P-V criticality of charged dilatonic black holes

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In this paper, we investigate the critical behavior of charged black holes of Einstein-Maxwell-dilaton gravity in the presence of two Liouville-type potentials which make the solution asymptotically neither flat nor AdS and has a parameter $% \Lambda $ treated as a thermodynamic quantity that can vary.

• We obtain a Smarr-type relation for charged dilatonic black holes and find out that the volume is different from the geometrical volume.
• We study the analogy of the Van der Waals liquid-gas system with the charged dilatonic black hole system while we treat the black hole charge as a fixed external parameter.
• Moreover, we show that the critical values for pressure, temperature and volume are physical provided the coupling constant of dilaton gravity is less than one and the horizon is sphere.