International Journal of Geometric Methods in Modern Physics

We propose a model-independent approach to study entanglement creation due to the dynamics between two asymptotic quantum regimes in the framework of homogeneous and isotropic universe. We realize it by Padé expansion to reconstruct the functional form of scale factor, rather than postulating it a priori. This amounts to fix the Padé approximants constraining the free parameters in terms of current cosmic observations. Assuming fermions, we solve the Dirac equation for massive particles and we investigate entanglement entropy in terms of modes $k$ and mass $m$. We consider two rational approximations of $(1,1)$ and $(1,2)$ orders, which turn out to be the most suitable choices for guaranteeing cosmic bounds. Our results show qualitative agreement with those known in literature and arising from toy models, but with sensible quantitative discrepancies. Moreover, our outcomes are model-independent reconstructions which show that any higher orders departing from $(1,1)$ do not significantly modify particle–antiparticle production (hence entanglement), if cosmic bounds are taken into account.

The present work is a second in the series of investigations of the background dynamics in brane cosmology when dark energy is coupled to dark matter by a suitable interaction. Here, dark matter is chosen in the form of perfect fluid with barotropic equation of state, while a real scalar field with self-interacting potential is chosen as dark energy. The scalar field potential is chosen as exponential or hyperbolic in nature and three different choices for the interactions between the dark species are considered. In the background of spatially flat, homogeneous and isotropic Friedmann–Robertson–Walker (FRW) brane model, the evolution equations are reduced to an autonomous system by suitable transformation of variables and a series of critical points are obtained for different interactions. By analyzing the critical points, we have found a cosmologically viable model describing an early inflationary scenario to dark energy-dominated era connecting through a matter-dominated phase.

In this work, we calculate the quantum correction effects on the deflection of light in the space-time geometry of a quantum improved Kerr black hole pierced by an infinitely long cosmic string. More precisely, we calculate the deflection angle by applying the Gauss–Bonnet theorem (GBT) to the osculating optical geometries related to the quantum improved rotating black hole in the weak limit approximation. We find that the deflection angle of light is affected by the quantum effects as well as the global topology due to the presence of the cosmic string. Besides, we have managed to find the same expression for the deflection angle in leading order terms using the geodesic equations.

In this paper, we relate the evolution equations of the electric field and magnetic field vectors of the polarized light ray traveling in a coiled optical fiber in the ordinary space into the nonlinear Schrödinger’s equation by proposing new kinds of binormal motions and new kinds of Hasimoto functions in addition to commonly known formula of the binormal motion and Hasimoto function. All these operations have been conducted by using the orthonormal frame of Bishop equations that is defined along with the coiled optical fiber. We also propose perturbed solutions of the nonlinear Schrödinger’s evolution equation that governs the propagation of solitons through the electric field $(E)$ and magnetic field $(M)$ vectors. Finally, we provide some numerical simulations to supplement the analytical outcomes.

In this paper, we obtain Chen’s inequalities for submanifolds of complex space forms and Sasakian space forms with quarter-symmetric connections.

A new picture of Quantum Mechanics based on the theory of groupoids is presented. This picture provides the mathematical background for Schwinger’s algebra of selective measurements and helps to understand its scope and eventual applications. In this first paper, the kinematical background is described using elementary notions from category theory, in particular the notion of 2-groupoids as well as their representations. Some basic results are presented, and the relation with the standard Dirac–Schrödinger and Born–Jordan–Heisenberg pictures are succinctly discussed.

We propose an analytic $C^1$ solution of the hydrodynamic equations for a main-sequence star in stationary and spherically symmetric conditions. We reach this result starting from convenient choices of mass density, specific function of the perfect gas, and luminosity function. The theoretical results, when applied to the Sun, are compared with the standard solar model data. A more accurate proof of Schwarzshild’s inequality and equation is given.

