How to Create a 2-D Black Hole

TL;DR

This paper investigates the geometry and physics of 2-D black holes formed by cosmic strings near Kerr-Newman black holes, revealing unique properties and potential implications for the information loss paradox.

Contribution

It proves a uniqueness theorem for stationary string configurations and explores the internal geometry and perturbation dynamics of 2-D string holes.

Findings

The minimal surface of a captured string is a principal Killing surface.

The internal geometry of the string hole resembles a 2-D black or white hole.

Interaction between interior and exterior of a string black hole can be acausal due to extra dimensions.

Abstract

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 $\Sigma$ describing a captured stationary string coincides with a {\it 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 $\Sigma$ coincides with the geometry of a 2-D black or white hole ({\it 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 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.