Troubles with Global Monopoles in Quantum Gravity

TL;DR

This paper explores the problematic implications of global monopoles with negative mass in quantum gravity, revealing potential instabilities and energy production issues due to their gravitational effects.

Contribution

It demonstrates that global monopoles acquire negative mass when gravity is included, leading to possible instabilities and divergence in decay rates.

Findings

Global monopoles have negative mass in gravitational theories.

Negative mass monopoles can induce instabilities and energy production.

Potential divergence in decay rates of monopole configurations.

Abstract

A theory with a global $O(3)$ symmetry broken at a scale $\eta$ admits topological configurations: global monopoles realized by Goldstone fields winding around the core of false vacuum. One may expect them to behave as heavy, big composite objects, difficult to make and therefore mostly harmless. However, after gravity is turned on, as long as Equivalence Principle holds, one finds that global monopoles have a negative mass, $M \sim - \eta/\sqrt{\lambda}$, where $\lambda$ is the field theory coupling. This could catalyze an instability in the space of a global monopole, by the production of additional global monopole-antimonopole pairs along with normal particles, leading to energy production {\it ab nihilo}, if the pair energy is dominated by their negative rest masses. In a theory with unbroken local Poincar\'e symmetry, this could lead to a divergent `decay rate' of the global monopole configurations.