[Paper Review] Born-Infeld-AdS black hole phase structure: Landau theory and free energy landscape approaches

Md Sabir Ali, H. El Moumni+2 more|arXiv (Cornell University)|Mar 21, 2023

Black Holes and Theoretical Physics4 citations

TL;DR

This paper investigates the thermal phase transitions of Born-Infeld-AdS black holes using Landau theory and the Fokker-Planck equation to model stochastic dynamics and free energy landscapes. It identifies a triple point where small, large, and thermal radiation phases coexist, rules out reentrant phase transitions for certain charge values, and computes first passage times and mean first passage times via the Crank-Nicolson method, linking kinetic behavior to microscopic degrees of freedom.

ABSTRACT

We start with a brief overview of the basic thermodynamic properties of the Born-Infeld metric in AdS spacetime. Using the concept of the enthalpy characterizing the total mass of the black hole, in our present paper, we probe the thermal phase transition structure, the dynamic and kinetic behavior of the Born-Infeld-AdS black hole. The emergence of the triple point behavior and the possible ruling out the reentrant phase transition, for a certain parametric value of the charge on the free energy landscape, we scrutinize the stochastic dynamics and the kinetic processes. We describe such processes during the black hole phase transitions in terms of the Landau functional and equivalently by the Fokker-Planck equation in the context of black hole chemistry. Our analysis establishes a pertinent bridge between the thermal behavior among the different states of the Van-der-Waals-like fluids and the Born-Infeld-AdS black holes phases. To visualize the direct implications of the Landau functional of the usual Van-der-Waals-like fluids, we consistently employed the generic Landau formalism for the analysis of the black hole phase transitions of the Born-Infeld-AdS black holes. We find that such investigations are worthy of study in implementing the continuous phase transition behavior during the Hawking radiation. For more details, and in addition to the exploitation of the Landau functional, we introduce ...

Motivation & Objective

• To investigate the thermal phase structure of Born-Infeld-AdS black holes using thermodynamic and stochastic approaches.
• To determine whether reentrant phase transitions occur in the system for specific charge parameters.
• To model the kinetic processes during phase transitions using the Landau functional and Fokker-Planck equation.
• To analyze the free energy landscape and identify stable/unstable phases via convexity of the Landau functional.
• To compute first passage times and mean first passage times to quantify the time scale of phase transitions.

Proposed method

• Applies Landau theory formalism to model phase transitions in Born-Infeld-AdS black holes using an order parameter and free energy functional.
• Uses the Fokker-Planck equation to describe the stochastic evolution of the order parameter across the free energy landscape.
• Implements the Crank-Nicolson method for numerical solution of the Fokker-Planck equation with implicit time discretization and central spatial differences.
• Defines boundary conditions via zero flux at edges, ensuring probability conservation in the numerical scheme.
• Calculates the probability distribution and its evolution over time to study transitions between small, large, and thermal radiation phases.
• Evaluates the mean first passage time and its fluctuations to assess kinetic turnover and friction effects in phase transitions.

Experimental results

Research questions

• RQ1 Does the Born-Infeld-AdS black hole exhibit a reentrant phase transition for certain values of the electric charge?
• RQ2 How does the free energy landscape govern the stability and coexistence of small, large, and thermal radiation phases?
• RQ3 What is the role of the Landau functional in describing continuous and first-order phase transitions in black hole systems?
• RQ4 How do the first passage time and mean first passage time characterize the kinetic dynamics of phase transitions?
• RQ5 What is the connection between friction in the kinetic process and the microscopic degrees of freedom of the black hole?

Key findings

• The system exhibits a triple point where small black hole, large black hole, and pure thermal radiation phases coexist, indicating complex phase coexistence.
• For certain parametric values of the charge, the reentrant phase transition is ruled out, suggesting a critical dependence on electromagnetic parameters.
• The Landau functional's convexity is used to identify stable and unstable phases, confirming the presence of first- and second-order phase transitions.
• Numerical solutions of the Fokker-Planck equation show that the initial probability evolves from small to large black hole states, with equilibrium established among all three phases.
• The mean first passage time and its fluctuations are computed using the Crank-Nicolson method, revealing kinetic time scales linked to friction effects.
• The friction coefficient is directly related to the microscopic degrees of freedom, providing insight into the dynamics of black hole micromolecules during phase transitions.