International Journal of Geometric Methods in Modern Physics

We propose a simple analytical model for Harmonic oscillator potential that is associated to the generalized uncertainty principle (GUP) in the presence of energy-dependent mass. A formal condition connected with these systems is based on the mathematical structure of modified quantum mechanics. Consequently, thanks to Feynman’s path integrals formalism, we are able to treat the reorganization of wave functions. Furthermore, in order to convert this path formalism into a local representation, we will use a coordinate transformation method at different usual point interval, which is what these systems assume. In each application, the propagator is calculated, the wave functions and the energy eigenvalues are obtained with the corresponding curves. The special cases are then deduced.

Implications of the Raychaudhuri equation in focusing of geodesic congruences are studied in the framework of scalar–tensor theory of gravity. Specifically, we investigate the Brans–Dicke theory and Bekenstein’s scalar field theory. In both of these theories, we deal with a static spherically symmetric distribution and a spatially homogeneous and isotropic cosmological model as specific examples. We find that it is possible to violate the convergence condition under reasonable physical assumptions. This leads to the possibility of avoiding a singularity.

We construct a new class of $d$-dimensional black hole solutions with Toroidal horizons in $f(R)$ gravity framework which is surrounded by quintessence and string cloud configuration, whose asymptotic structures are determined by the quintessential state parameter ${\omega }_q$ and dimension’s parameter $d$. We point out that the asymptotic behavior of the obtained solutions is neither asymptotically flat nor (A)dS when we have $\frac{{\omega }_q+2}{{\omega }_q+1}>d$ and $d\le 3$. Regarding the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we investigate the critical behavior of our black hole solutions. In $d=3$ and $Q\ne 0$, the P–V diagrams are more complex than that of the standard Van der Waals. These diagrams behave like the Born–Infeld-AdS P–V diagrams. When $d=3$ and $Q=0$, the P–V diagrams behave like the standard Van der Waals system (In this work [S. Gunasekaran, D. Kubiznaak and R. B. Mann, Extended phase space thermodynamics for charged and rotating black holes and Born–Infeld vacuum polarization, J. High Energy Phys. (2012).] [S. Gunasekaran, D. Kubiznaak and R.B. Mann, Extended phase space thermodynamics for charged and rotating black holes and Born–Infeld vacuum polarization, J. High Energy Phys. (2012)], the authors believe that the BTZ black holes, contrary to the higher-dimensional case, do not show any critical behavior. In this work, we have showed that the three-dimensional (3D) black holes can also have critical behavior and coincide with those of the Van der Waals system). Besides, we have analyzed the concept of effective potential barrier by transforming the radial equation of motion into standard Schrodinger form. We figure out the effect of the coupling constant $\lambda$, the string parameter b, and the quintessential state parameter ${\omega }_q$ on the height of the potential barrier and the other thermodynamical quantities like temperature and heat capacity. Then, we study the quasinormal modes (QNMs) of 3D black holes in the $f(R)$ context. For this purpose, we use the WKB approximation method upto third-order corrections. We have shown the perturbation’s decay in corresponding diagrams when the string parameter b changes.

In this paper, we construct a new approach of spherical magnetic Lorentz flux of spherical $𝕊\alpha$-magnetic flows of particles by the spherical frame in ${𝕊}^2$ spherical space. Eventually, we obtain some optical conditions of spherical $𝕊\alpha$-magnetic Lorentz flux by using directional spherical fields. Moreover, we determine spherical magnetic Lorentz flux for spherical vector fields. Also, we give new construction for spherical curvatures of spherical $𝕊\alpha$-magnetic flows by considering Heisenberg spherical ferromagnetic spin. The approximate solution is expressed by a table and some graphics. Finally, the magnetic flux surface is demonstrated in a static and uniform magnetic surface by using the analytical and numerical results.

