International Journal of Geometric Methods in Modern Physics

In this paper, Noether symmetry and Killing symmetry analyses of the curved traversable wormholes of $(3+1)$-dimensional spacetime metric in a Riemannian space are discussed. Moreover, a Lie algebra analysis is shown. Using the first and second Cartan’s structure equations, we find connection forms and then the curvature 2-forms are obtained. Finally, the Ricci scalar tensor and the components of Einstein curvature are computed.

A model for the dynamics of a classical point charged particle interacting with higher order jet fields is introduced. In this model, the dynamics of the charged particle is described by an implicit ordinary second-order differential equation. Such equation is free of run-away and pre-accelerated solutions of Dirac’s type. The theory is Lorentz invariant, compatible with the first law of Newton and Larmor’s power radiation formula. Few implications of the new equation in the phenomenology of non-neutral plasmas is considered.

This paper characterizes the warping functions for a multiply generalized Robertson–Walker space-time to get an Einstein space $M$ with a quarter-symmetric connection for different dimensions of $M$ (i.e. (1). dim $M=2,$ (2). dim $M\ge 3$) when all the fibers are Ricci flat. Then we have also computed the warping functions for a Ricci flat Einstein multiply warped product spaces M with a quarter-symmetric connection for different dimensions of $M$ (i.e. (1). dim $M=2,$ (2). dim $M=3,$ (3). dim $M\ge 4$) and all the fibers are Ricci flat. In the last section, we have given two examples of multiply generalized Robertson–Walker space-time with respect to quarter-symmetric connection.

In this paper, we study in Friedmann–Robertson–Walker universe the interaction between the viscous generalized Chaplygin gas with $f(R,T)$ gravity, which is an arbitrary function of the Ricci scalar $R$ and the trace $T$ of the energy–momentum tensor. Assuming that the contents of universe are dominated by a generalized Chaplygin gas and dark energy, we obtained the modified Friedmann equations and also the time-dependent energy density and pressure of dark energy due to the shear and bulk viscosities for three interacting models depending on an input parameter $Q$. Within the simple form of scale factor (power-law), we discuss the graphical representation of dark energy density parameter and investigate the shear and bulk viscosities effects on the accelerating expansion of the universe for each interacting model.

In this paper, we firstly recall some basic facts about the discrete KP(d-KP) and discrete modified KP(d-mKP) hierarchies, and then we find that d-KP hierarchy and d-mKP hierarchy are linked by a gauge transformation. What’s more, we give three gauge transformation operators of the d-mKP hierarchy and give their successive applications. We further construct the ghost symmetry and use this symmetry to give the definition the d-mKP hierarchy with self-consistent sources. We also give gauge transformations of a newly defined constrained d-mKP(cd-mKP) hierarchy and the constrained d-mKP hierarchy with self-consistent sources(cd-mKPHSCSs).

In this paper, we obtain the field equations of Weyl static axially symmetric space-time in the framework of $f(T)$ gravity, where $T$ is torsion scalar. We will see that, for $f(T)=T$ related to teleparallel equivalent general relativity, these equations reduce to Einstein field equations. We show that if the components of energy–momentum tensor are symmetric, the scalar torsion must be either constant or only a function of radial component $\rho$. The solutions of some functions $f(T)$ in which $T$ is a function of $\rho$ are obtained.

Following many theories that predict the existence of the multiverse and by conjecture that our space-time may have a generalized geometrical structure at the fundamental level, we are interested in using a non-commutative geometry (NCG) formalism to study a suggested two-layer space that contains our 4-dimensional (4D) universe and a re-derived photon propagator. It can be shown that the photon propagator and a cosmic microwave background (CMB) angular correlation function are comparable, and if there exists such a multiverse system, the distance between the two layers can be estimated to be within the observable universe’s radius. Furthermore, this study revealed that our results are not limited to CMB but can be applied to many other types of radiation, such as X-rays.

A discretization for the Schwarzschild spacetime manifold is introduced and investigated. It is shown that the discreteness of the area of space shown in loop gravity leads to a tetrahedral structure characterizing the Schwarzschild manifold.

In this paper, we prove an equivariant Kastler–Kalau–Walze type theorem for spin manifolds without boundary. For $6$-dimensional spin manifolds with boundary, we also give an equivariant Kastler–Kalau–Walze type theorem. Then we generalize this theorem to the general $n$-dimensional manifold. An equivariant Kastler–Kalau–Walze type theorem with torsion is also proved.

