ar X iv : h ep - t h / 95 11 06 9 v 2 1 5 N ov 1 99 5 How to Create a 2 - D Black Hole

The interaction of a cosmic string with a four-dimensional stationary black hole is considered. If a part of an infinitely long string passes close to a black hole it can be captured. The final stationary configurations of such captured strings are investigated. A uniqueness theorem is proved, namely it is shown that the minimal 2-D surface Σ describing a captured stationary string coincides with a principal Killing surface, i.e. a surface formed by Killing trajectories passing through a principal null ray of the Kerr-Newman geometry. Geometrical properties of principal Killing surfaces are investigated and it is shown that the internal geometry of Σ coincides with the geometry of a 2-D black or white hole (string hole). The equations for propagation of string perturbations are shown to be identical with the equations for a coupled pair of scalar fields 'living' in the spacetime of a 2-D string hole. Some interesting features of physics of 2-D string holes are described. In particular, it is shown that the existence of the extra dimensions of the surrounding spacetime makes interaction possible between the interior and exterior of a string black hole; from the 1 point of view of the 2-D geometry this interaction is acausal. Possible application of this result to the information loss puzzle is briefly discussed.