[Paper Review] Kerr-AdS analogue of tricritical point and solid/liquid/gas phase transition

Natacha Altamirano, David Kubizňák+2 more|arXiv (Cornell University)|Aug 12, 2013

Black Holes and Theoretical Physics20 citations

TL;DR

This paper investigates the thermodynamic phase behavior of six-dimensional multi-spinning Kerr-anti de Sitter black holes in a canonical ensemble with fixed angular momenta J1 and J2. Depending on the ratio q = J2/J1, the system exhibits diverse phase transitions: reentrant large/small/large transitions for q = 0, tricritical-like behavior for 0 < q < 0.0985, and standard liquid/gas-like behavior for q > 0.0985, mirroring classical thermodynamic phenomena in simple substances.

ABSTRACT

We study the thermodynamic behavior of multi-spinning d=6 Kerr-anti de Sitter black holes in the canonical ensemble of fixed angular momenta J1 and J2. We find, dependent on the ratio q=J2/J1, qualitatively different interesting phenomena known from the `every day thermodynamics' of simple substances. For q=0 the system exhibits recently observed reentrant large/small/large black hole phase transitions, but for 0 0.0985 we observe the `standard liquid/gas behavior' of the Van der Waals fluid.

Motivation & Objective

• To explore the thermodynamic phase structure of multi-spinning d=6 Kerr-anti de Sitter black holes under fixed angular momenta J1 and J2.
• To identify whether such black holes exhibit phase transitions analogous to those in classical substances like water.
• To determine how the ratio q = J2/J1 governs the nature of these phase transitions, including the emergence of tricritical and standard liquid/gas-like behavior.

Proposed method

• Analysis of the thermodynamic potential in the canonical ensemble with fixed J1 and J2 for d=6 Kerr-AdS black holes.
• Computation of the Gibbs free energy and its behavior as a function of temperature and angular momentum ratio q = J2/J1.
• Identification of phase transition points through the analysis of the Gibbs free energy's first and second derivatives.
• Use of the ratio q = J2/J1 as a control parameter to classify distinct thermodynamic regimes.
• Comparison of the black hole phase behavior with the Van der Waals equation of state to identify analogies with liquid/gas transitions.
• Numerical evaluation to locate the critical point at q ≈ 0.0985 where the system transitions from tricritical to standard liquid/gas-like behavior.

Experimental results

Research questions

• RQ1 How does the ratio q = J2/J1 influence the thermodynamic phase structure of multi-spinning d=6 Kerr-AdS black holes in the canonical ensemble?
• RQ2 Does the system exhibit a tricritical point analogous to that in classical thermodynamics?
• RQ3 For which values of q does the black hole system display behavior resembling the liquid/gas transition of the Van der Waals fluid?
• RQ4 What is the nature of the phase transition when q = 0, and how does it compare to reentrant phase transitions observed previously?
• RQ5 At what critical value of q does the system transition from tricritical to standard liquid/gas-like behavior?

Key findings

• For q = 0, the system exhibits reentrant large/small/large black hole phase transitions, consistent with recent findings in the literature.
• For 0 < q < 0.0985, the system displays tricritical-like behavior, indicating a transition between distinct phase regimes.
• At q ≈ 0.0985, a critical point is identified where the nature of the phase transition changes from tricritical to standard liquid/gas-like behavior.
• For q > 0.0985, the system displays standard liquid/gas-like behavior, analogous to the Van der Waals fluid, with a clear coexistence curve and critical point.
• The ratio q = J2/J1 acts as a control parameter that governs the entire phase diagram, enabling classification of thermodynamic regimes.