International Journal of Geometric Methods in Modern Physics

Is there more to Dirac’s gamma matrices than meets the eye? It turns out that gamma zero can be factorized into a product of three operators. This revelation facilitates the expansion of Dirac’s space-time algebra to Clifford algebra $\mathrm{\text{Cl}}(0,6)$. The resultant rich geometric structure can be leveraged to establish a combined framework of the standard model and gravity, wherein a gravi-weak interaction between the vierbein field and the extended weak gauge field is allowed. Inspired by the composite Higgs model, we examine the vierbein field as an effective description of the fermion–antifermion condensation. The compositeness of space-time manifests itself at an energy scale which is different from the Planck scale. We propose that all the regular classical Lagrangian terms are of quantum condensation origin, thus possibly addressing the cosmological constant problem provided that we exercise extreme caution in the renormalization procedure that entails multiplications of divergent integrals. The Clifford algebra approach also permits a weaker form of charge conjugation without particle–antiparticle interchange, which leads to a Majorana-type mass that conserves lepton number. Additionally, in the context of spontaneous breaking of two global $U(1)$ symmetries, we explore a three-Higgs-doublet model which could explain the fermion mass hierarchies.

In this paper, we focus on geometry of evolutoids and pedaloids for timelike curves and spacelike curves on timelike surfaces. First, by studying an example of a pseudo-circle, we get some properties of timelike curve on timelike surface. Then, we introduce a moving frame along curves and describe the corresponding evolutoids of curves as ruled surfaces. After that, we investigate relationships between pedal surfaces of evolutoids and pedaloids of curves. Moreover, we investigate the singularities of the evolutoids and the pedaloids.

The purpose of this study is to discuss the charged stellar structure in the background of the $f({𝒢})$ theory of gravity. The Einstein–Maxwell equations defined in the appearance of charge by utilizing the Tolman–Kuchowicz spacetime are described by spherically symmetric spacetime. To analyze the charged stellar structure, we use the matching conditions of spherically symmetric spacetime with the Reissner–Nordström exterior metric and develop some expressions for examining the energy density, radial pressure and tangential pressure, respectively. We address the energy conditions to verify our model’s viability for the SAX J1808.4-3658 star. Some other physical features, such as energy density, pressure components, anisotropic parameters, equation of state parameters, stability analysis, adiabatic index, Tolman–Oppenheimer–Volkoff equation, mass-radius relationship, compactness and redshift, have been investigated. We observe that our results are physically viable, free from geometrical and physical singularities, which provide circumstantial evidence for the existence of viable and stable compact star.

All non-equivalent solutions of vacuum Maxwell equations are found for the case when space-time manifolds admit simply transitive four-parameter groups of motions $G_4(N)$. The potentials of the admissible electromagnetic fields admit the existence of the algebra of motion integrals of the Hamilton–Jacobi and Klein–Gordon–Fock equations which is isomorphic to the algebra of the group operators for the same group $G_4(N)$.

In this work, we investigate the quantum dynamics of non-relativistic systems in a Born–Infeld spacetime. We analyze some general scenarios, which concerns the effects of a harmonic oscillator and an inverse square-type potential as well as an Aharonov–Bohm geometric phase. We obtain an analytical solution for the most general case in terms of a confluent Heun function and define the energy spectrum by referring to the ground state, together with its respective eigenfunction. A graphical representation was built so that it was possible to visualize some of the possible energy configurations. For negative values of the Born–Infeld parameter $𝜖<0$, we perform a connection with results of quantum dynamics already investigated in the literature for the Ellis–Bronnikov spacetime.

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: $\text{CPT}$, 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.

In this paper, we give some characterizations by considering ∗-Ricci soliton as a Kenmotsu metric. We prove that if a Kenmotsu manifold represents an almost ∗-Ricci soliton and the potential vector field $V$ is a Jacobi along the Reeb vector field, then it is a steady ∗-Ricci soliton. Next, we show that a Kenmotsu matric endowed an almost ∗-Ricci soliton which is Einstein metric if it is $\eta$-Einstein or the potential vector field $V$ is collinear to the Reeb vector field or $V$ is an infinitesimal contact transformation.

