Modeling the dynamics of global monopoles

A thin wall approximation is exploited to describe a global monopole coupled to gravity. The core is modeled by de Sitter space, its boundary by a thin wall with a constant energy density, and its exterior by the asymptotic Schwarzschild solution with negative gravitational mass (Formula presented) and solid angle deficit, (Formula presented), where (Formula presented) is the symmetry-breaking scale. The deficit angle equals (Formula presented) when (Formula presented) We find that (1) if (Formula presented) there exists a unique globally static nonsingular solution with a well-defined mass, (Formula presented). (Formula presented) provides a lower bound on (Formula presented). If (Formula presented), the solution oscillates. There are no inflating solutions in this symmetry-breaking regime. (2) If (Formula presented) nonsingular solutions with an inflating core and an asymptotically cosmological exterior will exist for all (Formula presented). (3) If (Formula presented) is not too large, there exists a finite range of values of (Formula presented) where a noninflating monopole will also exist. These solutions appear to be metastable towards inflation. If (Formula presented) is positive, all solutions are singular. We provide a detailed description of the configuration space of the model for each point in the space of parameters (Formula presented) and trace the wall trajectories on both the interior and the exterior spacetimes. Our results support the proposal that topological defects can undergo inflation.