Global Monopoles in the Extended Gauss-Bonnet Gravity

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 $Φ$ that couples to the Gauss-Bonnet higher curvature combination with a coupling parameter $α$. We obtain a range of values for $α< 0$ (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 $δ$ with a de-Sitter interior, guaranteeing the positivity of the ADM mass of the monopole, which, together with a positive core radius $δ> 0$, are both dynamically determined as a result of this matching. It should be stressed that in the General Relativity (GR) limit, where $α\to 0$, and $Φ\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.