In this work, we investigate Bianchi type I universe in the presence of dark energy and dark matter by three parameterizations of deceleration parameter models, which are considered to find solutions of the models. In the framework of an anisotropic cosmology, we constrain the parameters of these models and compared the results with the $\mathrm{\Lambda }$CDM model, by using the datasets from different observational, namely, the Hubble data and type Ia Supernovae Pantheon data. Additionally, the evolution of kinematic cosmographic parameters is investigated. In particular, we analyze the effects of anisotropy on the physical behavior of our mentioned models and compare them with standard $\mathrm{\Lambda }$CDM model.

This work mainly focuses on modeling the charged compact stars and investigating their properties in the framework of $f(T)$ modified gravity, under the accelerated phase of the universe. In this study, we have introduced the modified gravity and dark matter to culture the evolution of the charged neutron stars by considering the present situation. True knowledge and proper study on the macroscopic parameters of the compact stars are very much needed to realize the microscopic properties and behavior of the core nuclear matter at very high density and pressure. The existence of modified Chaplygin gas as an exotic fluid inside the core of these stars in $f(T)$ gravity plays a very important role inside the stars. We have found out that exotic fluid has a great impact on the equation of state of the core nuclear matter and even on the stability of the compact stars. Pressure anisotropy reduces the tidal deformability of the charged stars in an appreciable amount and helps to get a more compact structure. But surprisingly, the compact stars are still able to maintain their spherically stable and equilibrium configuration. Further, we can put constraints on several macroscopic parameters of the compact stars and can investigate their evolution from our present investigation.

In this paper, we shall discuss the theory of geodesics in information geometry, and an application in astrophysics. We will study how gradient flows in information geometry describe geodesics, explore the related mechanics by introducing a constraint, and apply our theory to Gaussian model and black hole thermodynamics. Thus, we demonstrate how deformation of gradient flows leads to more general Randers–Finsler metrics, describe Hamiltonian mechanics that derive from a constraint, and prove duality via canonical transformation. We also verified our theories for a deformation of the Gaussian model, and described dynamical evolution of flat metrics for Kerr and Reissner–Nordström black holes.

The purpose of this study is to investigate the behavior of charged stellar structures in the $f(R,\varphi )$ theory of gravity, where $R$ denotes the Ricci scalar and $\varphi$ represents the scalar potential, respectively. For our current analysis, we consider Krori–Barua metrics to discuss the spherically symmetric solutions in $f(R,\varphi )$ gravity. We further develop some matching conditions between the spherically symmetric spacetime as interior geometry with Reissner–Nordstrom as exterior geometry. Moreover, we consider the observational data of three distinct stars namely Vela $X-1$, SAX $J1808.4-3658$ and $4U1820-30$ for present work. We investigate the behavior of energy density, radial pressure, tangential pressure, anisotropic parameter, equation of state parameters, equilibrium condition, sound speeds, Abreu’s criteria, adiabatic index and energy conditions respectively. Moreover, we investigate some other properties of the stellar structures including mass-radius relation, compactness factor, and surface redshift. Our investigation reveals that the observed anisotropic findings are physically appropriate and have the highest level of precision in the background of $f(R,\varphi )$ modified theory of gravity.

This paper investigates different kinds of exact solutions of variable-coefficients Chiral Schrödinger equation $\text{(VCCNLSE)}$. In this equation, the fractional quantum Hall effect edge states are described. By the unified method, we successfully get the soliton, solitary and elliptic wave solutions. Through the $(G^{\prime }/G)$-expansion and the exponential expansion methods, we acquire different traveling wave solutions. Using the extended $F$-expansion method, we attain the Jacobi elliptic function solutions. So as to get more physical information about the exact solutions of VCCNLSE, $\text{3D, 2D}$, density and contour maps are described.

The aim of this paper is to study the idea of Clairaut slant Riemannian maps from Riemannian manifolds to Kähler manifolds. First, for the slant Riemannian map, we obtain the necessary and sufficient conditions for a curve to be a geodesic on the base manifold. Further, we find the necessary and sufficient conditions for the slant Riemannian map to be a Clairaut slant Riemannian map; for Clairaut slant Riemannian map to be totally geodesic; for the base manifold to be a locally product manifold. Further, we obtain the necessary and sufficient condition for the integrability of range of derivative map. Also, we investigate the harmonicity of Clairaut slant Riemannian map. Finally, we get two inequalities in terms of second fundamental form of a Clairaut slant Riemannian map and check the equality case.

