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

TL;DR

This paper investigates the behavior of gravitating Q-balls near their maximum charge, demonstrating analytically that inflation cannot occur inside them and numerically showing that solutions at maximum charge act as critical thresholds for black hole formation.

Contribution

It provides the first analytical proof ruling out inflation inside Q-balls and numerically characterizes the extremal and near-extremal solutions as critical solutions for black hole formation.

Findings

Inflation cannot occur in the core of a Q-ball.

Extremal solutions at maximum charge are critical solutions.

Solutions near maximum charge are thresholds for black-hole formation.

Abstract

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.