An Energetically Stable Q-ball solution in 3+1 Dimensions

TL;DR

This paper introduces a new class of energetically stable Q-ball solutions in a 3+1 dimensional Klein-Gordon field system, demonstrating their stability and deriving their dynamical equations.

Contribution

It presents a specific stable Q-ball solution in 3+1 dimensions and reduces its dynamics to known nonlinear Klein-Gordon equations, highlighting its energetic stability.

Findings

Q-ball solution is energetically stable against small perturbations

Dynamical equations reduce to known complex nonlinear Klein-Gordon form

Provides a new stable soliton solution in higher-dimensional field theory

Abstract

The paper, classically, presents an extended Klein-Gordon field system in 3+1 dimensions with a special Q-ball solution. The Q-ball solution is energetically stable, that is, for any arbitrary small deformation above the background of that, total energy always increases. The general dynamical equations, just for this special Q-ball solution, are reduced to the known versions of a complex nonlinear Klein-Gordon system, as its dominant dynamical equations.