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

TL;DR

This paper uses the Hamiltonian formalism to analyze Hawking-Page phase transitions in various black holes, revealing how charge and rotation influence the coexistence of black hole and thermal soliton states.

Contribution

It extends the Hamiltonian approach to off-shell black hole configurations, providing new insights into phase transitions influenced by charge and rotation.

Findings

Hamiltonian corresponds to thermodynamic free energy.

Charge and rotation affect phase transition behavior.

Coexistence of black hole and thermal soliton states observed.

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.