  A thin wall approximation is exploited to describe a global monopole coupled
to gravity. The core is modelled by de Sitter space; its boundary by a thin
wall with a constant energy density; its exterior by the asymptotic
Schwarzschild solution with negative gravitational mass $M$ and solid angle
deficit, $\Delta\Omega/4\pi = 8\pi G\eta^2$, where $\eta$ is the symmetry
breaking scale. The deficit angle equals $4\pi$ when $\eta=1/\sqrt{8\pi G}
\equiv M_p$. We find that: (1) if $\eta <M_p$, there exists a unique globally
static non-singular solution with a well defined mass, $M_0<0$. $M_0$ provides
a lower bound on $M$. If $M_0<M<0$, the solution oscillates. There are no
inflating solutions in this symmetry breaking regime. (2) if $\eta \ge M_p$,
non-singular solutions with an inflating core and an asymptotically
cosmological exterior will exist for all $M<0$. (3) if $\eta$ is not too large,
there exists a finite range of values of $M$ where a non-inflating monopole
will also exist. These solutions appear to be metastable towards inflation. If
$M$ 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, $(\eta, M)$ and trace the wall trajectories on both the interior
and the exterior spacetimes. Our results support the proposal that topological
defects can undergo inflation.

General Relativity and Quantum Cosmology;Astrophysics