Phase transitions of hairy black holes in massive gravity and thermodynamic behavior of charged AdS black holes in an extended phase space

摘要

We study the thermodynamic behavior of static and spherically symmetric hairyblack holes in massive gravity. In this case, the black hole is surrounded in aspherical cavity with a fixed temperature on the surface. It is observed thatthese black holes have a phase transition similar to the liquid-gas phasetransition of a Van der Waals fluid. Also, by treating the cosmologicalconstant $\Lambda$ as a thermodynamic pressure $P$, we study the thermodynamicbehavior of charged anti-de Sitter black holes in an ensemble with a pressureof $P$ and an electric potential $\Phi$ as the natural variables. A secondorder phase transition is observed to take place for all the values of theelectric potential $\Phi$.