ABSTRACT FROM AUTHOR]

The order horismos induces the Zeeman topology, which is coarser than the Fine Zeeman Topology . The causal curves in a spacetime under are piecewise null. is considered to be the most physical topology in a spacetime manifold , as the group of homeomorphisms of is isomorphic to the group of homothetic transformations of . was used in the a ambient boundary-ambient space cosmological model, in order to show that there is no possibility of formation of spacetime singularities. In this paper, we question this result, by reviewing the corresponding papers, and we propose new questions toward the improvement of this model. [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]

In this paper, we have investigated a spatially homogeneous and anisotropic accelerating Universe in Lyra's geometry. Einstein's field equations are solved explicitly by assuming dependent relation among the directional scale factors. In this paper, we use observational H (z) data (OHD) and Pantheon compilation of recent type Ia supernovae (SN Ia) data to constrain the model parameters of the Universe in derived model. We constrained the present value of Hubble parameter H 0 and deceleration parameter q 0 as H 0 = 6 9. 3 9 − 0. 7 8 + 0. 9 0 km/s/Mpc and q 0 = − 0. 5 8 3 − 0. 0 0 9 + 0. 0 1 0 together with transition redshift z t = 0. 6 6 − 0. 0 4 + 0. 0 5 . We have also constrained the present age of the Universe in close vicinity of its observational value. Furthermore, we diagnose the statefinder parameters to know a geometrical discrimination of this model with standard Λ CDM model. Some physical aspects of the Universe are also discussed. [ABSTRACT FROM AUTHOR]

This paper studies (2 + 1) -dimensional stochastic chiral nonlinear Schrödinger equation dynamically. A number of novel solutions such as periodic, singular, dark and bright solitons solutions are retrieved. The extraction of these solutions is helped by three efficient and robust integration tools such as the Kudryashov's R function method, Jacobi elliptic function method (JEFM) and the modified auxiliary equations (MAE) method. The parametric constraints for the existence of such solutions are also listed. Moreover, 3D plots of few obtained solutions are presented in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we present a static solution for the five-dimensional Einstein–Gauss–Bonnet (EGB) gravitational field equations with a cylindrical symmetry and an anisotropic fluid as a source. We consider whole set of equations in the interior space which sourced by static cylindrical anisotropic fluid and junction conditions required for smoothly matching with exterior space which is a cylindrical vacuum solution of five dimensional EGB equation. We achieve density and pressures as functions of cylindrical radial coordinate and give some graphically analysis under numerical solution. [ABSTRACT FROM AUTHOR]

In this paper, a generalized Darboux transformation is obtained for Fordy–Kulish NLS (nonlinear Schrödinger) systems on general Hermitian symmetric spaces in order to rigorously obtain rogue wave solutions for these systems. In particular, we express the generalized algebraic relations in a simple and elegant compact form. As an illustration, we derive multi-soliton, breather-type and mainly rogue wave solutions of triangular patterns for single- and multi-component NLS systems on C P 1 and S P (2) / U (2) , respectively. We also analyze the modulation instability of proper plane wave solutions. In order to get visual intuition for the dynamics of the result and solutions for the running examples, the associated simulations of profiles are furnished as well. [ABSTRACT FROM AUTHOR]

It is shown in this paper, that if the Einstein Equivalence Principle is valid on a particular metric theory of gravitation in a spherically symmetric space-time, then the time metric component is not equal to the negative of the inverse radial one unless the underlying potential is inversely proportional to the radial coordinate. At the weak field limit of approximation, a general formula is calculated and applied to some useful cases. [ABSTRACT FROM AUTHOR]

In this paper, we have explored the thermodynamic properties of static Modified Bardeen black hole in the background of Anti-de Sitter (AdS) extended phase space. Thermodynamic pressure is taken as a thermodynamic variable, defined by the negative cosmological constant. We have discussed the thermodynamic quantities like Hawking temperature, Gibbs energy and Helmholtz free energy along with specific heat capacity to analyze the stability. Next, Joule–Thomson expansion has been evaluated to determine cooling-heating phase transition. Followed by these, we have constructed a new heat engine where the black hole is considered as the working substance. We have determined the efficiency through a heat cycle in the P - V plane. As a result, we have been able to show the efficiency of a new heat engine and measure it against the Carnot efficiency. After evaluating the efficiency of the Rankine cycle, the paper has been concluded with a comparison analysis between the heat engine efficiencies of Modified Bardeen AdS Black hole and Regular Bardeen AdS Black hole. [ABSTRACT FROM AUTHOR]