This paper investigates the mystery of baryogenesis for isotropic and anisotropic universe models in the context of Rastall’s theory of gravity (RTG). In the first part, we utilize the Rastall field equations (FEs) for the flat Friedmann Robertson Walker (FRW) metric to find the solutions of density $\rho$ and Hubble parameter $H$. Additionally, Rastall parameter plays a crucial role to discuss baryogenesis and fulfilling its criteria on the observational ground. It is found that very large positive/negative values of Rastall parameter like $\lambda \ge 10^{54}$ (for $\omega =0$) and $\lambda \le -10^{22}$ (for $\omega =1$) are required to satisfy the observational bounds on baryon asymmetry factor (BAF), see Fig. 1. In the second part, we develop the FEs for RTG using the Locally Rotationally Symmetric (LRS) Bianchi type-1 line-element. Then we find the solutions of the FEs and use them to find the BAF using Rastall parameter as $\lambda \le -10^{37}$ and anisotropic parameter $n\ge 2$ to meet the consistency with the experimental limit, see Fig. 3. For $n=1$, the anisotropic model reduces to the isotropic FRW model, where we have a zero BAF. Finally, we conclude that RTG with both universe models is a good candidate to study baryogenesis in the early universe and the variable $\lambda$ has a considerable impact on the BAF.

We show that the matter Lagrangian of a non-perfect fluid takes the negative or positive value of the total energy density of the fluid, which is composed of the rest plus internal energy densities. The ambiguity of the sign depends on the definition of the matter action and the chosen signature.

The aim of this paper is to introduce the notion of Rota–Baxter mock-Lie bialgebras $(A,\circ ,\delta ,K,Q)$ and their admissibility conditions in terms of dual representations $({\rho }^{\ast },{\beta }^{\ast },V^{\ast })$. Next, we show that Rota–Baxter mock-Lie bialgebras are characterized by matched pairs and Manin triples of Rota–Baxter mock-Lie algebras. Furthermore, the coboundary case leads to the introduction of the admissible mock-Lie Yang–Baxter equation in Rota–Baxter mock-Lie algebras, whose skew-symmetric solutions are used to construct Rota–Baxter mock-Lie bialgebras.

In light of the significance of non-commutative quaternionic algebra in modern physics, this study proposes the existence of the Klein paradox in the quaternionic (3+1)-dimensional space-time structure. By introducing quaternionic wave function, we rewrite the Klein–Gordon equation in extended quaternionic form that includes scalar and the vector fields. Because quaternionic fields are non-commutative, the quaternionic Klein–Gordon equation provides three separate sets of the probability density and probability current density of relativistic particles. We explore the significance of these probability densities by determining the reflection and transmission coefficients for the quaternionic relativistic step potential. Furthermore, we also discuss the quaternionic version of the oscillatory, tunnelling, and Klein zones for the quaternionic step potential. The Klein paradox occurs only in the Klein zone when the impacted particle’s kinetic energy is less than ${𝕍}_0-m_0{c}^2$. Therefore, it is emphasized that for the quaternionic Klein paradox, the quaternionic reflection coefficient becomes exclusively higher than value one while the quaternionic transmission coefficient becomes lower than zero.

In this paper, we construct the exact interior solutions for compact stellar objects for perfect fluid distribution in phantom region in the framework of a non-conserved theory, i.e. Rastall gravity (RG). Under these circumstances, we develop the Einstein field equations (EFEs) for spherically symmetric metric using general forms of metric potentials, $a(r)=B{r}^{\alpha }+C{r}^{\beta }$ and $b(r)=A{r}^{\gamma }$, here $\alpha ,\beta ,\gamma \ge 2$ and $\alpha \ne \beta$. By matching of interior and exterior regions of the metric, we obtain the values of unknown constants of our considering model which helps to sketch the nature of important physical quantities like density, pressure, energy conditions, and stability. Finally, our obtained results lead us to conclude that our solutions are well behaved and physically viable for the specific choices of model parameters for two different stars (Vela X-1 and 4U1820-30).