Fluid model of a black hole-string transition

TL;DR

This paper introduces a fluid model for self-gravitating strings that captures the transition from black holes to strings near the Hagedorn temperature, aligning with previous models and extending understanding of this phase change.

Contribution

It demonstrates that winding strings can be modeled as a perfect fluid and provides solutions that describe the black hole-string transition.

Findings

Fluid of winding strings behaves as a perfect fluid.

Solution reproduces self-gravitating string behaviors near Hagedorn temperature.

Transition to Schwarzschild black hole at low temperatures.

Abstract

A fluid model of self-gravitating strings is proposed. It is expected that black holes turn into strings around the end of black hole evaporation. The transition will occur near the Hagedorn temperature. After the transition, strings would form a bound state by the self-gravitation. Horowitz and Polchinski formulated a model of self-gravitating strings by using winding strings wrapping on the Euclidean time circle [arXiv:hep-th/9707170]. In this paper, we first show that winding strings in the Horowitz-Polchinski model approximately behave as a perfect fluid. Then, we solve the Einstein equation for the fluid of winding strings. Our solution reproduces behaviors of the self-gravitating string solution in the Horowitz-Polchinski model near the Hagedorn temperature, while it approaches the Schwarzschild black hole at low temperatures. Thus, our fluid model of self-gravitating strings gives a description of the transition between black holes and strings.