Stress stability criterion of the isospinning $\mathbb{C}{P}^2$ solitons

We study the energy-momentum tensor of stationary rotating topological solitons in a (2 + 1)-dimensional $\mathbb{C}{P}^2$ nonlinear sigma model with a stabilizing potential term. We evaluate the distributions of the corresponding shear forces and pressure and study the stability criteria for these solutions. Our results suggest that these solitons become classically unstable for some range of values of the parameters of the system.