Global Monopole Spacetime Research Articles

On a Spin-1/2 Particle in the Global Monopole Spacetime

On a Spin-1/2 Particle in the Global Monopole Spacetime

On a Particle Confined to the Squared Cotangent Potential in the Global Monopole Spacetime

On a Particle Confined to the Squared Cotangent Potential in the Global Monopole Spacetime

Spherical quantum dot described by a scalar exponential potential under the influence of a linear scalar potential and a global monopole

Based on the power-exponential potential, we study the confinement of a particle to a spherical quantum dot under the influence of a linear scalar potential. We show that the energy eigenvalues s-waves can be obtained from approximate solutions to the Schrödinger equation. Further, we consider the global monopole spacetime and study the topological effects of this spacetime background on the confinement of a particle to a spherical quantum dot under the influence of a linear scalar potential.

Remarks on the global monopole topological effects on spherical symmetric potentials

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 [Formula: see text]-waves can be achieved, the WKB approximation is used based on the Langer transformation.

On the Klein–Gordon oscillators in Eddington-inspired Born-Infeld gravity global monopole spacetime and a Wu–Yang magnetic monopole

We consider Klein–Gordon (KG) particles in a global monopole (GM) spacetime within Eddington-inspired Born–Infeld gravity (EiBI-gravity) and in a Wu–Yang magnetic monopole (WYMM). We discuss a set of KG-oscillators in such spacetime settings. We propose a textbook power series expansion for the KG radial wave function that allows us to retrieve the exact energy levels for KG-oscillators in a GM spacetime and a WYMM without EiBI-gravity. We, moreover, report some conditionally exact, closed form, energy levels (through some parametric correlations) for KG-oscillators in a GM spacetime and a WYMM within EiBI-gravity, and for massless KG-oscillators in a GM spacetime and a WYMM within EiBI-gravity under the influence of a Coulomb plus linear Lorentz scalar potential. We report the effects of the Eddington parameter κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}, GM-parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}, WYMM strength σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document}, KG-oscillators’ frequency Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega $$\\end{document}, and the coupling parameters of the Coulomb plus linear Lorentz scalar potential, on the spectroscopic structure of the KG-oscillators at hand. Such effects are studied over a vast range of the radial quantum number nr≥0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_r\\ge 0$$\\end{document} and include energy levels clustering at κ>>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa>>1$$\\end{document} (i.e., extreme EiBI-gravity), and at |σ|>>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\sigma |>>1$$\\end{document} (i.e., extreme WYMM strength).

Klein–Gordon particles in a quasi-pointlike global monopole spacetime and a Wu-Yang magnetic monopole: invariance and isospectrality

We use two correlated metric functions and transform/deform the pointlike global monopole (PGM) spacetime metric into a quasi-PGM (QPGM) spacetime one. We study Klein–Gordon (KG) particles (manifestly introduced by the non-minimal coupling form of the operator D˜μ=Dμ+Fμ , with Fμ ∈R , and D μ = ∂ μ − ie A μ ) in such QPGM spacetime background. We show that the KG-particles in the QPGM spacetime are isospectral and invariant with KG-particles in the PGM spacetime, provided that the two metric functions are correlated. The Wu-Yang magnetic monopole (WYMM) is also included in the process. We report the effects of both monopoles PGM/QPGM and WYMM on the spectroscopic structure of two models, KG-oscillators and KG-Coulomb particles in such spacetime background. Moreover, we discuss KG-Coulomb particles and shifted KG-oscillators in a PGM spacetime and a WYMM, where such models are manifestly introduced by some Lorentz scalar interaction potentials S(r). The current study is not only of fundamental observability nature but also of pedagogical interest in quantum gravity.

On curvature related geometric properties of Hayward black hole spacetime

This paper is devoted to the study of curvature properties of Hayward black hole (briefly, HBH) spacetime, which is a solution of Einstein field equations (briefly, EFE) having non-vanishing cosmological constant. We have proved that the HBH spacetime is an Einstein manifold of level 2, 2-quasi Einstein, generalized quasi-Einstein and Roter type manifold. Also, it is shown that the nature of the HBH spacetime is pseudosymmetric and it obeys several types of pseudosymmetries, such as, pseudosymmetry due to concircular, conformal and conharmonic curvature (i.e., F⋅F=LQ(g,F) for F=W,C,K with a smooth scalar function L), and it also possesses the relation R⋅R−LQ(g,C)=Q(S,R). It is engrossing to mention that the nature of energy momentum tensor of the HBH spacetime is pseudosymmetric. On the basis of curvature related properties, we have made a comparison among Reissner–Nordström spacetime, interior black hole spacetime and HBH spacetime. It is noteworthy to mention that the gravitational force of the point-like global monopole spacetime is much stronger than that of HBH spacetime. Also, it is shown that the HBH spacetime admits an almost η-Ricci soliton as well as an almost η-Ricci-Yamabe soliton. Finally, an elegant comparative study is delineated between the HBH spacetime and the point-like global monopole spacetime with respect to different kinds of symmetry, such as, motion, curvature collineation, curvature inheritance etc.

