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Hawking-Page phase transitions of black holes in the Hamiltonian formalism

Tran Ngoc Thien, Vo Quoc Phong

Abstract

The Hawking-Page phase transition represents a critical phenomenon in black hole thermodynamics, marking the point at which a thermal radiation state in anti-de Sitter (AdS) spacetime becomes unstable. In this work, we apply the Hamiltonian formalism to study the Hawking-Page phase transition of the Banados-Teitelboim-Zenelli (BTZ) black hole in on-shell and off-shell configuration. The results show that the Hamiltonian of the black hole system corresponds to its thermodynamic free energy. Next, we examine the Hawking-Page phase transition of the Reissner-Nordstrom (RN) black hole and the Kerr-Newmann (KN) black hole, and compare our results with existing results in on-shell case. We then further extend this method to the previously unexplored off-shell case of the RN and KN black holes, thereby demonstrating the influence of the electric charge and the rotation of the black hole on their Hawking-Page phase transition. The results show that, in the presence of electric charge and totation, enables the coexistence of black hole and the thermal soliton states.

Hawking-Page phase transitions of black holes in the Hamiltonian formalism

Abstract

The Hawking-Page phase transition represents a critical phenomenon in black hole thermodynamics, marking the point at which a thermal radiation state in anti-de Sitter (AdS) spacetime becomes unstable. In this work, we apply the Hamiltonian formalism to study the Hawking-Page phase transition of the Banados-Teitelboim-Zenelli (BTZ) black hole in on-shell and off-shell configuration. The results show that the Hamiltonian of the black hole system corresponds to its thermodynamic free energy. Next, we examine the Hawking-Page phase transition of the Reissner-Nordstrom (RN) black hole and the Kerr-Newmann (KN) black hole, and compare our results with existing results in on-shell case. We then further extend this method to the previously unexplored off-shell case of the RN and KN black holes, thereby demonstrating the influence of the electric charge and the rotation of the black hole on their Hawking-Page phase transition. The results show that, in the presence of electric charge and totation, enables the coexistence of black hole and the thermal soliton states.
Paper Structure (20 sections, 95 equations, 6 figures)

This paper contains 20 sections, 95 equations, 6 figures.

Table of Contents

  1. Introduction
  2. The Hamiltonian formalism of the gravity theory
  3. The momenta tensor
  4. The Hamiltonian of the gravitational field
  5. Banados-Teitelboim-Zanelli black hole
  6. Hamiltonian of the black hole
  7. On-Shell
  8. Off-Shell
  9. Evaluation
  10. Reissner-Nordstrom black hole
  11. Hamiltonian of the black hole
  12. On-Shell
  13. Off-Shell
  14. Evaluation
  15. Kerr-Newman black hole
  16. ...and 5 more sections

Figures (6)

  • Figure 1: On-shell free energy as a function of temperature for BTZ black hole.
  • Figure 2: Off-shell free energy of soliton and BTZ black hole at fixed temperature $T$ with respect to $M$.
  • Figure 3: On-shell free energy and critical temperature at fixed charge of RN black hole against $M$.
  • Figure 4: Off-shell free energy of soliton and RN black hole at fixed temperature $T$ and electric charge $Q$ with respect to $M$.
  • Figure 5: On-shell free energy and critical temperature at fixed charge and rotation of KN black hole in terms of M.
  • ...and 1 more figures