Gravitational effects on critical Q-balls
  In a cosmological phase transition in theories that admit Q-balls there is a value of the soliton charge above which the soliton becomes unstable and expands, converting space to the true vacuum, much like a critical bubble in the case of ordinary tunneling. Here I consider the effects of gravity on these solitons and I calculate the lowest gravitational corrections to the critical radius and charge. 
Dimitrios Metaxas