Dynamic Monopoles and Spacetime Structure

Abstract

According to previous work on magnetic monopoles, static regular solutions are nonexistent if the vacuum expectation value of the Higgs field $η$ is larger than a critical value $η_{\rm cr}$, which is of the order of the Planck mass. In order to understand the properties of monopoles for $η>η_{\rm cr}$, we investigate their dynamics numerically and classify those dynamical solutions into three types as follows. If $η$ is larger than another critical value $η_{\rm inf}~(>η_{\rm cr})$, a monopole inflates and a wormhole structure appears around it. In the case of $η_{\rm cr}<η<η_{\rm inf}$, inflation does not occur and the dynamics depend on the ratio of the Higgs self coupling constant $λ$ and the gauge coupling constant $e^2$: if $λ/e^2\stackrel{<}{\sim}1$, a monopole just shrinks and becomes a black hole; otherwise, a monopole approaches a stable configuration.