Stress stability criterion of $U(1)$ gauged non-topological solitons in the 3+1 dimensional O(3) sigma-model

TL;DR

This paper analyzes the stability of non-topological solitons in a 3+1 dimensional $O(3)$ sigma-model, focusing on energy distribution and stability criteria, and finds that negative energy regions do not necessarily cause destabilization.

Contribution

It provides a detailed evaluation of energy-momentum distributions and stability conditions for $U(1)$ gauged non-topological solitons in the $O(3)$ sigma-model.

Findings

Negative energy density regions do not destabilize solitons.

Energy conditions are violated but stability is maintained.

Shear forces and pressure distributions are characterized.

Abstract

We study the energy-momentum tensor of the spherically symmetric non-topological solitons of the $O(3)$ non-linear sigma-model with a standard kinetic term and with a symmetry breaking potential in 3+1 dimensional flat space-time. We evaluate the distributions of the corresponding energy density, shear forces and pressure and study the stability criteria for these solutions. We argue that the presence of domains with negative energy density and violation of the energy conditions most likely do not lead to destabilization of solitons.