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arXiv · 2307.01569

Thermodynamic phase transition and winding number for the third-order Lovelock black hole

Yu-Shan Wang·Zhen-Ming Xu·Bin Wu
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Abstract

Phase transition is important for understanding the nature and evolution of the black hole thermodynamic system. In this study, the connection between the phase transition of a black hole and the winding number derived by the complex analysis is used to predict the type of the black hole phase transition. For the third-order Lovelock black holes, at the hyperbolic topology in any dimensions and the spherical topology in $7$ dimensions, we arrive at the winding numbers both are $W=3$ which predicts that the system will undergo both the first-order and second-order phase transitions. For the spherical topology in $7<d<12$ dimensions, the winding number is $W=4$ and the corresponding phase transition will occur in two situations: one with only pure second-order phase transition and the other with both first-order and second-order phase transitions. We further confirm the correctness and rationality of this prediction by placing the black hole thermodynamics system in the potential field.

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Yu-Shan Wang, Zhen-Ming Xu, Bin Wu. 2023-07-04. Thermodynamic phase transition and winding number for the third-order Lovelock black hole. https://doi.org/10.1088/1674-1137/ad53ba

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