Thermodynamic black di-rings

TL;DR

This paper explores the thermodynamic properties of five-dimensional black di-rings, demonstrating their equilibrium states, equivalence of solution sets, and analyzing their stability and peculiar characteristics.

Contribution

The authors analyze thermodynamic equilibrium and stability of five-dimensional black di-rings, revealing their equilibrium conditions and discussing their unique thermodynamic properties.

Findings

Existence of thermodynamic black di-rings with isothermality and isorotation.

Equivalence of different solution sets of black di-rings.

Discussion of thermodynamic stability and instability.

Abstract

Previously the five dimensional $S^1$-rotating black rings have been superposed in a concentric way by some solitonic methods, and regular systems of two $S^1$-rotating black rings were constructed by the authors and then Evslin and Krishnan (we called these solutions "black di-rings"). In this place we show some characteristics of the solutions of five dimensional black di-rings, especially in thermodynamic equilibrium. After the summary of the di-ring expressions and their physical quantities, first we comment on the equivalence of the two different solution sets of the black di-rings. Then the existence of thermodynamic black di-rings is shown, in which both isothermality and isorotation between the inner black ring and the outer black ring are realized. We also give detailed analysis of peculiar properties of the thermodynamic black di-ring including discussion about a certain kind of thermodynamic stability (instability) of the system.