It has been recently shown that topological defects can arise in symmetry b
reaking models where the scalar field potential V(phi) has no minima and is
a monotonically decreasing function of \phi\. Here we study the gravitatio
nal 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 simil
ar to that in de Sitter space. A gauge monopole spacetime is essentially th
at of a magnetically charged black hole. The gravitational field of a globa
l string is repulsive and that of a gauge string is attractive at small dis
tances and repulsive at large distances. Both gauge and global string space
times have singularities at a finite distance from the string core. [S0556-
2821(99)01806-8].