From Black Strings to Fundamental Strings: Non-uniformity and Phase Transitions

TL;DR

This paper investigates phase transitions between black strings and fundamental strings in higher dimensions, analyzing stability, non-uniform solutions, and the role of string theory models in these gravitational phenomena.

Contribution

It provides a detailed analysis of the stability and phase transitions of black strings, including the identification of critical masses and the introduction of new solutions with symmetry breaking.

Findings

Critical mass for Gregory-Laflamme instability identified.

Transition from uniform black strings to localized black holes described.

Stability analysis using string theory models like SL(2)_k/U(1).

Abstract

We discuss the transition between black strings and fundamental strings in the presence of a compact dimension, $\mathbb{S}^1_z$. In particular, we study the Horowitz-Polchinski effective field theory in $\mathbb{R}^d\times\mathbb{S}^1_z$, with a reduction on the Euclidean time circle $\mathbb{S}_\tau^1$. The classical solution of this theory describes a bound state of self-gravitating strings, known as a ``string star'', in Lorentzian spacetime. By analyzing non-uniform perturbations to the uniform solution, we identify the critical mass at which the string star becomes unstable towards non-uniformity along the spatial circle (i.e., Gregory-Laflamme instability) and determine the order of the associated phase transition. For $3\le d<4$, we argue that at the critical mass, the uniform string star can transition into a localized black hole. More generally, we describe the sequence of transitions from a large uniform black string as its mass decreases, depending on the value of $d$. Additionally, using the $SL(2)_k/U(1)$ model in string theory, we show that for sufficiently large $d$, the uniform black string is stable against non-uniformity before transitioning into fundamental strings. We also present a novel solution that exhibits double winding symmetry breaking in the asymptotically $\mathbb{R}^d\times\mathbb{S}^1_\tau\times\mathbb{S}^1_z$ Euclidean spacetime.