Spherically symmetric classical model of an elementary particle or a black hole spacetime without central singularity had been constructed by O. B. Zaslavskii, Classical model of an elementary particle with a Bertotti–Robinson core and extremal black holes, Phys. Rev. D 70 (2004) 104017. In this model, an extremal Reissner–Nordström (RN) black hole and a Bertotti–Robinson (BR) spacetime are glued at the horizon such that the inner/core spacetime is the regular BR while outside is the extremal RN. The fact that near horizon geometry of the extremal RN coincides with BR spacetime becomes helpful in the construction. We investigate the stability of such a particle/regular black hole against linear radial perturbations. The model turns out to be stable against such perturbations with a linear equation of state for a perfect fluid after the perturbation. To complete our study, we give a generic particle model whose inner and outer metrics must satisfy more general conditions.

We consider the effects of vacuum polarization and particle creation of a scalar field on Lie groups with a non-stationary bi-invariant metric of the Robertson–Walker type. The vacuum expectation values of the energy momentum tensor for a scalar field determined by the group representation are found using the noncommutative integration method for the field equations instead of separation of variables. The results obtained are illustrated by the example of the three-dimensional rotation group.

We define the coordinate equations of killing magnetic curves $\gamma (s)$ in ${ℝ}_1^3$ with the magnetic vector field $V$ under the frame $\{{\gamma }^{\prime }(s),V,V\wedge {\gamma }^{\prime }(s)\}$. In particular, this yields to describe the geometrical properties and singularities of the magnetic curves and the magnetic normal binormal surfaces. Meanwhile, we establish the relationships between singularity types of the magnetic normal binormal surfaces and geometrical invariants of the magnetic curves. As an application, we give an example to explain the main results in this paper, where we give the classification of singularity types of the magnetic curves.

Recently, it is proven that generalized Robertson–Walker space-times in all orthogonal subspaces of Gray’s decomposition except one (unrestricted) are perfect fluid space-times. GRW space-times in the unrestricted subspace are identified by having constant scalar curvature. Generalized quasi-Einstein GRW space-times have a constant scalar curvature. It is shown that generalized quasi-Einstein GRW space-times reduce to Einstein space-times or perfect fluid space-times.

Non-trivial examples of Riemannian almost product structures are constructed on the product bundle of the positive and negative twistor spaces of an oriented Riemannian four-manifold. The Gil–Medrano and Naveira types of these structures are determined and a geometric interpretation of the corresponding classes is given.

In this paper, we introduce a time-like line congruence which has the parameter ruled surfaces as principal ruled surfaces. Then we extend several well-known formulae of line congruence in the Euclidean 3-space to the Minkowski 3-space. Meanwhile, we report some geometric descriptions of these formulae. Finally, an example of application is introduced and described in detail.

We investigate the dynamical systems analysis of Friedmann–Robertson–Walker (FRW) cosmological model with wet dark fluid. A new equation of state for the dark energy component of the Universe has been used. It is modeled by the equation of state $p=\gamma (\rho -{\rho }^{\ast })$, which can describe a liquid, e.g. water. To analyze the evolution equations, we have introduced suitable transformation of variables. The evolution of corresponding solutions is presented by curves in the phase–plane diagram. The nature of critical points are analyzed and stable attractors are examined for our cosmological model. We determine the classical stabilities of these cosmologies. We also examine the transition of early decelerating stage of the Universe to present the accelerating stage of the Universe.

In this paper, we investigate a scenario in which late-time cosmic acceleration might arise due to coupling between dark matter and baryonic matter without resorting to dark energy or large-scale modification of gravity associated with extra degrees of freedom. The scenario can give rise to late-time acceleration in Jordan frame and no acceleration in Einstein frame — generic modification of gravity caused by disformal coupling. Using a simple parametrization of the coupling function, in maximally disformal case, we constrain the model parameters by using the age constraints due to globular cluster data. We also obtain observational constraints on the parameters using $H(z)+\mathrm{\text{SNIa}}+\mathrm{\text{BAO}}$ datasets. In this case, we distinguish between phantom and non-phantom acceleration and show that the model can give rise to phantom behavior in a narrow region of parameter space.

Motivated by one of the problems proposed by [Vilcu and Vilcu, Statistical manifolds with almost quaternionic structures and quaternionic Kaehler-like statistical submersions, Entropy 17 (2015) 6213–6228] in this paper, we study the statistical submanifolds of quaternion Kaehler-like statistical space forms and provide an answer to the problem. Further, we derive the statistical version of Chen inequality for totally real statistical submanifold in such ambient.