Static Gravitational Global Monopoles

TL;DR

This paper investigates static solutions for gravitating global monopoles in spherical symmetry, identifying conditions for regular solutions with and without horizons, and relating these to topological inflation thresholds.

Contribution

It presents new static solutions for gravitating global monopoles, including regular and horizon-containing solutions, and analyzes their properties relative to the symmetry breaking scale.

Findings

Regular solutions exist for η < 1/√(8π)

Solutions with horizons appear for 1/√(8π) ≤ η ≲ √(3/8π)

No static solutions are found for η > √(3/8π), aligning with topological inflation onset

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 $\eta \approx 0.33$.