International Journal of Geometric Methods in Modern Physics

In several classes of modified gravity theories, extra degrees of freedom are not completely screened in the interiors of stellar and substellar objects. In such theories, the hydrostatic equilibrium condition inside these objects is altered. Moreover, the interior structures of these objects might have a small pressure anisotropy induced by several physical phenomena, including rotation and magnetic fields. All these effects, both individually and collectively, induce changes in predicted stellar observables. Such changes have an impact on different phases of the stellar life cycle, starting from its birth to its death, covering almost all the branches of the Hertzsprung–Russell diagram. The aim of this work is to systematically review the current literature on the topic. We discuss the main results and constraints obtained on a class of modified gravity theories.

In the current analysis, we considered a spatially flat FRW universe with $f(Q,T)$ gravity. To understand the dark energy via the equation of state, we start with the phenomenological parametrization of the deceleration parameter $q(z)$. One of the most preferred parametrizations of the dark energy equation of state served as the idea for the deceleration parameter. The best-fit value of $z_t$ (the redshift at which the universe transitions from before decelerating to the present accelerating phase) and the current value of the deceleration parameter are explored. The negative behavior indicates that the universe is accelerating, which can be verified from the combined datasets (CC + SC + unCor BAO). Additionally, we examine the current scenario of the well-reconstructed $q(z)$ and $\omega (z)$ fitting behavior via $\mathrm{\Lambda }$CDM. As we are working within $f(Q,T)$ gravity, so, two specific models like $f(Q,T)=\alpha Q+\beta T$ and $f(Q,T)={\alpha }_1{Q}^2+{\beta }_{1}T$ with $\alpha$, ${\alpha }_1$, $\beta$ model parameters are considered to complete the current analysis. Last, we have concluding remarks regarding the current analysis.

In this study, we investigate the literature on anisotropic stellar spheres in $f(R,\varphi )$ gravity utilizing Tolman–Kuchowicz (TK) spacetime. Due to the existence of anisotropic matter distribution, we derive the equations of motion for spherically symmetric spacetime by taking into account physically accurate formulations of the metric potentials. For this purpose, we develop the matching conditions by comparing them with the exterior solution to determine the TK constants. We have also discussed the graphical analysis of energy density, pressure components, equation of state components, equilibrium condition, and stability analysis. Moreover, other properties of a compact star, like the mass–radius function, compactness, and redshift function, have also been investigated. It is also noticed that energy conditions are satisfied, which justifies that our considered stars are viable. The validity of our proposed model has been proven by studying the development of various physical characteristics, and it is determined that our system is physically stable and free of any singularities.

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.

Quantum theory suggests that the three observed gauge groups U(1), SU(2) and SU(3) are related to the three Reidemeister moves: twists, pokes and slides. The background for the relation is provided. It is then shown that twists generate the group U(1), whereas pokes generate SU(2). Emphasis is placed on proving the relation between slides, the Gell-Mann matrices, and the Lie group SU(3). Consequences for unification are deduced.

The lie group invariance method is used to study a cylindrical shock wave in a self-gravitating, rotating perfect gas in the presence of monochromatic radiation and an azimuthal or axial magnetic field. The density of the ambient medium is taken as variable according as the law of shock path. For the system of equations of motion, the one-dimensional optimal system of subalgebra is determined by using Lie group analysis. We have utilized optimal classes of infinitesimal generators to acquire the flow variable transformation and the similarity variable, which are important prerequisites for obtaining the system of ordinary differential equations from the system of partial differential equations. In detail, we have numerically solved and discussed the results in two cases: with power and exponential laws shock path. The effects of variation of the rotational parameter, gravitational parameter, Alfvén Mach number, adiabatic exponent, and dimensionless parameter that characterize the interaction between incident radiation flux and gas are studied in depth. A comparative study is done between power law and exponential law in respect of the strength of shock wave and the flow variables distribution in the flow-field region behind the shock front. The shock is stronger with an axial magnetic field in a power law case; whereas shock is stronger with an azimuthal magnetic field in an exponential law case. The shock strength is observed to decline when the adiabatic index of the gas or the Alfvén Mach number increases. The shock decay with rotational parameter in case of exponential law, but it strength enhanced in case of power law. Also, the rotational parameter and gravitational parameter have an exact opposite impact on the strength of shock in power law and exponential law cases.

