A spin on Hagedorn temperatures and string stars

TL;DR

This paper explores the relationship between highly excited rotating strings and black holes, identifying a rotating string star phase and analyzing the effects of angular momentum on the Hagedorn temperature and string-black hole correspondence.

Contribution

It introduces a novel rotating string star saddle, extending the string-black hole correspondence to include angular momentum effects and providing exact Hagedorn temperature formulas.

Findings

Identification of a rotating string star phase.

Exact determination of Hagedorn temperature with angular momentum.

Interpolation between rotating strings and black holes.

Abstract

We discuss the correspondence between highly excited strings and black holes in the presence of angular momentum. At fixed imaginary angular velocity $\nu$, we show that free strings exhibit a Hagedorn instability due to a thermal-winding mode turning tachyonic. This allows us to determine the exact Hagedorn temperature $\beta_H(\nu)$ for bosonic, type II, and heterotic strings. Using the effective field theory for the thermal-winding mode around the $\nu$-dependent background, we find a novel `rotating string star' saddle (perturbatively in the angular velocity) and study its properties. This configuration describes a self-gravitating bound state of highly excited rotating strings. As in the non-rotating case, the saddle is qualitatively shown to interpolate between the rotating strings phase and a rotating black hole. We also comment on the implications of these results for anti-de Sitter space.