International Journal of Geometric Methods in Modern Physics

The goal of this paper is to study conformal almost Ricci solitons within the framework of Kenmotsu manifolds. First, we demonstrate that if the potential vector field is Jacobi along the Reeb vector field, then the soliton reduces to a conformal Ricci soliton. If the manifold is $\eta$-Einstein Kenmotsu manifold, we show that either the manifold is of constant scalar curvature or the potential vector field is an infinitesimal contact transformation. In addition, if we consider the soliton vector field as a contact vector field, then either the gradient of $\lambda$ is pointwise collinear with the Reeb vector field or the manifold becomes $\eta$-Einstein. Lastly, we develop an example of a conformal almost Ricci soliton on the Kenmotsu manifold.

We revisit the relativistic (2+1)-dimensional Lee model on flat space in light-front coordinates and on a space-time with a spatial section given by a compact manifold, in the usual canonical formalism. The simpler 2+1 dimension is chosen because renormalization is needed only for the mass difference but not required for the coupling constant and the wave function. The model is constructed non-perturbatively based on the resolvent formulation [B. T. Kaynak and O. T. Turgut, The relativistic Lee model on Riemannian manifolds, J. Phys. A: Math. Theor. 42(22) (2009) 225402]. The bound state spectrum is studied through its “principal operator” and bounds for the ground state energy are obtained. We show that the formal expression found indeed defines the resolvent of a self-adjoint operator–the Hamiltonian of the interacting system. Moreover, we prove an essential result that the principal operator corresponds to a self-adjoint holomorphic family of type-A, in the sense of Kato.

We develop a complex fermionic field-based method to model the properties of the filled bands of topological two-dimensional (2D) matter with time reversal (TR)-symmetry. Using this fermionic representation, we give an explicit calculation of the ${\mathbb{Z}}_2$ index for 2D topological matter invariant under TR and comment on the emergence of Majorana states at the TR-fix points. Moreover, motivated by recent theoretical results on possible signatures of topological supersymmetric matter, we also give the supersymmetric generalization of our TR-invariant construction and calculate the underlying topological ${\mathbb{Z}}_2$ index. Other features such as the topological obstruction of basis sections in the fermionic determinant bundle are also investigated. Applications for the calculations of the supersymmetric charge ${\widehat{Q}}_{\mathrm{\text{susy}}}$ operator and the super-Hamiltonian ${Ĥ}_{\text{susy}}$ for the three-dimensional topological class AII are undertaken; these operators are given by Eqs. (5.48)–(5.51).

The formalism of geometrothermodynamics has been developed to describe the properties of thermodynamic systems in terms of concepts of differential geometry. On the other hand, in econophysics, it is argued that under certain conditions the behavior of economic systems can be described by using the laws of classical thermodynamics. These two results are used in this work to propose a geometric description of economic systems. We obtain as a result that most systems can be described by two different geometries corresponding to the Boltzmann–Gibbs and Pareto distributions, which represent two different population groups that are usually present in most economic systems. The geometrothermodynamic analysis shows that no phase transitions are present in the Boltzmann–Gibbs sector, whereas the Pareto sector is characterized by a strong thermodynamic interaction that leads to the appearance of a rich phase transition structure. We argue that those phase transitions could be interpreted as financial crises.

The aim of this work is to discuss the evolution of compact stars from the view point of a string fluid in Rastall theory using Krori–Barua (KB) metric as interior geometry. The exterior spacetime is considered as Schwarzschild metric while matching of interior and exterior spacetimes lead to coefficients of KB ansatz. The field equations and dynamical variables of the string fluid are explored. We found the values of Rastall parameter $\eta$ for which the dynamical variables satisfy the energy conditions which shows the existence of physical matter. The model is applied to specific physical features including energy conditions, anisotropy, stability, Tolman–Oppenheimer–Volkoff equation, mass function, compactness and redshift of compact stars, in particular, SAX J1808.4-3658, Vela X-12 and Hercules X-1. It is found that the presented model fulfills all the physical requirements and thus, is realistic. We conclude that the string fluid is responsible for the evolution of compact stars in the cosmos.

We study the trivialization and the reduction of Tulczyjew’s triplet, in the presence of a symmetry and an Ehresmann connection associated to it. We thus establish a geometric pathway for the Legendre transformations on singular dynamical systems.