In this paper, we prove that all spherically symmetric Landsberg surfaces are Berwaldian. We modify the classification of spherically symmetric Finsler metrics, done by the author in [S. G. Elgendi, On the classification of Landsberg spherically symmetric Finsler metrics, Int. J. Geom. Methods Mod. Phys. 18 (2021)], of Berwald type of dimension n ≥ 3. Precisely, we show that all Berwald spherically symmetric metrics of dimension n ≥ 3 are Riemannian or given by a certain formula. As a simple class of Berwaldian metrics, we prove that all spherically symmetric metrics in which the function ϕ is homogeneous of degree − 1 in r and s are Berwaldian. [ABSTRACT FROM AUTHOR]

The aim of this paper is to characterize almost co-Kähler manifolds and co-Kähler three-manifolds whose metrices are the gradient ρ -Einstein solitons. At first we prove that a proper (κ ̃ , μ ̃) -almost co-Kähler manifold with κ ̃ < 0 does not admit gradient ρ -Einstein soliton. It is also shown that if a proper -Einstein almost co-Kähler manifold with constant coefficients admits a gradient ρ -Einstein soliton, then either the manifold is a K -almost co-Kähler manifold or the soliton is trivial. Next, we prove that in case of co-Kähler three-manifold the manifold is of constant scalar curvature. Moreover, either the manifold is flat or the gradient of the potential function is collinear with the Reeb vector field ξ. Finally, we construct two examples to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper looks at how changes of coordinates on a pseudo-Riemannian manifold induce homogeneous linear transformations on its tangent spaces. We see that a pseudo-orthonormal frame in a given tangent space is the basis for a set of Riemann normal coordinates. A Lorentz subgroup of the general linear transformations preserves this pseudo-orthonormality. We borrow techniques from the methodology of non-linear realizations to analyze this group-subgroup structure. "Parallel maps" are used to relate tangent space at different points. "Parallelisms" across a finite region of the manifold may be built up from them. These are used to define Weitzenböck connections and Levi-Civita connections. This provides a new formulation of teleparallel gravity, in which the tetrad field is viewed as a field-valued group element relating the coordinate basis to the frame basis used in defining a parallelism. This formulation separates the metric degrees of freedom from those associated with the choice of parallelism. The group element can be combined by matrix multiplication with Lorentz transformations of frame or with other Jacobian matrices. We show how this facilitates a new understanding of inertial forces and local Lorentz transformations. The analysis is also applied to translations of the coordinates. If they are constant across spacetime, this has no effect on the tangent space bases. If the translation parameters become fields, they induce general linear transformations of the coordinate basis; however, the tetrad components can only be expressed in terms of translations on a flat spacetime. [ABSTRACT FROM AUTHOR]

In this paper, we developed, in detail, the geometric structure of a certain type of geometry usually used in physical applications. This paper contains building blocks (BB), tensors of different orders, curves admitted by the geometry and a comparison between this geometry and others used in the literature. Second-order symmetric and skew-symmetric tensors, usually used for physical applications in the context of the geometrization philosophy, are given. Also, in the framework of the same philosophy, the admitted curves can be used as equations of motion of test particles for any field theory constructed in this geometry. [ABSTRACT FROM AUTHOR]

Recently, Barrow et al. showed that chaotic dynamical systems may be obtained from small fluctuations of torsion in cosmological plasmas. Following this idea our goal in this paper is to show analytically that torsion fluctuations in primordial plasmas induce chiral fluctuations, magnetic field fluctuations, dynamo plasma instabilities, as well as rapid oscillations in the chiral plasma. These phenomena are important in plasma relaxation to allow for a plasma dynamo instability to induce a lower electric voltage in plasmas. This phenomenon is induced in Minkowskian plasma physics, but to our knowledge it is proved for the first time in Einstein–Cartan sort of cosmology. In cosmological models where torsion gravity and electromagnetic fields are non-minimally coupled, dynamo instability is obtained when conductivity fluctuations are driven by torsion. Moreover, symmetry breaking of plasmas is shown here to be obtained from conductivity torsion fluctuations, which serves to bypass Zeldovich anti-dynamo theorem, inducing a dynamo onset, as shown recently in domain planar walls [L. Garcia de Andrade, Einstein–Cartan spin-polarised nucleons in domain wall dynamos, Ann Phys. (N.Y.) 432 (2021) 168558.]. Moreover, chiral charge fluctuations are shown to be induced by torsion fluctuations. It is shown that chiral charges may vanish, whereas the effective chiral charges may be driven by torsional fluctuations. It is also shown that dynamo electric field induces a magnetic helicity which oscillates and dynamo action is shown to dominate oscillations. This agrees with the results obtained from loop voltage. Chiral effective charges' fluctuations are derived to be proportional to the product of anisotropic conductivity and magnetic field fluctuations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Jacobi stability of the Shimizu–Morioka model by using the KCC-theory. First, by associating the nonlinear connection and Berwald connection, five geometrical invariants of the dynamical model are obtained. Furthermore, the Jacobi stability of the Shimizu–Morioka model at equilibrium is studied in terms of the eigenvalues of the deviation curvature tensor. It shows that the three equilibria are always Jacobi unstable. Finally, the dynamical behavior of the components of the deviation vector is discussed, which geometrically characterizes the chaotic behavior of studied model near the origin. It proved the onset of chaos in the Shimizu–Morioka model. [ABSTRACT FROM AUTHOR]

