Instability and phase transitions of a rotating black hole in the presence of perfect fluid dark matter

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In this paper, we study the thermodynamic features of a rotating black hole surrounded by perfect fluid dark matter.

• We analyze the critical behavior of the black hole by considering the known relationship between pressure and cosmological constant.
• We show that the black hole admits a first order phase transition and, both rotation and perfect fluid dark matter parameters have a significant impact on the critical quantities.
• We also introduce a new ad hoc pressure related to the perfect fluid dark matter and find a first order van der Waals like phase transition.