  We study the gravi-dilaton field of a Schwarzschild black hole pierced by a
thin cosmic string in both massless and massive dilatonic gravity. We conclude
that in the thin vortex approximation the string's spacetime is asymptotically
flat with a conical deficit angle and that the inertial mass of the black hole
is different from the gravitational one. We generalize our results to charged
black holes.
