Abstract
We investigate the thermodynamic curvature in the Hawking-Page phase transition and the second-order phase transition of the AdS black hole. It is shown that the thermodynamic curvature has the same behavior in these two different phase transitions. Specifically, the thermodynamic curvature in the Hawking-Page phase transition is the power function of the Hawking-Page phase transition temperature with exponent related to the spacetime dimension, or is invariably proportional to the reciprocal of the Hawking-Page phase transition entropy. For the thermodynamic curvature in the second-order phase transition, the conclusion is similar. The more enlightening result is that the ratio of thermodynamic curvatures along the two different phase transitions tends to the natural constant in the limit that the number of spacetime dimensions is infinite. The universal and novel result provides an essential difference between the Hawking-Page phase transition and the second-order phase transition of the AdS black hole in the large dimension paradigm.
Highlights
Phase transition has always been an important issue in theoretical physics
We find that there are some common characteristics between the two different phase transitions of the anti-de Sitter (AdS) black hole system from the perspective of thermodynamic geometry
We study the behavior of the thermodynamic curvature in the two different phase transition to find some common characteristics and essential differences of these two phase transitions
Summary
Phase transition has always been an important issue in theoretical physics. Especially when the black hole is mapped to the thermodynamic system, the analysis of the phase transition of the black hole can help us to explore the connotation of quantum gravity. It is helpful to understand the meaning of thermodynamics geometry in black hole by studying the behavior of thermodynamic curvature in the Hawking-Page phase transition and the second-order phase transition. A universal and novel result is that the ratio tends to the natural constant e when we consider the large dimension limit It provides an essential difference between the Hawking-Page phase transition and the second-order phase transition of the AdS black hole in the large dimension paradigm. This result reflects some unique characteristics of thermodynamic curvature in black hole physics. It is of great significance for us to further understand thermodynamics geometry in gravitational theory and dual field theory
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