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Home > Advances in High Energy Physics (Hindawi) > New Phase Transition Related to the Black Hole’s Topological Charge |

Lan, Shan-Quan (Department of Physics, Lingnan Normal University, Zhanjiang, Guangdong 524048, China) ; Li, Gu-Qiang (Department of Physics, Lingnan Normal University, Zhanjiang, Guangdong 524048, China) ; Mo, Jie-Xiong (Department of Physics, Lingnan Normal University, Zhanjiang, Guangdong 524048, China) ; Xu, Xiao-Bao (Department of Physics, Lingnan Normal University, Zhanjiang, Guangdong 524048, China)

23 January 2019

**Abstract: **The topological charge $\u03f5$ of AdS black hole is introduced by Tian et al. in their papers, where a complete thermodynamic first law is obtained. In this paper, we investigate a new phase transition related to the topological charge in Einstein-Maxwell theory. Firstly, we derive the explicit solutions corresponding to the divergence of specific heat ${C}_{\u03f5}$ and determine the phase transition critical point. Secondly, the $T-r$ curve and $T-S$ curve are investigated and they exhibit an interesting van der Waals system’s behavior. Critical physical quantities are also obtained which are consistent with those derived from the specific heat analysis. Thirdly, a van der Waals system’s swallow tail behavior is observed when $\u03f5>{\u03f5}_{c}$ in the $F-T$ graph. What is more, the analytic phase transition coexistence lines are obtained by using the Maxwell equal area law and free energy analysis, the results of which are consistent with each other.

**Published in: ****Advances in High Energy Physics 2019 (2019) 8270265**
**Published by: **Hindawi

**DOI: **10.1155/2019/8270265

**arXiv: **1804.06652v1

**License: **CC-BY-3.0