Folded strings falling into a black hole

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Abstract
We find all the classical solutions (minimal surfaces) of open or closed strings in any two-dimensional (2D) curved spacetime. As examples we consider the SL(2,R)/R two-dimensional black hole, and any 4D black hole in the Schwarzschild family, provided the motion is restricted to the time-radial components. The solutions, which describe longitudinally oscillating folded strings (radial oscillations in 4D), must be given in latticelike patches of the world sheet, and a transfer operation analogous to a transfer matrix determines the future evolution. Then the swallowing of a string by a black hole is analyzed. We find several new features that are not shared by particle motions. The most surprising effect is the tunneling of the string into the bare singularity region that lies beyond the black hole that is classically forbidden to particles.