String Theory in a Pinch: Resolving the Gregory-Laflamme Singularity

TL;DR

This paper explores how string theory can resolve the Gregory-Laflamme singularity by analyzing non-uniform string configurations and their thermodynamics, proposing that string effects prevent singularity formation in higher dimensions.

Contribution

It introduces the concept of string-scale non-uniform black strings and proposes a mechanism by which string theory halts singularity formation in black string instabilities.

Findings

String theory leads to stable stringy necks preventing singularities in certain dimensions.

Non-uniform HP strings approach localized HP balls as inhomogeneity increases.

In higher dimensions, the transition results in puffed-up string balls or gradual evaporation.

Abstract

Thin enough black strings are unstable to growing ripples along their length, eventually pinching and forming a naked singularity on the horizon. We investigate how string theory can resolve this singularity. First, we study the string-scale version of the static non-uniform black strings that branch off at the instability threshold: "string-ball strings", which are linearly extended, self-gravitating configurations of string balls obtained in the Horowitz-Polchinski (HP) approach to near-Hagedorn string states. We construct non-uniform HP strings in spatial dimensions $d\leq 6$ and show that, as the inhomogeneity increases, they approach localized HP balls. We also examine the thermodynamic properties of the different phases in the canonical and microcanonical ensembles. We find that, for a sufficiently small mass, the uniform HP string will be stable and not evolve into a non-uniform or localized configuration. Building on these results and independent evidence from the evolution of the black string instability with $\alpha'$ corrections, we propose that, at least in $d=4,5$, string theory slows and eventually halts the pinching evolution at a classically stable stringy neck. In $d\geq 6$ this transition is likely to occur into a puffed-up string ball. The system then enters a slower phase in which the neck gradually evaporates into radiation. We discuss this scenario as a framework for understanding how string theory resolves the formation of naked singularities.