  It has been recently shown that topological defects can arise in symmetry
breaking models where the scalar field potential $V(\phi)$ has no minima and is
a monotonically decreasing function of $|\phi|$. Here we study the
gravitational fields produced by such vacuumless defects in the cases of both
global and gauge symmetry breaking. We find that a global monopole has a
strongly repulsive gravitational field, and its spacetime has an event horizon
similar to that in de Sitter space. A gauge monopole spacetime is essentially
that of a magnetically charged black hole. The gravitational field of a global
string is repulsive and that of a gauge string is attractive at small distances
and repulsive at large distances. Both gauge and global string spacetimes have
singularities at a finite distance from the string core.