In this work, we solve the radial Schrödinger wave equation in three dimensions under Aharonov–Bohm (AB)-flux field with potential superposition of generalized q-deformed Hulthen potential, Coulomb potential, and inverse quadratic Yukawa potential in a point-like defect. We determine the approximate eigenvalue solution using the parametric Nikiforov–Uvarov (NU) method and analyze the effects of topological defect and the magnetic flux field with this superposed potential. We show an analogous of the AB effect because the eigenvalue solution depends on the geometric quantum phase and bound state solutions are possible under condition. Finally, we utilize the approximate eigenvalue solution to some molecular potential models, such as Deng–Fan potential and inverse quadratic Hulthen potential and analyze the effects on the energy levels and the radial wave functions.

The purpose of this paper is to examine the anisotropic matter distribution concerning one of the well-known $f(R,T)$ theories of gravity, where $R$ and $T$ represent the Ricci scalar and trace of the energy–momentum tensor, respectively. We consider anisotropic matter distribution in spherically symmetric spacetime for our desired work. We investigate the physical behavior of pressure components, energy density, anisotropic function, equation of state parameters, and energy conditions. Furthermore, we analyze the stability of compact stars by investigating the causality condition, adiabatic index, and generalized Tolman–Oppenheimer–Volkoff equation. Some fundamental features of compact stars have been investigated, like compactness factor, mass function, and surface redshift. Our calculated solutions for Bardeen stellar structures are consistent and stable in the background of the $f(R,T)$ theory of gravity.

Based on the two-component Hirota and Maxwell–Bloch (H-MB) system, which describes the propagation of ultra-short pulses in erbium-doped nonlinear optical fibers, we derive two kinds of two-component nonlocal H-MB (NH-MB) systems by choosing suitable symmetries, namely $PT$-symmetric two-component NH-MB system and reverse space-time two-component NH-MB system. Then the explicit solutions of these two systems are obtained by the Darboux transformation.

Here, I introduce a method to obtain the stress-energy tensor of the perfect fluid by adding a suitable term to the Einstein–Hilbert action. This term has the physical interpretation of pressure and variation should be understood with respect to the metric. In this derivation, velocity potentials are not needed.

The Kantowski–Sachs cosmological model for viscous generalized Chaplygin gas has been investigated in the Brans–Dicke theory of gravitation. To determine the solutions of field equations, we have considered the power-law relation for the average scale factor. We have computed some cosmological parameters and discussed their physical importance. Furthermore, we have discussed the nature of statefinder and $Om$ diagnostics in our model. It is also worth noting that the conclusions of the cosmological parameter are consistent with modern observational data.

We regard the cosmological fluid within an exponentially expanding FLRW spacetime as the probability fluid of a nonrelativistic Schroedinger field. The scalar Schroedinger particle so described has a mass equal to the total (baryonic plus dark) matter content of the Universe. This procedure allows a description of the cosmological fluid by means of the operator formalism of nonrelativistic quantum theory. Under the assumption of radial symmetry, a quantum operator proportional to $1/r^2$ represents the cosmological constant $\mathrm{\Lambda }$. The experimentally measured value of $\mathrm{\Lambda }$ is one of the eigenvalues of $1/r^2$. Next we solve the Poisson equation ${\nabla }^{2}U=\mathrm{\Lambda }$ for the gravitational potential $U(r)$, with the cosmological constant $\mathrm{\Lambda }(r)=1/r^2$ playing the role of a source term. It turns out that $U(r)$ includes, besides the standard Newtonian potential $1/r$, a correction term proportional to $lnr$ identical to that appearing in theories of modified Newtonian dynamics.

A Finsler metric is geodesically reversible if geodesic remain geodesics after a change of orientation. For a reversible Minkowski space, we alter the geodesically reversible Finsler metric without conjugate points in a strictly convex compact subset and show that its central symmetrization is geodesically conjugate to the original reversible Minkowski norm.