Schrödinger oscillators in a deformed point-like global monopole spacetime and a Wu–Yang magnetic monopole: Position-dependent mass correspondence and isospectrality

We show that a specific transformation/deformation in a point-like global monopole (PGM) spacetime background would yield an effective position-dependent mass (PDM) Schrödinger equation (i.e., a von Roos PDM Schrödinger equation). We discuss PDM Schrödinger oscillators in a PGM spacetime in the presence of a Wu–Yang magnetic monopole. Within our transformed/deformed global monopole spacetime, we show that all PDM Schrödinger oscillators admit isospectrality and invariance with the constant mass Schrödinger oscillators in the regular global monopole spacetime in the presence of a Wu–Yang magnetic monopole. The exclusive dependence of the thermodynamical partition function on the energy eigenvalues manifestly suggests that the Schrödinger oscillators and the PDM Schrödinger oscillators share the same thermodynamical properties as mandated by their isospectrality. Moreover, we discuss the hard-wall effect on the energy levels of the PDM Schrödinger oscillators in a PGM spacetime without and with a Wu–Yang magnetic monopole. Drastic energy levels’ shift-ups are observed as a consequence of such hard-wall effect.

Exact and approximate bound state solutions of the Schrödinger equation with a class of Kratzer-type potentials in the global monopole spacetime

This work investigates the motion of a non-relativistic charged particle in the spacetime of a global monopole. We introduce the Schrödinger equation to describe the particle’s motion with two interactions by considering the Kratzer and the screened modified Kratzer potential. The problem’s eigenfunctions and eigenvalues are obtained by deriving and solving the radial equation. The effective potential encompasses both the Kratzer and electrostatic self-interaction potential and leads to bound states solutions. The energy spectrum is investigated, particularly emphasizing its dependence on the system’s physical parameters. The screened modified Kratzer potential, and the screened self-interaction potential reveal an important role in influencing both the effective potential and the energy spectrum. Additionally, it also accommodates the existence of bound states. All these behaviors are illustrated with graphs and discussed in detail.

Topological effects on generalized Duffin-Kemmer-Petiau oscillator under Aharonov–Bohm flux field and Coulomb potential

In this paper, we study the relativistic quantum motions of the oscillator field of the wave equation under the influence of the Aharonov–Bohm (AB) flux field with a Coulomb vector potential in the background of the topological defects produced by a cosmic string and global monopole space-time. We derive the radial equation of the generalized Duffin-Kemmer-Petiau (DKP) oscillator in a static cosmic string space-time and solve it through the Heun function equation. Afterwards, we derive the radial equation of the same generalized DKP oscillator in a point-like global monopole background and obtain the eigenvalue solutions using the same procedure. The generalized oscillator field is studied by substituting the radial momentum operator ∂ r → (∂ r + i M ω η 0 f(r)), where f(r) is an arbitrary function other than linear and introduces a vector potential of Coulomb-types through a minimal substitution via ∂ μ → (∂ μ − i q A μ ) in the relativistic wave equation. It is shown that the eigenvalue solutions of the oscillator field are influenced by the topological defects of the cosmic string and point-like global monopole space-times and get them modified. Furthermore, we see that the eigenvalue solutions depend on the geometric quantum phase, and hence, shifted them more in addition to the topological defects that show the gravitational analogue to the Aharonov–Bohm effect for the bound-states.

Approximate Analytical Solutions of the Schrödinger Equation with Hulthén Potential in the Global Monopole Spacetime

In this paper, we studied the nonrelativistic quantum mechanics of an electron in a spacetime containing a topological defect. We also considered that the electron is influenced by the Hulthén potential. In particular, we dealt with the Schrödinger equation in the presence of a global monopole. We obtained approximate solutions for the problem, determined the scattering phase shift and the S-matrix, and analyzed bound states.

Topological effects produced by point-like global monopole with Hulthen plus screened Kratzer potential on Eigenvalue solutions and NU-method

In this article, the approximate eigenvalue solution of the Schrödinger non-relativistic equation in 3D with a non-central potential of superposition of Hulthen potential and screened Kratzer potential in a point-like global monopole space-time is obtained. We employ a suitable approximation scheme like the Greene-Aldrich approximation in the centrifugal and reciprocal terms that appear in the radial equation and solve it using the parametric Nikiforov-Uvarov method. The results are analyzed for the topological defects and the magnetic flux and show that the eigenvalue solution gets modified in comparison to the flat space result with this superposed potential. Finally, we utilize the eigenvalue solution to some diatomic molecular potential models, such as screened Kratzer and Varshni potential and discuss the effects on the eigenvalue solutions.

