$Q-\Phi$ criticality in the extended phase space of $(n+1)$-dimensional   RN-AdS black holes
  In order to achieve a deeper understanding of gravity theories, it is important to further investigate the thermodynamic properties of black hole at the critical point, besides the phase transition and critical behaviors. In this paper, by using Maxwell's equal area law, we choose $T,Q,\Phi$ as the state parameters and study the phase equilibrium problem of general $(n+1)$-dimensional RN-AdS black holes thermodynamic system. The boundary of the two-phase coexistence region and its isotherm and isopotential lines are presented, which may provide theoretical foundation for studying the phase transition and phase structure of black hole systems. 
Yu-Bo Ma, Ren Zhao, Shuo Cao
hep-th