Global Monopoles in the Extended Gauss-Bonnet Gravity

TL;DR

This paper explores global monopole solutions in extended Gauss-Bonnet gravity, revealing conditions under which these monopoles have positive ADM mass and potential stability, contrasting with negative mass monopoles in general relativity.

Contribution

It introduces a new class of global monopole solutions in extended Gauss-Bonnet gravity with positive ADM mass, addressing stability issues of monopoles in general relativity.

Findings

Positive ADM mass for monopoles with specific coupling parameters

Matching exterior and interior solutions yields stable configurations

Potential phenomenological and cosmological implications

Abstract

We discuss self-gravitating global O(3) monopole solutions associated with the spontaneous breaking of O(3) down to a global O(2) in an extended Gauss Bonnet theory of gravity in (3+1)-dimensions, in the presence of a non-trivial scalar field $\Phi$ that couples to the Gauss-Bonnet higher curvature combination with a coupling parameter $\alpha$. We obtain a range of values for $\alpha < 0$ (in our notation and conventions), which are such that a global (Israel type) matching is possible of the space time exterior to the monopole core $\delta$ with a de-Sitter interior, guaranteeing the positivity of the ADM mass of the monopole, which, together with a positive core radius $\delta > 0$, are both dynamically determined as a result of this matching. It should be stressed that in the General Relativity (GR) limit, where $\alpha \to 0$, and $\Phi \to $ constant, such a matching yields a negative ADM monopole mass, which might be related to the stability issues the (Barriola-Vilenkin (BV)) global monopole of GR faces. Thus, our global monopole solution, which shares many features with the BV monopole, such as an asymptotic-space-time deficit angle, of potential phenomenological/cosmological interest, but has, par contrast, a positive ADM mass, has a chance of being a stable configuration, although a detailed stability analysis is pending.