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In this paper, considering the influence of the principle of generalized uncertainty (GUP), the phase transition of a Schwarzschild black hole with global monopole is discussed. First, we use the generalized Dirac equation to obtain corrected Hawking temperature, local temperature, black hole residues, black hole entropy, thermal capacity, and other thermodynamic quantities. Then, we analyze the effects of generalized uncertainty parameters and the monopole parameter on phase transitions. Finally, we study the thermodynamic stability and phase transition structure under the influence of GUP. The results show that, for the black hole with global monopole, there are first–order and second–order phase transitions. In addition, the general uncertainty parameter and monopole parameter will affect the black hole residues. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Very recently, via the covariant form of the adiabatic invariant I = ... pi dqi instead of I = ∫ pidqi, an equally spaced spectroscopy of a Schwarzschild black hole was derived. The emphasis was given to the covariant of results. In this paper, we extend that work in a spherically symmetric spacetime to the case of a rotating Bañados--Teitelboim--Zanelli (BTZ) black hole. It is noteworthy that the adiabatic covariant action I = ... pidqi gives the same value for the black hole spectroscopy in different coordinates. The result shows that the area spectrum is ΔA = 8π/²P, which confirms Bekenstein's initial proposal. And the result is consistent with that already obtained by other methods. [ABSTRACT FROM AUTHOR]

In the framework of holography, we discuss on the phase transition behavior from a novel Gauss–Bonnet AdS black hole discovered in [Phys. Rev. Lett. 124, 081301 (2020)] in both charged and neutral cases. First, we explore the thermodynamic behavior for the black hole entropy by investigating T - S diagram, specific heat capacity and free energy, and we find that, in the T - S plane, the black hole exhibits a van der Waals phase transition similar to that in P - V plane in extended phase space. Secondly, we detect thermodynamic phase transition for the two point correlation function, and find that, the van der Waals phase transition can also be displayed in the T - δ L plane which is completely similar to that of black hole entropy in the T - S plane. Our result turns out that, not only the charged but also neutral cases, we can observe holographic van der Waals phase transition for the novel Gauss–Bonnet AdS black hole by employing the black hole entropy and two point correlation function. [ABSTRACT FROM AUTHOR]