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

TL;DR

This work analyzes stress stability of $U(1)$ gauged non-topological solitons in the 3+1 dimensional $O(3)$ sigma-model with a symmetry-breaking potential. It uses the energy-momentum tensor to obtain distributions of energy density, pressure, and shear forces for spherically symmetric configurations with a harmonic time dependence, and derives a virial identity and von Laue condition. Numerical results show that energy-density can be negative in the interior and the D-term is negative, yet the von Laue condition is satisfied and the configurations are classically stable across parameter ranges. The findings highlight a mechanical-stability perspective for solitons even when standard energy conditions are violated and suggest directions for axial solutions and spectral stability analyses.

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.

Figures (11)

• Figure 1: The potential (\ref{['pot']}) for different values of the parameter $\beta$, $\mu^2=1$ (left) and the effective potential $U_{eff} = U+\frac{1}{2} \omega^2 \sin^2 f$ for $e=0$ and different values of the frequency $\omega$ at $\beta=0.5$ and $\mu^2=1$ (right), vs the value of the radial function $f$.
• Figure 2: Profiles of the radial profile functions of the soliton $f(r),A_0(r)$ for different values of the parameter $\beta$ at $\omega=0.5$ and $e=0$ (solid lines), $e=0.2$ (dashed doted lines) and $e=0.6$ (dashed lines). (A logarithmic scale is used for the function $A_0$).
• Figure 3: Spherically symmetric $U(1)$ gauged $O(3)$ solitons: The mass $M$ vs the frequency $\omega$ (upper plots) and vs the Noether charge $Q$ (bottom plots) for some set of values of the gauge coupling $e$ for $\beta=0.5$ (left) and for some set of values of the parameter $\beta$ (right) for $e=0$ (red line), $e=0.2$ (green line), $e=0.6$ (blue line).
• Figure 4: The central value of the scalar profile function $f(0)$ vs the frequency $\omega$ for some set of values of $e$ at $\beta=0.5$ (left plot) and for some set of values of $\beta$ at $e=0$ (red line), $e=0.2$ (green line) and $e=0.6$ (blue line), right plot.
• Figure 5: The central value of electric potential $A_0(0)$ vs the frequency $\omega$ for some set of values of $e$ at $\beta=0.5$ (left plot) and for some set of values of $\beta$ at $e=0.2$ (green line) and $e=0.6$ (blue line), right plot.