Critical phenomena

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Event horizon

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Gravitation

Massive gravity

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Mathematical physics

Black hole thermodynamics

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Classical mechanics

van der Waals force

AdS black hole

Thermodynamics

The European Physical Journal C

Considering de Rham–Gabadadze–Tolley theory of massive gravity coupled with (ghost free) higher curvature terms arisen from the Lovelock Lagrangian, we obtain charged-AdS black hole solutions in diverse dimensions. We compute thermodynamic quantities in the extended phase space by considering the variations of the negative cosmological constant, Lovelock coefficients ( $$\alpha _{i}$$ ) and massive couplings ( $$c_{i}$$ ). We also prove that such variations are necessary in order to satisfy the extended first law of thermodynamics as well as associated Smarr formula. In addition, by performing a comprehensive thermal stability analysis for the topological black hole solutions, we show that in which regions thermally stable phases exist. Calculations show the results are radically different from those in the Einstein gravity. We find that the phase structure and critical behavior of topological AdS black holes are drastically restricted by the geometry of the event horizon. We also show that the phase structure of AdS black holes with non-compact (hyperbolic) horizon could give birth to three critical points corresponds to a reverse van der Waals behavior for phase transition which is accompanied with two distinct van der Waals phase transitions. For black holes with the spherical horizon, the van der Waals, reentrant and analogue of solid/liquid/gas phase transitions are observed.

Criticality and extended phase space thermodynamics of AdS black holes in higher curvature massive gravity