CompactQ-balls andQ-shells in a scalar electrodynamics

Abstract

We investigate spherically symmetric non topological solitons in electrodynamics with a scalar field self interaction U ∼ |ψ| taken from the complex signum-Gordon model. We find Q-balls for small absolute values of the total electric charge Q, and Q-shells when |Q| is large enough. In both cases the charge density exactly vanishes outside certain compact region in the three dimensional space. The dependence of the total energy E of small Q-balls on the total electric charge has the form E ∼ |Q| 5/6 , while in the case of very large Q-shells E ∼ |Q| 7/6 .

Problem with classical stability of U(1) gauged Q-balls

“…Possible instabilities are described by solutions to equations (8), (9) with Im ρ = 0. Using equations (8) and (9) it is possible to show (see the detailed derivation in Appendix A) that the following relation fulfills…”

“…Using equations (8) and (9) it is possible to show (see the detailed derivation in Appendix A) that the following relation fulfills…”

“…Later such a theory was examined in the well-known paper [4]. One can also recall papers [5][6][7], where gauged Q-balls 1 were examined mainly from a theoretical point of view, as well as papers [8][9][10][11][12][13][14], where solutions for gauged Q-ball were obtained numerically. Stability of such nontopological soliton solutions, in particular, the classical stability, is an important problem.…”

Gauss–Bonnet boson stars

“…Hence, there are different possibilities to define the "radius" of our boson star solutions. Let us remark that models with a V-shaped potential have been considered [30,31] that possess compact boson stars with a well-defined outer radius (very similar to those of "standard stars") [32][33][34]. Here we follow [35] and define the radius of the boson star as an averaged radial coordinate…”

Some properties ofU(1)gaugedQ-balls

“…Later this subject was examined in the well-known paper [4], in which gauged Q-balls (for simplicity, from here on, we call U(1) gauged Q-balls "gauged Q-balls") were examined analytically and numerically. One can also recall papers [5,6,7], where gauged Q-balls were examined mainly from a theoretical point of view, as well as papers [8,9,10,11,12], where solutions for gauged Q-ball were obtained numerically.…”