Relativistic motions of spin-zero quantum oscillator field in a global monopole space-time with external potential and AB-effect

In this paper, we analyze a spin-zero relativistic quantum oscillator in the presence of the Aharonov–Bohm magnetic flux in a space-time background produced by a point-like global monopole (PGM). Afterwards, we introduce a static Coulomb-type scalar potential and subsequently with the same type of vector potential in the quantum system. We solve the generalized Klein–Gordon oscillator analytically for different functions (e.g. Coulomb- and Cornell-type functions) and obtain the bound-states solutions in each case. We discuss the effects of topological defects associated with the scalar curvature of the space-time and the Coulomb-type external potentials on the energy profiles and the wave function of these oscillator fields. Furthermore, we show that the obtained energy eigenvalues depend on the magnetic quantum flux which gives rise to the gravitational analogue of the Aharonov–Bohm (AB) effect.

Deriving the Hawking Temperature of (Massive) Global Monopole Spacetime via a Topological Formula.

In this work, we study the Hawking temperature of the global monopole spacetime (non-spherical symmetrical black hole) based on the topological method proposed by Robson, Villari, and Biancalana (RVB). By connecting the Hawking temperature with the topological properties of black holes, the Hawking temperature of the global monopole spacetime can be obtained by the RVB method. We also discuss the Hawking temperature in massive gravity, and find that the effect of the mass term cannot be ignored in the calculation of the Hawking temperature; the corrected Hawking temperature in massive gravity can be derived by adding an integral constant, which can be determined by the standard definition.

Klein–Gordon oscillator in a global monopole space–time with rainbow gravity

Klein–Gordon oscillator in a global monopole space–time with rainbow gravity

Thermal effects on a global monopole with Robin boundary conditions

Within quantum field theory on a global monopole spacetime, we study thermal effects on a naked singularity and their relation to boundary conditions. We first obtain the two-point functions for the ground state and for thermal states of a massive, arbitrarily coupled, free scalar field compatible with Robin boundary conditions at the singularity. We then probe these states using a static Unruh-Dewitt particle detector. The transition rate is analyzed for the particular cases of massless minimally or conformally coupled fields at finite temperature. To interpret the detector's behavior, we compute the thermal contribution to the ground-state fluctuations and to the energy density. We verify that the behavior of the transition rate, the fluctuations, and the energy density are closely intertwined. In addition, we find that these renormalized quantities remain finite at the singularity for, and only for, the Dirichlet boundary condition.

Exact solutions of the generalized Klein–Gordon oscillator in a global monopole space-time

Exact solutions of the generalized Klein–Gordon oscillator in a global monopole space-time

⟨ϕ2⟩ for a massive scalar field in global monopole spacetime

We study the vacuum polarization of a massive scalar field $\phi$ with arbitrary coupling to gravity in pointlike global monopole spacetime. Using Schwinger-DeWitt proper time formalism, we calculate the vacuum expectation value $<\phi^{2}>$, when the Compton length of the quantum field is much less than the characteristic radius of the curvature of the background geometry, and we can ignore nonlocal contributions. Explicit analytic expressions are obtained for a general curvature coupling parameter, and specified to the more physical cases of minimal and conformal coupling. Comparing the leading term of $<\phi^{2}>$, proportional to the coincident limit of the Hadamard-DeWitt coeficcient $a_{2}$, with higher order terms, that include the coincident limits of coefficients up to $a_{5}$, we conclude that the next to next to next to leading approximation need to be used to give a more precise description of vacuum polarization effects in this structures. We also find the trace of the renormalized stress energy tensor for the quantized field in the leading approximation, using the existing relationship between this magnitude, the trace anomaly and the field fluctuation.

Relativistic quantum oscillators in the global monopole spacetime

We investigated the effects of the global monopole spacetime on the Dirac and Klein–Gordon relativistic quantum oscillators. In order to do this, we solve the Dirac and Klein–Gordon equations analytically and discuss the influence of this background, which is characterised by the curvature of the spacetime, on the energy profiles of these oscillators. In addition, we introduce a hard-wall potential and, for a particular case, determine the energy spectrum for relativistic quantum oscillators in this background.

Renormalized quantum stress–energy tensor for massive spinor fields around global monopoles

The renormalized quantum stress–energy tensor [Formula: see text] for a massive spinor field around global monopoles is constructed within the framework of Schwinger–DeWitt approximation, valid whenever the Compton length of the quantum field is much less than the characteristic radius of the curvature of the background geometry. The results obtained show that the quantum massive spinor field in the global monopole spacetime violates all the pointwise energy conditions.