How to Create a 2-D Black Hole

TL;DR

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

Contribution

It proves a uniqueness theorem for stationary string configurations, characterizes the internal geometry of string holes, and explores their perturbation equations and implications for causality and information loss.

Findings

The minimal 2-D surface of a captured string coincides with a principal Killing surface.

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

Perturbation equations are equivalent to scalar fields in the string hole spacetime.

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.