What happens to Q-balls if QQ is so large?

In the system of a gravitating Q-ball, there is a maximum charge $Q_{{\rm max}}$ inevitably, while in flat spacetime there is no upper bound on $Q$ in typical models such as the Affleck-Dine model. Theoretically the charge $Q$ is a free parameter, and phenomenologically it could increase by charge accumulation. We address a question of what happens to Q-balls if $Q$ is close to $Q_{{\rm max}}$. First, without specifying a model, we show analytically that inflation cannot take place in the core of a Q-ball, contrary to the claim of previous work. Next, for the Affleck-Dine model, we analyze perturbation of equilibrium solutions with $Q\approx Q_{{\rm max}}$ by numerical analysis of dynamical field equations. We find that the extremal solution with $Q=Q_{{\rm max}}$ and unstable solutions around it are "critical solutions", which means the threshold of black-hole formation.Comment: 9 pages, 10 figures, results for large $\kappa$ added, to appear in PR

How does gravity save or kill Q-balls?

We explore stability of gravitating Q-balls with potential $V_4(\phi)={m^2\over2}\phi^2-\lambda\phi^4+\frac{\phi^6}{M^2}$ via catastrophe theory, as an extension of our previous work on Q-balls with potential $V_3(\phi)={m^2\over2}\phi^2-\mu\phi^3+\lambda\phi^4$. In flat spacetime Q-balls with $V_4$ in the thick-wall limit are unstable and there is a minimum charge $Q_{{\rm min}}$, where Q-balls with $Q<Q_{{\rm min}}$ are nonexistent. If we take self-gravity into account, on the other hand, there exist stable Q-balls with arbitrarily small charge, no matter how weak gravity is. That is, gravity saves Q-balls with small charge. We also show how stability of Q-balls changes as gravity becomes strong.Comment: 10 pages, 10 figure