String spreading on a black hole horizon

The phenomenon of string spreading on the black hole horizon, as originally discussed by Susskind, is considered in the exact curved Schwarzschild background. We consider an oscillating macroscopic string encircling the black hole and contracting towards the horizon. We then compute the angular and radial spreading of the string, as seen by a static observer at spatial infinity using fixed finite resolution time. Within our case study we find that there is indeed a spreading of the string in the angular direction, such that the string eventually covers the whole horizon. However, regarding the radial direction, we find that Lorentz-contraction suppresses the radial string spreading.