Scalar self-energy for a charged particle in global monopole spacetime with a spherical boundary

Abstract

We analyze combined effects of the geometry produced by global monopole and a concentric spherical boundary on the self-energy of a point-like scalar charged test particle at rest. We assume that the boundary is outside the monopole's core with a general spherically symmetric inner structure. An important quantity to this analysis is the three-dimensional Green function associated with this system. For both Dirichlet and Neumann boundary conditions obeyed by the scalar field on the sphere, the Green function presents a structure that contains contributions due to the background geometry of the spacetime and the boundary. Consequently the corresponding induced scalar self-energy present also similar structure. For points near the sphere the boundary-induced part dominates and the self-force is repulsive/attractive with respect to the boundary for Dirichlet/Neumann boundary condition. In the region outside the sphere at large distances from it, the boundary-free part in the self-energy dominates and the corresponding self-force can be either attractive or repulsive with dependence of the curvature coupling parameter for scalar field. In particular, for the minimal coupling we show the presence of a stable equilibrium point for Dirichlet boundary condition. In the region inside the sphere the nature of the self-force depends on the specific model for the monopole's core. As illustrations of the general procedure adopted we shall consider two distinct models, namely flower-pot and the ballpoint-pen ones.

Regularization of static self-forces

“…This is the case of all computations of self-forces acting on static particles in static spacetimes [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], which involved a variety of regularization methods. In the pioneering Smith-Will paper [13], for example, the field of a static electric charge in the spacetime of a Schwarzschild black hole was regularized by the Copson solution [28], which was shown to be as singular as the particle's own field but to exert no force.…”

“…In the pioneering Smith-Will paper [13], for example, the field of a static electric charge in the spacetime of a Schwarzschild black hole was regularized by the Copson solution [28], which was shown to be as singular as the particle's own field but to exert no force. As other examples, self-force computations for charges in wormhole spacetimes [20][21][22][23], or for charges near global monopoles [24][25][26][27], were regularized with the help of Hadamard's two-point function, defined in each spatial section of the four-dimensional spacetime (or in a conformally related space). Because Copson's solution is known to be an exact representation of Hadamard's function in the (conformally related) spatial sections of the Schwarzschild spacetime, these regularization methods are essentially the same.…”

Relativistic Motions of Spin-Zero Quantum Oscillator Field in a Global Monopole Space-Time with External Potential and AB-effect

“…The radial wave function is given by We can see that the energy spectrum (35) and the radial wave function (37) of oscillator field are influenced by the topological defects parameter α 2 which is associated with the curvature of the space-time, the function f (r) = b r as well as the Coulomb-types scalar and vector potentials present in the system. Furthermore, the energy eigenvalues E n,l (Φ B ) depends on the Aharonov-Bohm magnetic flux and are influenced by this.…”

“…In the relativistic limit, studies on hydrogen and pionic atom [31], exact solutions of scalar bosons in the presence of potential [32], the Dirac and Klein-Gordon oscillators [33], and the generalized Klein-Gordon oscillator [34]. In addition, global monopole spacetime have been studied in scalar self-energy for a charged particle [35,36], induced self-energy on a static scalar charged particle [37], vacuum polarization for a massless scalar field [38], vacuum polarization for a mass-less spin-1/2 field [39], vacuum polarization effects in the presence of the Wu-Yang magnetic monopole [40]. Also, the gravitational deflection of light by a rotating global monopole space-time have been studied in Ref.…”

Non-Relativistic Particles Interact with Potential Under the effect of Quantum flux in a space-time with a distortion of a vertical line into a vertical spiral

“…But some of them are so obvious that they are expected (a) E-mail: prudra.math@gmail.com (b) E-mail: faizuddinahmed15@gmail.com (c) E-mail: houcine12400@gmail.com to be observed in near future. Out of the probable candidates, the global monopole is the most promising one that is expected to be observed; hence, a lot of research has been dedicated to it in recent years [7][8][9][10][11][12][13]. In addition, exact solutions of the KG-equation have been extensively investigated in the background of global monopole [14][15][16][17][18][19][20][21][22].…”