Induced self-energy on a static scalar charged particle in the spacetime of a global monopole with finite core

Abstract

We analyze the induced self-energy and self-force on a scalar point-like charged test particle placed at rest in the spacetime of a global monopole admitting a general spherically symmetric inner structure to it. In order to develop this analysis we calculate the threedimensional Green function associated with this physical system. We explicitly show that for points outside the monopole's core the scalar self-energy presents two distinct contributions. The first one is induced by the non-trivial topology of the global monopole considered as a point-like defect and the second is a correction induced by the non-vanishing inner structure attributed to it. For points inside the monopole, the self-energy also present a similar structure, where now the first contribution depends on the geometry of the spacetime inside. As illustrations of the general procedure adopted, two specific models, namely flower-pot and the ballpoint-pen, are considered for the region inside. For these two different situations, we were able to obtain exact expressions for the self-energies and self-forces in the regions outside and inside the global monopole.Although the geometric properties of the spacetime outside the monopole are very well understood, there are no explicit expressions for the components of the metric tensor in the region inside. 1 As a consequence of this fact, many interesting investigations of physical effects associated with global monopole consider this object as a point-like defect. Adopting this simple model, calculations of vacuum polarization effects associated with bosonic [6] and fermionic quantum fields [7], in four-dimensional global monopole spacetime, present divergence on the monopole's core. Moreover, considering higher-dimensional spacetime, vacuum polarization effects associated with bosonic [8] and fermionic [9] quantum fields, also present divergences on the monopole's core.A very well known phenomenon that occur with an electric charged test particle placed at rest in a curved spacetime, is that it may become subjected to an electrostatic self-interactions. The origin of this induced self-interaction resides on the non-local structure of the field caused by the spacetime curvature and/or non-trivial topology. This phenomenon has been analyzed in an idealized cosmic string spacetime by Linet [10] and Smith [11], independently, and also in the spacetime of a global monopole considered as a point-like defect in [12]. In these analysis, the corresponding self-forces are repulsive and depend on the square of electric charge; moreover they present divergences on the respective defects' core. A possible way to circumvent the divergence problem is to consider these defects as having a non-vanishing radius, and attributing for the region inside a structure. For the cosmic string, two different models have been adopted to describe the geometry inside it: the ballpoint-pen model proposed independently by Gott and Hiscock [13], replaces the conical singularity at the string axis by a constant curvature spacetime in...

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

“…In [26], we have shown that the core-induced part in the self-energy above is finite for points away from the core. It remains to analyze the boundary-induced part for point near the boundary itself.…”

“…The above expressions for g l are reduced to the previously obtained ones in [26] for mR → ∞. The functions (2.41) and (2.42) obey DBC or NBC for r ′ = R and for r > = R, respectively.…”

“…By this expression we can investigate the behavior of the self-energy due to the coreinduced part for points near the core. In fact this analysis has been done in [26], and there we have proved that the boundary-free part…”

“…(Note that the energy considered in [26] is the 0-th covariant component of the four-momentum and differs by sign from (2.9)). In appendix A we show that, considering a spherical boundary with radius R on background of the manifold described by the line element (2.1), this energy may be presented in the form 10) for fields obeying, separately, Dirichlet…”

“…This situation also happens for the cosmic string spacetime; however two different models have been proposed to describe the geometry inside the string's core, named the ballpoint pen and flower-pot models proposed in [13] and [14], respectively. These two models have been also used in [26] to analyze the self-energy associated with a massive scalar field in the global monopole spacetime. So, motivated by this result, we decided to continue along the same line of investigation considering here both models, and analyzing the influence on the self-energies induced by the spherical boundary.…”