We examine the metric of an isolated self-gravitating abelian-Higgs vortex in
dilatonic gravity for arbitrary coupling of the vortex fields to the dilaton.
We look for solutions in both massless and massive dilaton gravity. We compare
our results to existing metrics for strings in Einstein and Jordan-Brans-Dicke
theory. We explore the generalization of Bogomolnyi arguments for our vortices
and comment on the effects on test particles.Comment: 24 pages plain TEX, 4 figures -- references amended, some additional
comments added, version to appear in journa