The anomaly cancellation in superstring theory is known to hold at leading order in the curvature for the gauge groups $SO(32)$ and $E_8\times E_8$. The coefficients of the next-to-leading order terms may be evaluated, and a mechanism for cancellation is described, which would remain valid at higher genus when there exists a global splitting of the coordinates of supermoduli space. Since the spin-$\frac{1}{2}$ fields transform under the adjoint representation in these models, compactification of the heterotic string over $G_2/SU(3)$ or a fundamental 12-dimensional theory, from which superstrings are produced through an elliptic fibration, over $\frac{G_2\times SU(2)\times U(1)}{SU(3)\times U{(1)}^{\prime }\times U{(1)}^{\prime \prime }}$, provides another phenomenologically viable theory at lower energies compatible with the standard description of the elementary particle interactions. The 96 spin-$\frac{1}{2}$ fields now would transform under the fundamental representation of $G_2\times SU(2)\times U(1)$ and the spin-one gauge fields would belong to the adjoint representation. The sum of the anomaly polynomials for the particle content of the $G_2\times SU(2)\times U(1)$ model vanishes at $n_{\frac{1}{2}}\simeq 103.34271924$. The contributions to the gravitational anomaly from the particles and antiparticles cancel by the CPT theorem and the duality transformations of polynomials of degree 6 in the curvature and the field strength. The existence of the interaction of a spin-2 charge, which is conserved only over a finite time interval, can be traced to nonlocal terms in the reduction of the string field theory to the gravitational sector. The source of the global gravitational anomaly cancellation in the modular form equations derived from an elliptic fibration of a 12-dimensional theory would restrict the compactifications and provide a method for preserving the absence of anomalies in four dimensions.

In this study, we consider the Bianchi type I model in the framework of $f(R,T)$ gravity theory. We solve the field equations with the help of an anisotropy parameter that can show the anisotropic behavior of the universe in the past and its approximation to isotropy today. For two different models, we examine the phase transition in the expansion of the universe by analyzing some cosmologic parameters. We conduct our investigation by applying the Markov Chain Monte-Carlo analysis and Bayesian technique to the Cosmic Chronometer, Phanteon and BAO datasets, taking into account the observational constraints on the parameters. We show that the two different models we obtained explain the transition from the slowing phase to the accelerating phase in the expansion of the universe, that the models behave in harmony with the $\mathrm{\Lambda }$CDM model today, and that the current values of the cosmological parameters predicted by the models are compatible with the values indicated by the observations and we conclude that the Model-I is more compatible than the Model-II in this conformity.

In this paper, we inspect the stable geometry of thin-shell wormholes in the background of static spherically-symmetric AdS black holes solution bounded by dark fluid and Chaplygin-like equation of state $p=-{ℬ}/\rho$, where $p$ and $\rho$ denote the pressure and energy density that are related through positive constant ${ℬ}$. For this purpose, we consider the two equivalent copies of black holes and connected them at the hypersurface through cut and paste approach. Then, we employ the linearized radial perturbation to discuss the stability of the developed wormhole geometry by assuming variable equations of state. We obtain the maximum stable configuration for massive black holes for both barotropic and Chaplygin variable equations of state while for higher values of $n$, stable regions decrease. It is found that for every selection of physical parameters of black hole geometry with low intensity of Chaplygin dark fluid, we get the stable configuration of thin-shell wormholes.

This paper concerns with the characterization of a spacetime and modified gravity such as $f(R,G)$, $f(R,T)$ and $f(R,L_m)$-gravity equipped with the projective curvature tensor. We establish that a projectively flat perfect fluid spacetime represents dark energy era. Also, we prove that a projectively flat perfect fluid spacetime is either locally isometric to Minkowski spacetime or a de-Sitter spacetime. Furthermore, it is shown that a perfect fluid spacetime admitting harmonic projective curvature tensor becomes a generalized Robertson–Walker spacetime and is of Petrov type $I$, $D$ or $O$. Lastly, we investigate the effect of projectively flat perfect fluid spacetime solutions in $f(R,G)$, $f(R,T)$ and $f(R,L_m)$-gravity, respectively. We also investigate the spacetime as a $f(R,G)$-gravity solution and use the flat Friedmann–Robertson–Walker metric to establish a relation among jerk, snap, and deceleration parameters. Numerous energy conditions are studied in terms of Ricci scalar with the model $f(R,G)=exp(R)+\alpha {(6G)}^{\beta }$. For this model, the strong energy condition is violated but the weak, dominant and null energy conditions are fulfilled, which is in excellent accordance with current observational investigations that show the universe is now accelerating.

