What Does a Strongly Excited ’t Hooft–Polyakov Magnetic Monopole Do?

The time evolution of strongly excited $\mathrm{SU}(2)$ Bogomol’nyi-Prasad-Sommerfield magnetic monopoles in Minkowski spacetime is investigated by using numerical simulations based on the technique of conformal compactification and on the use of the hyperboloidal initial value problem. It is found that an initially static monopole does not radiate the entire energy of the exciting pulse toward future null infinity. Rather, a long-lasting quasistable “breathing state” develops in the central region and certain expanding shell structures—built up by very high frequency oscillations—are formed in the far away region.

Figure 1

Spacetime diagram showing the time evolution of the energy density $\mathcal{E}$ associated with shells of radius $R$; i.e., $E(T)={\int }_0^1\mathcal{E}dR$ gives the total energy of a $T=\mathrm{const}$ hypersurface.

Figure 2

The time dependence of the product of the energy current density $S$ and $4\pi r^2$ at ${ℐ}^{+}$ is shown on the intervals $0.8\le T\le 4$ and $0.8\le T\le 250$.

Figure 3

The difference $w-w_0$ is plotted on the time slice $T=1.695$.

Figure 4

The deviation $\epsilon -{\epsilon }_0$ is plotted against the physical time intervals $0\le t\le 100$ and $100\le t\le 6700$ at $R=0.0254$.

Figure 5

The frequency difference $m_w-\omega$ and the amplitude $a$ of the oscillations of the breathing state, shown in Fig. 4, is plotted against the physical time $t$.

Figure 6

The power spectrum of the oscillations of $\epsilon -{\epsilon }_0$ at $R=0.0254$ is plotted for various time intervals $[t_1,t_2]$.