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arXiv · 2603.16560

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

Tran Ngoc Thien·Vo Quoc Phong
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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.

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Tran Ngoc Thien, Vo Quoc Phong. 2026-03-17. Hawking-Page phase transitions of black holes in the Hamiltonian formalism. https://arxiv.org/abs/2603.16560

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