Network of Domain Walls on Soliton Stars

We explore the idea of a network of domain walls to appear at the surface of a soliton star. We show that for a suitable fine tuning among the parameters of the model we can find localized fermion zero modes only on the network of domain walls. In this scenario the soliton star gets unstable and decays into free particles before the cold matter upper mass limit is achieved. However, if fermions do not bind to the network of domain walls, the network becomes neutral, imposing a new lower bound on the charge of the soliton star, slightly raising its critical mass.