How to create a two-dimensional 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. It is shown that the minimal 2D surface $\Sigma$ 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. A uniqueness theorem is proved, namely, it is shown that the principal Killing surfaces are the only stationary solutions of the string equations which enter the ergosphere and remain timelike and regular at the static limit surface. Geometrical properties of principal Killing surfaces are investigated and it is shown that the internal geometry of $\Sigma$ coincides with the geometry of a 2D 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 2D string hole. Some interesting features of the physics of 2D 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 point of view of the 2D geometry this interaction is acausal. Possible application of this result to the information loss puzzle is briefly discussed.