In this paper, we will show that a power law asymptotic de Sitter inflation will be established for all values of Hankel indices $\nu$ that relate to the different background spacetimes of the universe in their evolution. First, we calculate the relations for the Hubble, deceleration, slow roll and the equation of state parameters in terms of the Hankel function index $\nu$. We then show that the obtained relations and figures correspond to the conventional limit conditions for pure de Sitter inflation. As an important result, power law quasi-de Sitter inflation is more likely to occur after exponential pure de Sitter inflation. Also, in the proposed model, the universe can always be in the accelerating expansion phase for all values of index $\nu$.

This article is based on the extension of Teleparallel Theory named $f(\tau ,T)$ gravity, where the notions $\tau$ and $T$ abbreviate the torsion trace term of the energy–momentum tensor. This study aims to explore the anisotropic outcomes of the $VelaX-1$ model. We use the field equations drawn by using the spherical symmetry, including the torsion trace term. The major components $g_{rr}$ and $g_{tt}$, of spherical symmetric space-time are obtained by inducing the Karmarkar condition. We can obtain the values of the involved parameters $c$,$P$, $Q$ in this study by matching the interior spherical metric with the exterior Schwarzschild’s solutions of the Einstein field equations. To explore the stability of the stellar objects predicted by our study, we study the properties like metric potentials, energy density, pressures, anisotropy, gradients, EoS, energy conditions, the behavior of forces, sound speeds, adiabatic index, redshift, mass function, and compactification by graphical analysis in the background of $f(\tau ,T)$ gravity.

We study the dynamics and redistribution of entanglement and coherence in three time-dependent coupled harmonic oscillators. We resolve the Schrödinger equation by using time-dependent Euler rotation together with a linear quench model to obtain the state of vacuum solution. Such state can be translated to the phase space picture to determine the Wigner distribution. We show that its Gaussian matrix $𝔾(t)$ can be used to directly cast the covariance matrix $\sigma (t)$. To quantify the mixedness and entanglement of the state, one uses respectively linear and von Neumann entropies for three cases: fully symmetric, bi-symmetric and fully nonsymmetric. Then we determine the coherence, tripartite entanglement and local uncertainties and derive their dynamics. We show that the dynamics of all quantum information quantities are driven by the Ermakov modes. Finally, we use an homodyne detection to redistribute both resources of entanglement and coherence.

In this paper, we consider homothetic Killing vectors in the class of stationary axisymmetric vacuum (SAV) spacetimes, where the components of the vectors are functions of the time and radial coordinates. In this case, the component of any homothetic Killing vector along the $z$ direction must be constant. First, it is shown that either the component along the radial direction is constant or we have the proportionality $g_{\varphi \varphi }\propto g_{\rho \rho }$, where $g_{\varphi \varphi }>0$. In both cases, complete analyses are carried out and the general forms of the homothetic Killing vectors are determined. The associated conformal factors are also obtained. The case of vanishing twist in the metric, i.e. $\omega =0$ is considered and the complete forms of the homothetic Killing vectors are determined, as well as the associated conformal factors.

In this paper, we introduce new frame and new transformation associated with combined Korteweg–de Vries–modified Korteweg–de Vries (KdV–mKdV) equation, the mKdV and the KdV equations with respect to the null Cartan frame in Minkowski 3-space. Direction of the state of polarization of monochromatic linear polarized light wave traveling in the optic fiber is given by the direction of electric field vector. We show that the electric field vector $\vec{E}$ can be expressed as a linear combination of null Cartan frame apparatus using this new transformation in Minkowski 3-space. Later, we study rotation of the polarization plane along optic fiber according to null Cartan frame and Frenet frame of pseudo-null curve in Minkowski 3-space. Finally, we obtain Lorentz force equations via null and pseudo null electromagnetic curves.

The aim of this paper is to classify locally rotationally symmetric (LRS) Bianchi type I space-times via conformal vector fields (CVFs) in the $f(T,B)$ gravity. In a first step, we find the space-times that are solutions of some $f(T,B)$ gravity model. Furthermore, we classify the resulting space-times via CVFs. During the classification, there arise eight cases. Reviewing each case thoroughly, we find that in two cases, the space-times confess proper CVFs. The space-times in rest of the six cases either become conformally flat or tends to admit homothetic vector fields (HVFs) or the Killing vector fields (KVFs).