In this paper, using the framework of Saez–Ballester theory, Bianchi Type-V metric Tsallis holographic dark energy models with interacting and non-interacting elements have been constructed. To obtain solutions for the model, we used correlation between metric potentials and varying deceleration parameters. There is additional discussion of the models’ physical characteristics and behavior.

The exciton system is described by means of specially constructed coherent states (CS), according to an idea of L.V. Keldysh long ago. The system is analyzed from the geometric point of view and from the relevant symmetry group contained in the displacement operator as generador of the CS system in the Klauder–Perelomov sense. Explicitly important quantities involving the quantum statistics of the system (partition function, mean density n and the Yuen limit) are calculated and briefly discussed in relation to the known case of pure bosons (e.g. photons). The Bogoliubov type transformations for the field operators of the Wannier–Mott type exciton system are presented in an exact way (in sharp contrast with the case of [11] where only a rough approximation was given) showing how these transformations induce nonlinearity (cubic at first order) in the Schrodinger equation of the system. The conditions for a hydrodynamic description of the original Keldysh model, as the possibility of a BEC (Bose–Einstein Condensation), are discussed.

In this study, we take the striction line which only exists on a ruled surface as an optical fiber. We examine Berry phase model of an optical fiber with a geodesic Frenet frame. We find the direction of the polarized light concerning the plane in which the electric field $Ê$ is located. Also, the electromagnetic trajectories of optical fiber are obtained. Finally, we give the electromagnetic flux ruled surfaces formed by the Killing vector fields of the EM-trajectories of the optical fiber and numerical examples.

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.

A quantum injective frame is a frame whose measurements for density operators can be used as a distinguishing feature in a quantum system, and the frame quantum detection problem demands a characterization of all such frames. Very recently, the quantum detection problem for continuous as well as discrete frames in both finite and infinite dimensional Hilbert spaces received significant attention. The quantum detection problem pertaining to the characterization of informationally complete positive operator-valued measures (POVM) can be split into two cases: The quantum injectivity or state separability problem and the rang analysis or quantum state estimation problem. Building upon this notion, this note is aimed at the quantum detection problem for fusion frames. The injectivity of a family of vectors and a family of closed subspaces is characterized in terms of some operator equations in Hilbert–Schmidt and trace classes.

The spherical indicatrix of a ruled surface is the image curve of its rulings on the sphere $S^2$. In this paper, we present Lorentz forces and magnetic curves produced by the Frenet frame $\{T_e,N_e,B_e\}$ of the spherical indicatrix of a ruled surface in a magnetic field. We calculate magnetic vector fields of magnetic curves for $T_e,N_e,B_e$. Furthermore, we define magnetic flux surfaces constructed by magnetic vector fields along magnetic spherical indicatrix. We obtain developability conditions for these surfaces. Finally, we give some examples to show magnetic flux surfaces.

This paper explores the dynamic behavior of the universe within the framework of the $f(R,G)$ theory of gravity. Here, $R$ and $G$ represent the Ricci scalar and Gauss–Bonnet invariant, respectively. By solving the modified field equations with the chosen $f(R,G)$ function, specifically $f(R,G)=R+m{R}^2+n{G}^2$, we determine the best fit values of model parameters that are consistent with recent observational datasets. These datasets include 57 data points from the Cosmic Chronometers, Pantheon, and BAO datasets. Furthermore, we analyze the physical properties of cosmographic parameters, such as energy density and pressure, corresponding to the constrained values of the model parameters. The evolution of the deceleration parameter in our study indicates a transition from a decelerated phase to an accelerated phase in the universe. Remarkably, our $f(R,G)$ cosmological model effectively describes the late-time cosmic acceleration without requiring the introduction of a dark energy component in the field equations.

In this paper, we consider the framework of the newly proposed modified theory of gravity named $f(R,A)$ gravity, wherein $R$ and $A$ signify the Ricci and anticurvature scalars, respectively. For our cosmic discussions, we evaluate a renowned $f(R,A)$ model, incorporating various forms of the scale factor within the context of Friedmann–Robertson–Walker (FRW) spacetime. Our exploration delves into energy conditions, the effective equation of state parameter and the stability of models within the $f(R,A)$ theory. These models are further elucidated through graphical representations plotted against time and their respective model constants. Notably, it is observed that scale factors with exponential terms yield more consistent results in comparison to those of power-law forms, given specific values of model constants.