This document is a correction notice for an article titled "Curvature inheritance symmetry on M-projectively flat spacetimes" published in the International Journal of Geometric Methods in Modern Physics. The authors have noted that the results presented in Section 3 of the paper hold for perfect fluid spacetimes in general, not just M-projectively flat spacetimes. Therefore, the term "M-projectively flat" should be removed from the heading, contents of Section 3, abstract, and introduction. The correct form of Equation (26) is also provided in the correction notice. [Extracted from the article]

In this paper, we introduce two new shape functions of wormholes in f (R , T) gravity. Both shape functions are satisfied by various geometric conditions. We will also discuss the different energy conditions and geometric behavior corresponding to each shape function in different states. Finally, we investigate the system's stability with a solution corresponding to the two shape functions. [ABSTRACT FROM AUTHOR]

Based on the new macroscopic two-velocity difference model, this paper analyzes the linear stability of the new model and studies the nonlinear bifurcation theory. First, the linear stability analysis method is used to study the stability conditions of the shock wave in the model. Then, considering the long wave model in the coarse-grained scale, the reduced perturbation method is used to analyze the characteristics of the traffic flow in the metastable region, and the solitary wave solution of the Korteweg-de Vries (KdV) equation in the metastable region is derived. In addition, by using the bifurcation analysis method, the type, and stability of the equilibrium solution are discussed and the existing conditions of the saddle-node bifurcation are proven. Then, taking the saddle-node bifurcation as the starting point, we draw the density space-time diagram and phase plane diagram of the system. It is proven that the newly proposed model can describe complex traffic phenomena such as stop-and-go and sudden changes in stability, which is of great help to solve traffic congestion. [ABSTRACT FROM AUTHOR]

This paper reviews the persistent rigid-body motions and examines the geometric conditions of the persistence of some special frame motions on a slant helix. Unlike the Frenet–Serret motion on general helices, the Frenet–Serret motion on slant helices can be persistent. Moreover, even the adapted frame motion on slant helices can be persistent. This paper begins by explaining one-dimensional rigid-body motions and persistent motions. Then, it continues to present persistent frame motions in terms of their instantaneous twists and axode surfaces. Accordingly, the persistence of any frame motions attached to a curve can be characterized by the pitch of an instantaneous twist. This work investigates different frame motions that are persistent, namely frame motions whose instantaneous twist has a constant pitch. In particular, by expressing the connection between the pitch of Frenet–Serret motion and the pitch of adapted frame motion, it demonstrates that both the Frenet–Serret motion and the adapted frame motion are persistent on slant helices. [ABSTRACT FROM AUTHOR]

The movement of a thin vortex in a thin viscous fluid by the motion of a curve propagating in Lorentz–Minkowski space E 1 3 is described by the vortex filament or smoke ring equation and can be viewed as a dynamical system on the space curves in E 1 3 . This paper investigates the harmonic evolute surfaces of time-like Hasimoto surfaces in E 1 3 . Also, we discuss the geometric properties of these surfaces, namely, we obtain the Gaussian and mean curvatures of the first and second fundamental forms. As a verification, we construct a concrete example for the meant surfaces to demonstrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this expository paper, we want to give a brief introduction, with few key references for further reading, to the inner functioning of the new and successful algorithms of Deep Learning and Geometric Deep Learning with a focus on Graph Neural Networks. We go over the key ingredients for these algorithms: the score and loss function and we explain the main steps for the training of a model. We do not aim to give a complete and exhaustive treatment, but we isolate few concepts to give a fast introduction to the subject. We provide some appendices to complement our treatment discussing Kullback–Leibler divergence, regression, Multi-layer Perceptrons and the Universal Approximation theorem. [ABSTRACT FROM AUTHOR]

This paper is intended to review the consequences of assuming tachyon scalar field as a candidate for dark energy from dynamical system technique and observational cosmology point of views. In the contexts of general relativity and teleparallel gravity, a variety of non-minimally coupled tachyon fields have been taken into consideration. These models provide us subclasses of scalar-tensor and scalar-torsion theories. This review covers the tachyonic chameleon, the non-minimally coupled tachyon field to the Gauss–Bonnet invariant and the tachyonic teleparallel dark energy models. Type Ia supernovae and baryonic acoustic oscillations datasets are the observational data that have been used to constrain the model parameters. [ABSTRACT FROM AUTHOR]

