[Paper Review] Notes on Black Hole Phase Transitions

G. J. Stephens, B. L. Hu|ArXiv.org|Feb 12, 2001

Relativity and Gravitational Theory4 citations

TL;DR

This paper proposes that black hole phase transitions in semiclassical gravity are entropically driven and analogous to known phase transitions in condensed matter and string theory. By drawing parallels with the Kosterlitz-Thouless transition and the Hagedorn transition in classical and quantum string systems, the authors suggest that the dynamics of black hole formation may be understood through nonequilibrium dynamics of large-N gauge theories and classical strings, offering a novel pathway to probe black hole thermodynamics beyond equilibrium and perturbative approaches.

ABSTRACT

In these notes we present a summary of existing ideas about phase transitions of black hole spacetimes in semiclassical gravity and offer some thoughts on three possible scenarios by which these transitions could take place. Our first theme is ilustrated by a quantum atomic black hole system, generalizing to finite-temperature a model originally offered by Bekenstein. In this equilibrium atomic model, the black hole phase transition is realized as the abrupt excitation of a high energy state, suggesting analogies with the study of two-level atoms. Our second theme argues that the black hole system shares similarities with the defect-mediated Kosterlitz-Thouless transition in condensed matter. These similarities suggest that the black hole phase transition may be more fully understood by focusing upon the dynamics of black holes and white holes, the spacetime analogy of vortex and anti-vortex topological defects. Finally we compare the black hole phase transition to another transition driven by an exponentially increasing density of states, the Hagedorn transition first found in hadron physics in the context of dual models or the old string theory. In modern string theory, the Hagedorn transition is linked by the Maldacena conjecture to the Hawking-Page black hole phase transition in Anti-deSitter space, as observed by Witten. Understanding the dynamics of the Hagedorn transition may thus yield insight into the dynamics of the black hole phase transition. We argue that characteristics of the Hagedorn transition are already contained within classical string systems where a nonperturbative and dynamical analysis is possible.

Motivation & Objective

• To understand the entropic driving force behind black hole phase transitions in semiclassical gravity.
• To explore dynamical mechanisms for black hole formation by drawing analogies with topological defect transitions in condensed matter physics.
• To investigate the connection between the Hagedorn transition in string systems and the Hawking-Page black hole transition in AdS space.
• To propose that nonequilibrium dynamics of classical string systems may model the dynamical formation of black holes.
• To use the AdS/CFT correspondence to link gauge theory deconfinement transitions to black hole phase transitions, enabling new theoretical insights.

Proposed method

• Analyzes black hole thermodynamics using the Bekenstein-Hawking entropy formula, emphasizing entropy-driven phase transitions.
• Introduces a quantum atomic black hole model to illustrate abrupt high-energy state excitation as a phase transition mechanism.
• Draws analogy between black hole formation and the defect-mediated Kosterlitz-Thouless transition, focusing on vortex-anti-vortex pair dynamics.
• Examines the Hagedorn transition in classical string systems with exponential density of states, linking it to black hole formation via the AdS/CFT correspondence.
• Proposes a nonperturbative, nonequilibrium analysis of large-N SU(N) gauge theories to model the Hagedorn transition and its relation to black hole dynamics.
• Uses the Maldacena conjecture to connect the deconfinement transition in boundary gauge theories to the Hawking-Page transition in bulk AdS spacetime.

Experimental results

Research questions

• RQ1 What drives the black hole phase transition in semiclassical gravity, and why does it occur despite the energy cost of black hole formation?
• RQ2 How does the dynamics of black hole formation compare to known phase transitions such as the Kosterlitz-Thouless transition in condensed matter systems?
• RQ3 To what extent do the dynamics of the Hagedorn transition in classical string systems mirror the nonequilibrium formation of black holes?
• RQ4 Can the nonequilibrium dynamics of classical string systems provide a tractable model for the black hole phase transition?
• RQ5 How does the AdS/CFT correspondence link the Hagedorn transition in string theory to the Hawking-Page black hole transition in anti-de Sitter space?

Key findings

• The black hole phase transition is entropically driven, with the large horizon entropy compensating for the energy cost and lowering the system's free energy.
• In the quantum atomic black hole model, the phase transition corresponds to the abrupt excitation of a high-energy state above a critical temperature, analogous to atomic transitions.
• The black hole phase transition shares structural similarities with the Kosterlitz-Thouless transition, particularly in the role of topological defects like vortices and anti-vortices.
• The Hagedorn transition in classical string systems exhibits an exponential density of states, a feature also present in black hole systems and linked to the Hawking-Page transition via the AdS/CFT correspondence.
• The dynamics of the Hagedorn transition—particularly the abrupt formation of infinite strings—may serve as a universal model for the nonequilibrium dynamics of black hole formation.
• A full nonperturbative and nonequilibrium analysis of large-N SU(N) gauge theories is proposed as a viable route to understanding the dynamics of black hole phase transitions in AdS space.