International Journal of Geometric Methods in Modern Physics最新文献

Wormholes are considered both from the Wheeler deWitt equation, as well as from the field equations in the Euclidean background of Robertson Walker mini-superspace in $R^2$ gravity. Quantum wormhole satisfies Hawking Page wormhole boundary condition in the Euclidean background of mini-superspace, however, in the Lorentzian background wave functional turns to the usual oscillatory function. The Euclidean field equations for $\kappa =0,\pm 1$ lead to the wormhole configuration, as well as oscillating universe in Euclidean time $\tau$. The oscillating universe in Euclidean time $\tau$ transforms to an expanding universe only for $\kappa =1$ in Lorentz time $t$ under analytic continuation $\tau =it$ and asymptotically leads to an exponential solution. An Euclidean wormhole in the very early era evolves to an oscillating universe in $\tau$, thereafter crossing deSitter radius transition to an inflationary era is evident at later epoch only for $\kappa =1$.

In this paper, we study a class of conformal metric deformations in the quasi-radial coordinate parametrizing the three-sphere in the conformally compactified Minkowski spacetime $S^1\times S^3$. Prior to reduction of the associated Laplace–Beltrami operators to a Schrödinger form, a corresponding class of exactly solvable potentials (each one containing a scalar and a gradient term) is found. In particular, the scalar piece of these potentials can be exactly or quasi-exactly solvable, and among them we find the finite range confining trigonometric potentials of Pöschl–Teller, Scarf and Rosen–Morse. As an application of the results developed in the paper, the large compactification radius limit of the interaction described by some of these potentials is studied, and this regime is shown to be relevant to a quantum mechanical quark deconfinement mechanism.

We proceed to obtain an exact analytical solution of the Brans–Dicke (BD) equations for the spatially flat ($k=0$) Friedmann–Lamaître–Robertson–Walker (FLRW) cosmological model in both cases of the absence and presence of the cosmological constant. The solution method that we use to solve the field equations of the BD equations is called the “invariants of symmetry groups method” (ISG method). This method is based on the extended Prelle–Singer (PS) method and it employs the Lie point symmetries, $\lambda$-symmetries, and Darboux polynomials (DPs). Indeed, the ISG method tries to provide two independent first-order invariants associated to the one-parameter Lie groups of transformations keeping the ordinary differential equations (ODEs) invariant, as solutions. It should be noted for integrable ODEs that the ISG method guarantees the extraction of these two invariants. In this work, for the BD equations in FLRW cosmological model, we find the Lie point symmetries, $\lambda$-symmetries, and DPs, and obtain the basic quantities of the extended PS method (which are the null forms and the integrating factors). By making use of the extended PS method we find two independent first-order invariants in such a way that appropriate cosmological solutions from solving these invariants as a system of algebraic equations are simultaneously obtained. These solutions are wealthy in that they include many known special solutions, such as the O’Hanlon–Tupper vacuum solutions, Nariai’s solutions, Brans–Dicke dust solutions, inflationary solutions, etc.

A new definition of entropy is introduced using a model that simulates an expanding space-time compatible with the fundamental principle of cosmology. The entropy is obtained by mean of a state function that measures the variation of the space-time normal curvature, from a highly compressed space to a lower compressed space. The defined entropy leads to work out a new understanding of the earliest conditions that last for a period estimated to 380,000 years after the Big Bang. It leads to understand via a short period of inflation the process that generates the uniform distribution of matter and energy at the surface of the last scattering. It involves gravitational singularities in a process of gradual decompression propitious to the incubation of matter recombination, and it allows to trace back gravity origin.

In this study, the structures of stars are examined using the Karmarkar condition (KC) to assess the metric components. The study also takes into account the anisotropic source of the matter distribution in the context of Modified Teleparallel Rastall Gravity (MTRG). Various values of the model parameter $\eta$ are tested by assuming different metric coefficients for the embedding spacetime. To calculate the involved model parameters, the Schwarzschild black hole solution is employed as an exterior solution. The stability and admissibility of the solutions obtained are demonstrated by analyzing some core properties of stellar objects, using observed data from established stellar models such as “PSRJ1416-2230”. It is worth noting that the results obtained in this study are physically feasible and acceptable.

This study explores the deflection angle of photon rays or light-like geodesics within the framework of Eddington-inspired Born–Infeld (EiBI) gravity background space-time, taking into account the influence of cosmic strings. The primary focus lies in deriving the effective potential of the system applicable to both null and time-like geodesics, as well as determining the angle of deflection for light-like geodesics. Our analysis shows that the presence of cosmic strings induces modifications in these physical quantities, leading to shifts in their respective values.

In this paper, we study the topological effects of the global monopole spacetime on the energy eigenvalues of spherical symmetric potentials in the nonrelativistic regime. We deal with the radial equation by using the Wentzel, Kramers and Brillouim (WKB) approximation. In the cases where the energy levels of the $\ell$-waves can be achieved, the WKB approximation is used based on the Langer transformation.

In this paper, we explore the characteristics of two novel regular spacetimes that exhibit a nonzero vacuum energy term, under the form of a (quasi) anti-de Sitter phase. Specifically, the first metric is spherical, while the second, derived by applying the generalized Newman–Janis algorithm to the first, is axisymmetric. We show that the equations of state of the effective fluids associated with the two metrics asymptotically tend to negative values, resembling quintessence. In addition, we study test particle motions, illustrating the main discrepancies among our models and more conventional metrics exhibiting non-vanishing anti-de Sitter phase.

In this review, we provide a concrete overview of the Raychaudhuri equation, Focusing Theorem and convergence conditions in a plethora of backgrounds and discuss the consequences. We also present various classical and quantum approaches suggested in the literature that could potentially mitigate the initial big-bang singularity and the black-hole singularity.

In this paper, we investigate the geometric phase (GP) of two-mode entangled squeezed-coherent states (ESCSs), undergoing unitary cyclic evolution. Results show that increasing the squeezing parameter of either mode of the balanced ESCS compresses the GP elliptically with respect to the coherence parameter of the corresponding mode. While in the case of unbalanced ESCS, the GP is compressed hyperbolically by increasing the squeezing parameters of the either mode. By generalizing the approach to higher constituting-state dimensions, it is found that the GPs of both balanced and unbalanced ESCSs, increase for a specific value of the coherence parameter. By analyzing the states through the Schmidt decomposition method, we find that, locally, the balanced and unbalanced ESCSs are unitarily equivalent. Finally, based on the interferometry technique, we suggest a theoretical scheme for the physical generation of ESCSs.