Static Gravitational Global Monopoles

Abstract

Static solutions in spherical symmetry are found for gravitating global monopoles. Regular solutions lacking a horizon are found for $\eta < 1/\sqrt{8\pi}$, where $\eta$ is the scale of symmetry breaking. Apparently regular solutions with a horizon are found for $1/\sqrt{8\pi} \le \eta \alt \sqrt{3/8\pi}$. Though they have a horizon, they are not Schwarzschild. The solution for $\eta = 1/\sqrt{8\pi}$ is argued to have a horizon at infinity. The failure to find static solutions for $\eta > \sqrt{3/8\pi} \approx 0.3455$ is consistent with findings that topological inflation begins at $\eta \approx 0.33$.