Static Gravitational Global Monopoles

Abstract

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