Dilatonic String through black holes

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.