# Internal force distributions in 't Hooft-Polyakov monopole and Julia-Zee dyon

## TL;DR

This paper analyzes the energy-momentum tensor of 't Hooft-Polyakov monopoles and Julia-Zee dyons, decomposing it into long- and short-range parts to understand their mechanical properties and stability.

## Contribution

It introduces a decomposition method for the energy-momentum tensor of monopoles and dyons, using a modified 't Hooft definition, and computes related physical quantities.

## Key findings

- Violation of local stability criterion for monopoles and dyons
- Computed masses, D-terms, and mean square radii
- Derived new equilibrium equations

## Abstract

The energy-momentum tensor of the 't Hooft-Polyakov monopole and the Julia-Zee dyon are studied. This tensor contains important information about the pressure and the shear force distributions which define the mechanical properties of systems. Obtaining the violation of the local stability criterion for the magnetic monopole and dyon we decompose the EMTs into long- and short-range parts. This decomposition depends on the abelian field strength tensor which can not be uniquely defined. We suggest to use the modified 't Hooft definition for the tensor. Finally, the long- and short-range parts of the EMTs are computed and new equilibrium equations are obtained. Numerical values for masses, $D$-terms and various mean square radii for the monopole and the dyon are also computed.