Maxwell's equal area law for charged Anti-deSitter black holes

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In this paper we present the construction of the Maxwell equal area law in the Hawking temperature graph for a charged black hole in Anti-deSitter background.

• We are able to find exact solution for the corresponding isotherm and entropies for "gaseous" (large) black holes and "liquid" (near-extremal) black holes.
• Isothermal construction removes the unphysical, negative heat capacity, regions.
• Furthermore, extremal black holes turn out to be dual to "un-shrinkable" molecules of Van der Waals real fluid, which may explain their thermodynamical stability.