STATIONARY STRINGS AND 2-D BLACK HOLES

TL;DR

This paper develops a framework for understanding string excitations in stationary spacetimes, revealing that strings passing through black hole ergospheres behave like 2D black holes, with implications for black hole thermodynamics and information paradox.

Contribution

It introduces a general description of string excitations near stationary black holes, linking 2D black hole physics to cosmic strings in Kerr black hole environments.

Findings

String modes are thermally excited near black holes.

String excitations reduce to scalar field equations in specific cases.

Potential applications to the black hole information puzzle.

Abstract

A general description of string excitations in stationary spacetimes is developed. If a stationary string passes through the ergosphere of a 4-dimensional black hole, its world-sheet describes a 2-dimensional black (or white) hole with horizon coinciding with the static limit of the 4-dimensional black hole. Mathematical results for 2-dimensional black holes can therefore be applied to physical objects (say) cosmic strings in the vicinity of Kerr black holes. An immediate general result is that the string modes are thermally excited. The string excitations are determined by a coupled system of scalar field equations in the world-sheet metric. In the special case of excitations propagating along a stationary string in the equatorial plane of the Kerr-Newman black hole, they reduce to the $s$-wave scalar field equations in the 4-dimensional Reissner-Nordstr\"{o}m black hole. We briefly discuss possible applications of our results to the black hole information puzzle.