A Puncture in the Euclidean Black Hole

TL;DR

This paper investigates how winding condensates affect the geometry of Euclidean black holes, revealing a critical solution with a puncture that may facilitate information escape in Lorentzian black holes.

Contribution

It provides a numerical analysis of winding condensate backreaction on the cigar background and identifies a critical solution with a puncture at the tip.

Findings

Existence of a critical amplitude A_c for winding condensate

Exact agreement between A_c and the string theory fixed amplitude A_s in large k limit

Critical solution features a puncture at the cigar tip, affecting black hole entropy and information escape

Abstract

We consider the backreaction of the winding condensate on the cigar background. We focus on the case of the $SL(2,\mathbb{R})_k/U(1)$ cigar associated with, e.g., the near-horizon limit of $k$ NS5 black-branes. We solve the equations of motion numerically in the large $k$ limit as a function of the amplitude, $A$, of the winding mode at infinity. We find that there is a critical amplitude, $A_c=\exp(-\gamma/2)$, that admits a critical solution. In string theory, the exact $SL(2,\mathbb{R})_k/U(1)$ cigar CFT fixes completely the winding amplitude, $A_s$, at infinity. We find that in the large $k$ limit there is an exact agreement, $A_c=A_s$. The critical solution is a cigar with a puncture at its tip; consequently, the black-hole entropy is carried entirely by the winding condensate. We argue that, in the Lorentzian case, the information escapes the black hole through this puncture.