Perfect fluid dark matter influence on thermodynamics and phase transition for a Reissner-Nordstrom-anti-de Sitter black hole

Understand

Based on Reissner-Nordstrom-anti-de Sitter(RN-AdS) black hole surrounded by perfect fluid dark matter, we study the thermodynamics and phase transition by extending the phase space defined by the charge square $Q^{2}$ and the conjugate quantity $\psi$, where $\psi$ is a function of horizon radius.

• The first law of thermodynamics and the equation of state are derived in the form $Q^{2}=Q^{2}(T,\psi)$.
• By investigating the critical behaviour of perfect fluid dark matter around Reissner-Nordstrom-anti-de Sitter black hole, we find that these thermodynamics system are similar to Van der Waals system, and can be explained by mean field theory.
• We also explore the Ruppeiner thermodynamic geometry feature and their connection with microscopic structure.