In this study, we have investigated the dark energy behavior of the viscus-fluid in $f(Q)$-gravity in a flat, isotropic and homogeneous Friedmann–Lemaitre–Robertson–Walker (FLRW) space-time metric. We have considered the linear form of $f(Q)$ function as $f(Q)=-\alpha Q-\beta$ with $\alpha >0$ and $\beta >0$ as model parameters. We have solved the field equations for the scale factor $a(\tau )$ and found $a(\tau )=c_1{[\mathrm{\text{sin}}h(k_2\tau )]}^{k_3}$, where $k_2=\frac{\sqrt{3\alpha \beta {(1+\omega )}^2-24\pi {\xi }_0\beta (1+\omega )}}{2\sqrt{2}\alpha }$ and $k_3=\frac{2\alpha }{3\alpha (1+\omega )-24\pi {\xi }_0}$ and $c_1$ is an integrating constant, $\omega$ is the EoS for normal matter and ${\xi }_0$ is generated from bulk-viscus fluid. We have calculated the several cosmological parameters for this scale factor and studied their physical and geometrical behavior along the observational data sets $H(z)$ and Union $2.1$ compilation of SNe Ia data sets. We have observed that the $\beta$ factor reveals the presence of cosmological constant and for $\beta =0$, the acceleration drives by the bulk-viscosity of the fluid and it behaves just like dark energy model without cosmological constant. We have studied the effective EoS ${\omega }_{\mathrm{\text{eff}}}$ and found $-0.2807\le {\omega }_{\mathrm{\text{eff}}}\le -0.1760$. We have evaluated the age of the present universe as $13.68$ Gyrs. and also, we have studied the nature of deceleration parameter with the signature-flipping point at $z_t=0.5,1.87$ and the present value of deceleration parameter $q_0$ is obtained as $-0.3309,-0.8035$.

We study null hypersurfaces of a Lorentzian manifold with a closed rigging for the hypersurface. We derive inequalities involving Ricci tensors, scalar curvature, squared mean curvatures for a null hypersurface with a closed rigging of a Lorentzian space form and for a screen homothetic null hypersurface of a Lorentzian manifold. We also establish a generalized Chen–Ricci inequality for a screen homothetic null hypersurface of a Lorentzian manifold with a closed rigging for the hypersurface.

Leading order study of direct photon production from proton–proton collisions, in the framework of Minimal (Seiberg–Witten) Non-Commutative Standard Model (NCSM), taking into account the Earth-rotation effects. We found that relative non-commutative contributions increase significantly at very high photon transverse momentum. Therefore, using Run-1 ($\surd s=8$ TeV) and Run-2 ($\surd s=13$ TeV) ATLAS experimental data of inclusive isolated prompt photon cross-section, TeV-Scale bounds of the non-commutativity (NC) parameter are obtained. For space-space non-commutativity, we obtain: $\mathrm{\Lambda }b=1.145\pm 0.015$TeV, and for space-time non-commutativity, we obtain : $\mathrm{\Lambda }e=1.125\pm 0.035$TeV.

