Scattering of string-waves on black hole background

We consider the propagation of perturbations along an infinitely long stationary open string in the background of a Schwarzschild black hole. The equations of motion for the perturbations in the 2 transverse physical directions are solved to second order in a weak field expansion. We then set up a scattering formalism where an ingoing wave is partly transmitted and partly reflected due to the interaction with the gravitational field of the black hole. We finally calculate the reflection coefficient to third order in our weak field expansion.