Abstract:
By considering the concept of the modified
Chaplygin gas (MCG) as a single fluid model unifying dark
energy and dark matter, we construct a static, spherically
charged black hole (BH) solution in the framework of General Relativity. The P–V criticality of the charged anti-de
Sitter (AdS) BH with a surrounding MCG is explored in
the context of the extended phase space, where the negative
cosmological constant operates as a thermodynamical pressure. This critical behavior shows that the small/large BH
phase transition is analogous to the van der Waals liquid/gas
phase transition. Accordingly, along the P–V phase spaces,
we derive the BH equations of state and then numerically
evaluate the corresponding critical quantities. Similarly, critical exponents are identified, along with outcomes demonstrating the scaling behavior of thermodynamic quantities
near criticality to a universal class. The use of geometrothermodynamic (GT) tools finally offers a new perspective on
the discovery of the critical phase transition point. At this
stage, we apply a class of GT tools, such as Weinhold, Ruppeiner, HPEM, and Quevedo classes I and II. The findings
are therefore non-trivial, as each GT class metric captures at
least either the physical limitation point or the phase transition critical point. Overall, this paper provides a detailed study of the critical behavior of the charged AdS BH with
surrounding MCG.