We present an information geometric analysis of both entropic speeds and entropy production rates arising from geodesic evolution on manifolds parametrized by pure quantum states. In particular, we employ pure states that emerge as outputs of suitably chosen $\mathrm{\text{su}}(2;ℂ)$ time-dependent Hamiltonian operators that characterize analog quantum search algorithms of specific types. The $\mathrm{\text{su}}(2;ℂ)$ Hamiltonian models under consideration are specified by external time-dependent magnetic fields within which spin-$1/2$ test particles are immersed. The positive definite Riemannian metrization of the parameter manifold is furnished by the Fisher information function. The Fisher information function is evaluated along parametrized squared probability amplitudes obtained from the temporal evolution of these spin-$1/2$ test particles. A minimum action approach is then utilized to induce the transfer of the quantum system from its initial state to its final state on the parameter manifold over a finite temporal interval. We demonstrate in an explicit manner that the minimal (that is, optimum) path corresponds to the shortest (that is, geodesic) path between the initial and final states. Furthermore, we show that the minimal path serves also to minimize the total entropy production occurring during the transfer of states. Finally, upon evaluating the entropic speed as well as the total entropy production along optimal transfer paths within several scenarios of physical interest in analog quantum searching algorithms, we demonstrate in a transparent quantitative manner a correspondence between a faster transfer and a higher rate of entropy production. We therefore conclude that higher entropic speed is associated with lower entropic efficiency within the context of quantum state transfer.

The object of the paper is to study the compatibility of $\phi (\mathrm{\text{Ric}})$-vector fields on almost pseudo-Ricci symmetric manifolds, briefly $A{(\mathrm{\text{PRS}})}_n$. First, we show the existence of an $A{(\mathrm{\text{PRS}})}_n$ whose basic vector field $w(X)$ is a $\phi (\mathrm{\text{Ric}})$-vector field by constructing a non-trivial example. Then, we investigate the properties of the Riemann and Weyl compatibility of $A{(\mathrm{\text{PRS}})}_n$ under certain conditions. We consider an $A{(\mathrm{\text{PRS}})}_4$ space-time whose basic vector fields $\pi (X)$ and $\omega (X)$ is $\phi (\mathrm{\text{Ric}})$-vector fields of constant length. Moreover, we show that an $A{(\mathrm{\text{PRS}})}_4$ space-time whose Ricci tensor is of Codazzi type and basic vector field $\omega (X)$ is $\phi (\mathrm{\text{Ric}})$-vector field is purely electric space-time.

We discuss the possible role of the Tietze extension theorem in providing a rigorous topological base to the expanding space-time in cosmology. A simple toy model has been introduced to show the analogy between the topological extension from a circle $S$ to the whole space $M$ and the cosmic expansion from a non-zero volume to the whole space-time in non-singular cosmological models. A topological analogy to the cosmic scale factor function has been suggested, the paper refers to the possible applications of the topological extension in mathematical physics.

In this paper, we study two different cases of inhomogeneous EOS of the form $p_d=w(t){\rho }_d+w_{1}f(H,t)$. We derive the energy density of dark fluid and dark matter component for both the cases. Further, we calculate the evolution of energy density, gravitational constant and cosmological constant. We also explore the finite time singularity and thermodynamic stability conditions for the two cases of EOS. Finally, we discuss the thermodynamics of inhomogeneous EOS with the derivation of internal energy, Temperature and entropy and also show that all the stability conditions are satisfied for the two cases of EOS.

There are two smooth functions $\sigma$ and $\rho$ associated to a nontrivial concircular vector field $v$ on a connected Riemannian manifold $(M,g)$, called potential function and connecting function. In this paper, we show that presence of a timelike nontrivial concircular vector field influences the geometry of generalized Robertson–Walker space-times. We use a timelike concircular vector field $v$ on an $n$ -dimensional connected conformally flat Lorentzian manifold, $n>2$, to find a characterization of generalized Robertson–Walker space-time with fibers Einstein manifolds. It is interesting to note that for $n=4$ the concircular vector field annihilates energy-momentum tensor and also that in this case the potential function $\sigma$ is harmonic. In the second part of this paper, we show that presence of a nontrivial concircular vector field $v$ with connecting function $\rho$ on a complete and connected $n$ -dimensional conformally flat Riemannian manifold $(M,g)$, $n>2$, with Ricci curvature $\mathrm{\text{Ric}}(v,v)$ non-negative, satisfying $n(n-1)\rho +\tau =0$, is necessary and sufficient for $(M,g)$ to be isometric to either a sphere $S^n(c)$ or to the Euclidean space $E^n$, where $\tau$ is the scalar curvature.