Phases of String Stars in the Presence of a Spatial Circle

TL;DR

This paper investigates phase transitions of string stars in various dimensions using an effective field theory, revealing novel solutions, stability properties, and phase diagrams, especially highlighting differences between canonical and microcanonical ensembles.

Contribution

It introduces new solutions and phase transition behaviors for string stars in different dimensions, incorporating quartic corrections to the effective action.

Findings

In $d=2$, uniform string stars lack a critical transition point.

Quartic corrections resolve mass degeneracy in $d=4$.

In $d=5$, phase diagrams exhibit swallowtail structures due to quartic terms.

Abstract

In string theory, black holes are expected to transition into string stars as their Hawking temperatures approach the Hagedorn temperature. We study string stars and their phase transitions in the Euclidean spacetime $\mathbb{R}^d\times\mathbb{S}_\tau^1\times\mathbb{S}_z^1$. Using the Horowitz-Polchinski (HP) effective field theory, we discover novel solutions for $d=2$. The uniform string star exhibits a scaling symmetry that results in the absence of a critical point for its transition into the non-uniform solution. For $d=4$, we show that quartic corrections to the effective action resolve the mass degeneracy of uniform string stars. At $d=5$, we find that as non-uniformity increases, the quartic terms become significant (while higher-order terms remain negligible) and reverse the direction of temperature variation, leading to a swallowtail-type phase diagram in the canonical ensemble. Extending the quartic-corrected EFT to $d=6$, we find that string stars with small non-uniformity dominate the microcanonical ensemble but not the canonical ensemble, similar to the $d=5$ case. However, in the microcanonical ensemble, the uniform string star is anomalously (un)stable when the spatial circle is larger (smaller) than the critical size.