# Hawking-Page phase transitions of the charged AdS black holes surrounded by quintessence

• The Hawking-Page phase transitions between the thermal anti-de Sitter vacuum and the charged black holes surrounded by quintessence are studied in the extended phase space. The quintessence field, with a state parameter $-1 < w < -1/3$, modifies the temperature and the Gibbs free energy of the black hole. The phase transition temperature $T_{\rm{HP}}$ and the Gibbs free energy $G$ are first analytically investigated for the special case with $w=-2/3$, and then numerically illustrated for the cases with general $w$. The phase transition temperature $T_{\rm{HP}}$ is found to increase with pressure and to decrease with electric potential. Moreover, $T_{\rm{HP}}$ is also significantly decreased by the quintessence field, which presents a negative pressure around the black hole.

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Da-Wei Yan, Ze-Rong Huang and Nan Li. Hawking-Page phase transitions of the charged AdS black holes surrounded by quintessence[J]. Chinese Physics C.
Da-Wei Yan, Ze-Rong Huang and Nan Li. Hawking-Page phase transitions of the charged AdS black holes surrounded by quintessence[J]. Chinese Physics C.
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沈阳化工大学材料科学与工程学院 沈阳 110142

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## Hawking-Page phase transitions of the charged AdS black holes surrounded by quintessence

###### Corresponding author: Nan Li, linan@mail.neu.edu.cn
• 1. Department of Physics, College of Sciences, Northeastern University, Shenyang 110819, China
• 2. Department of Material Physics, School of Material Sciences and Engineering, Northeastern University, Shenyang 110819, China

Abstract: The Hawking-Page phase transitions between the thermal anti-de Sitter vacuum and the charged black holes surrounded by quintessence are studied in the extended phase space. The quintessence field, with a state parameter $-1 < w < -1/3$, modifies the temperature and the Gibbs free energy of the black hole. The phase transition temperature $T_{\rm{HP}}$ and the Gibbs free energy $G$ are first analytically investigated for the special case with $w=-2/3$, and then numerically illustrated for the cases with general $w$. The phase transition temperature $T_{\rm{HP}}$ is found to increase with pressure and to decrease with electric potential. Moreover, $T_{\rm{HP}}$ is also significantly decreased by the quintessence field, which presents a negative pressure around the black hole.

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