In this paper, the $q$-deformed circular unit and hyperbolic imaginary unit are studied. With a help of these units, the invariant $q$-deformed length is defined. As applications, the $q$-deformed rotation in two dimension and $q$-deformed special relativity in $1+1$ dimension are also investigated.

In this paper, by using Lorentzian matrix multiplication, $L$-Tangent operator is obtained in Lorentzian space. The $L$-Tangent operators related with planar, spherical and spatial motion are computed via special matrix groups. $L$-Tangent operators are related to vectors. Some illustrative examples for applications of $L$-Tangent operators are also presented.

In this paper, the generalized fermion algebra is introduced so as to have the $p$-dimensional Fock space. The generalized Pauli spin matrices of order $p$ are introduced by identifying these matrices with the step operators of the generalized fermion algebra. From the $Z_p$-graded parity relation $p$ generalized Pauli matrices are obtained. Finally, the para super symmetry (SUSY) is realized in terms of these matrices and ordinary bosonic operators.

The normalized even and odd $q$-cat states corresponding to Arik–Coon $q$-oscillator on the noncommutative complex plane ${ℂ}_{q^{-1}}$ are constructed as the eigenstates of the lowering operator of a $q$-deformed $\mathrm{\text{su}}(1,1)$ algebra with the left eigenvalues. We present the appropriate noncommutative measures in order to realize the resolution of the identity condition by the even and odd $q$-cat states. Then, we obtain the $q$-Bargmann–Fock realizations of the Fock representation of the $q$-deformed $\mathrm{\text{su}}(1,1)$ algebra as well as the inner products of standard states in the $q$-Bargmann representations of the even and odd subspaces. Also, the Euler’s formula of the $q$-factorial and the Gaussian integrals based on the noncommutative $q$-integration are obtained. Violation of the uncertainty relation, photon antibunching effect and sub-Poissonian photon statistics by the even and odd $q$-cat states are considered in the cases $0<q<1$ and $q>1$.

We investigate the early-time accelerated universe after the Big Bang. We pay attention to the dissipative properties of the inflationary universe in the presence of a soft type singularity, making use of the parameters of the generalized equation of state of the fluid. Flat Friedmann–Robertson–Walker metric is being used. We consider cosmological models leading to the so-called type IV singular inflation. Our obtained theoretical results are compared with observational data from the Planck satellite. The theoretical predictions for the spectral index turn out to be in agreement with the data, while for the scalar-to-tensor ratio, there are minor deviations.

Monge Gauge (MG) in differential geometry is generalized. The original MG is based on a surface defined as a height function $h(x,y)$ above a flat reference plane. The total curvature and the Gaussian curvature are found in terms of the height function. Getting benefits from our mathematical knowledge of general relativity, we shall extend the MG toward more complicated surfaces. Here, in this study, we consider the height function above a curved surface, namely a sphere of radius $R$. The proposed height function is a function of $\theta$ and $\phi$ on a closed interval. We find the first, second fundamental forms and the total and Gaussian curvatures in terms of the new height function. Some specific limits are discussed and two illustrative examples are given.

In the course of investigation of our present universe by considering the five-dimensional locally rotationally symmetric (LRS) Bianchi type-I universe with time-dependent deceleration parameters in Lyra manifold, it is excitingly found that the geometry itself of Lyra manifold behaves and consistent with present observational findings for accelerating universe. The behavior of the universes and their contribution to the process of evolution are examined. While studying their physical, dynamical and kinematical properties for different cases, it is found that this model is a new and viable form of model universe containing dark energy. It will be very helpful in explaining the present accelerated expansion behavior of the universe.

This paper is about geometric quantization of the Hitchin system. We quantize a Kahler form on the Hitchin moduli space (which is half the first Kahler form defined by Hitchin) by considering the Quillen bundle as the prequantum line bundle and modifying the Quillen metric using the Higgs field so that the curvature is proportional to the Kahler form. We show that this Kahler form is integral and the Quillen bundle descends as a prequantum line bundle on the moduli space. It is holomorphic and hence one can take holomorphic square integrable sections as the Hilbert space of quantization of the Hitchin moduli space.