In this paper, we investigate non-inertial effects induced by a rotating frame on a non-relativistic quantum harmonic oscillator as well as of the topology associated to a screw dislocation, which corresponds to a distortion of a vertical line into a vertical spiral. To do this, we obtain the analytical solutions of the time-independent Schrdinger equation for this harmonic oscillator potential in this background. The expressions for the energy spectrum are obtained and the solutions for four quantum states, namely, $n=0,1,2$ and $3$, are analyzed. Our results show that the presence of the topological defect (screw dislocation) as well the fact that we are analyzing the system from the point of view of a rotating frame, changes the solutions of Schrdinger equation and the corresponding spectrum. Now these quantities depend on the angular velocity of the rotating frame, $\mathrm{\Omega }$, and also on the parameter $\beta$, which codifies the presence of the screw dislocation. Particularly, with respect to the energy spectrum of the system the changing is such that when $\mathrm{\Omega }$ increases, the energy can increase or decrease depending on the values we assign to the eigenvalues of the angular and linear momenta. Additionally, we observe that the values of the parameter $\beta$ that characterizes the screw dislocation cause a shift in the energy spectrum.

This paper inspects the impact of minimal matter-geometry coupling present in $R+\alpha R^2+\gamma T$ model of $f(R,T)$ theory on the physical attributes of anisotropic quark stars. The geometry of considered stellar candidates is modeled via spherically symmetric static spacetime whose metric functions are influenced by Heintzmann solutions. The inner matter distribution of the stellar system is assumed as anisotropic with the phenomenological MIT bag model equation of state. The expressions of unknown parameters that appear in Heintzmann solution are evaluated in terms of mass and radius by the continuity of interior and exterior geometries. Further, insertion of masses and radii of some particular observed stellar models will yield their numerical values. In order to discuss the physical acceptability as well as stability of the quarks stars based on the considered solutions, we have checked the physical behavior of matter variables, mass and related quantities, energy conditions, equilibrium of forces, adiabatic index and Herrera’s cracking concept. The energy conditions are fulfilled ensuring the compatibility of assumed matter and geometry of quark stars. It is also found that all compact star candidates exhibit stable structures corresponding to the proposed values of the model parameters. Hence, the considered $f(R,T)$ model shows consistency with all the physical conditions and presents a viable study to the nature of anisotropic massive stellar system.

We present principles of Measurement Quantization (MQ) and approaches to measurement that support the discreteness of measure. Several claims are addressed. Notably, that measure is discrete with respect to the internal frame, non-discrete with respect to the system frame and that length is contracted due to the discreteness of measure. We address the relation of angular measure to momentum, the physical significance of count bounds and that the fundamental measures — more precise expressions for Planck’s units — are an emergent property of the internal frame. Quantum experiments by Shwartz, et. al and CODATA provide physical support. We predict and derive values for elementary charge and the gravitational, Hubble, reduced Planck, electric, magnetic, Coulomb, and fine structure constants. We then correlate gravity with electromagnetism (unification). We present expressions for galactic rotation, dark matter, dark energy, and accelerating expansion. MQ advances over Loop Quantum Gravity with two frames, the difference which leads to the physical constants and the laws of nature. We correlate the quantum and cosmological, describing an inflation free quantum epoch, why it ceases and expansion. Therein are solutions to the horizon problem and homogenous, isotropic properties of the universe. Predictions include length contraction unrelated to special or general relativity (SR/GR), 13-digit measures of the gravitational constant, the Planck momentum, and universal mass accretion. A calculation of CMB age, quantity, present-day density and temperature provides additional support. Also offered, discrete solutions to the size and age of the universe, ground state orbital, SR, GR, and equivalence.

In this paper, we initiate the study of critical point equation and *-critical point equation within the substructure of Sasakian manifolds. We prove that if a compact Sasakian manifold admits CPE, then either the manifold is Einstein or the potential function is harmonic in an open subset. Later, we demonstrate that if the manifold satisfies *-CPE, it is $\eta$-Einstein and obtain an expression for the *-Ricci tensor. Finally, we construct an example to illustrate the existence of CPE and *-CPE on the Sasakian manifold.

Both algebraic equations $\mathrm{\text{Det}}(\widehat{p}-m)=0$ and $\mathrm{\text{Det}}(\widehat{p}+m)=0$ for $u$- and $v$- 4-spinors have solutions with $p_0=\pm E_p=\pm \sqrt{p^2+m^2}$. The same is true for higher-spin equations (or they may even have more complicated dispersion relations). Meanwhile, every book considers the equality $p_0=E_p$ for both $u$- and $v$-spinors of the $(1/2,0)\oplus (0,1/2))$ representation only, thus applying the Dirac–Feynman–Stueckelberg procedure for elimination of negative-energy solutions. The recent Ziino works (and, independently, the articles of several other authors) show that the Fock space can be doubled. We re-consider this possibility on the quantum-field level.