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Thermodynamic Phase Transition of Black Hole Hui-Ling Li1

· Wei Li1

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Abstract In the thermodynamic evolution of black holes, the generalized uncertainty principle and quantum tunneling effect prevent the complete evaporation of black holes and produce remnants, and thermodynamic phase transition occurs during evaporation. Based on the generalized uncertainty principle and the method of quantum tunneling, we study the phase transition of the quantum–corrected black hole. Using the modified Hamiltonian–Jacobi equation to analyze the corrected thermodynamic quantity, we find that the thermodynamic phase transition of the black hole is not only depending on the nature of the black hole itself, it also depends on quantum parameter ξ , generalized uncertainty parameter β and parameter λ. Keywords Generalized uncertainty principle · Remnant · Phase transition

1 Introduction With the development of astrophysics, we have made some achievements in thermodynamics research on black holes. The study of the phase transition helps us to understand the nature of the black hole in more detail. However, the classical method studies that the radiation spectrum obtained by the tunneling radiation is purely hot, and it is impossible to extract any physical information about the black hole from the pure heat radiation particles, resulting in the black hole “information paradox” [1] and “naked singularity” problems. Such problems have repeatedly appeared in research, which makes people think that the classical Hawking radiation theory and the corresponding black hole evolution process need to be corrected by using the generalized uncertainty principle, and the modified quantum black hole produces residuals in the final stage of evolution, making the black hole physics information is retained. In 1977, Davies [2] first studied the phase transition of black holes.

 Hui-Ling Li

[email protected] 1

College of Physics Science and Technology, Shenyang Normal University, Shenyang 110034, China

International Journal of Theoretical Physics

He found that the Kerr–Newman black hole experienced a phase transition in the ratio of angular momentum to mass or the amount of charge, and its heat capacity had infinite discontinuity. This feature also exists in general thermodynamic systems and exhibits a second-order phase transition. Later, Pavon discovered an unbalanced second-order phase transition in the charged Reissner–Nordstrom (RN) black hole. In 1983, Hawking and Page [3] explored the thermodynamic phase transition in the asymptotic anti-de sitter (ADS) space. They found that in the Schwarzschild ADS black hole, there is a minimum temperature above which there are two black holes, one for the large horizon and the other for the smaller horizon. And a large black hole has a positive heat capacity, so it is thermally stable, while a smaller black hole has a negative heat capacity and is therefore not a thermally stable black hole. It can be seen from the study of the free