The theory of Hybrid metric-Palatini gravity was proposed by Harko et al. [Metric-Palatini gravity unifying local constraints and late-time cosmic acceleration, Phys. Rev. D 85 (2012) 084016.] in 2012 which could explain both local and cosmological observations. In this paper, this theory has been taken into account to obtain static, spherical, and symmetric charged traversable wormhole solutions. The shape of the wormhole is determined in two different cases with the simplest form of scalar field potential. It is obtained that asymptotically flat wormholes are possible in each case. The energy conditions, namely, null, weak, and strong energy conditions are tested in each case and the results are compared. [ABSTRACT FROM AUTHOR]

This research paper is an investigation of dark energy nature of logarithmic f (R , T) -gravity cosmology in a flat FLRW space–time universe. We have derived modified Einstein's field equations for the function f (R , T) = R − 1 6 π G α ln (T) where R is the Ricci scalar curvature, T is the trace of the stress energy momentum tensor, and α is a model parameter. We have solved field equations in the form of two fluid scenarios as perfect fluid and dark fluid, where dark fluid term is derived in the form of perfect fluid source. We have made an observational constraint on the cosmological parameters Ω (m) , ω (de) and H 0 using χ 2 test with observational datasets like Pantheon sample of SNe Ia and H (z). With these constraints, we have discussed our model with deceleration parameter q , energy parameters Ω (m) , Ω (de) , EoS parameter ω (de) , etc. Also, we have done Om diagnostic analysis. The derived f (R , T) model shows a quintessence dark energy model ω (de) > − 1 and late-time universe approaches to Λ CDM model. [ABSTRACT FROM AUTHOR]

This paper explores the existence of static wormholes in 4-Dimensional Einstein Gauss–Bonnet (4D EGB) gravity. We discuss some possibilities for constructing radial-dependent shape functions via different strategies to develop some non-conventional wormhole geometries by considering anisotropic matter sources. In this regard, we assume a specific form of the equation of state and investigate its effects on Gauss–Bonnet (GB) coupling parameter. Next, we impose a traceless condition on the anisotropic fluid distribution as well as radial-dependent energy density profile to explore wormhole geometries as separate cases. It is seen that the obtained results can be reduced into Morris–Throne wormholes for the zero value of GB-coupled parameter for anisotropic fluid distribution. Furthermore, we scrutinize flaring-out conditions and examine asymptotically flatness constraints for the existence of wormholes. Our analysis shows that the weak energy condition (WEC) is satisfied for a particular range by constraining GB-coupled parameter. We study the dynamics of GB-coupled parameter for both cases μ > 0 and μ < 0. It is concluded that wormhole solutions are possible for μ > 0 and, in some cases, μ < 0. The active gravitational mass of developed wormholes is calculated and plotted graphically. The wormhole geometry is discussed by plotting 2D and 3D embedding diagrams. In order to analyze the complexity of the system, we have plotted the complexity factor for each wormhole. [ABSTRACT FROM AUTHOR]

In this paper, we define the notion of Bott connection in the Heisenberg group (ℍ 3 , g) and derive the expression of the Bott connection by using the Levi-Civita connection. Moreover, we derive the expressions of killing vector fields by using the killing equation and obtain some explicit formulas for killing magnetic curves associated to the Bott connection. Furthermore, we give some examples of killing magnetic curves. [ABSTRACT FROM AUTHOR]

In [S. Liu and Y. Wang, A Kastler–Kalau–Walze type theorem for the J-twist DJ of the Dirac operator, preprint (2022), arXiv:2203.10467], the authors proved a Kastler–Kalau–Walze type theorem for the J -twist D J of the Dirac operator on 3 -dimensional and 4 -dimensional almost product Riemannian spin manifold with boundary. In this paper, we develop the Kastler–Kalau–Walze type theorem for the J -twist D J of the Dirac operator on a 6 -dimensional almost product Riemannian spin manifold with boundary. [ABSTRACT FROM AUTHOR]

In this paper, we present a different technique for investigating spherical S t -microfluidic optical mKdV electromotive ϕ (r) , ϕ (t) , ϕ (n) forces in 2. Then, we give some relations for ferromagnetic spherical S t -microfluidic optical mKdV magnetic ϕ (r) , ϕ (t) , ϕ (n)  flux density. Ferromagnetic spherical S t -microfluidic optical mKdV magnetic ϕ (r) , ϕ (t) , ϕ (n) flux surface model. Finally, we obtain spherical S t -microfluidic optical mKdV magnetic ϕ (r) , ϕ (t) , ϕ (n) flux density. [ABSTRACT FROM AUTHOR]