https://doi.org/10.1140/epjc/s10052-017-4978-3
Regular Article - Theoretical Physics
Validity of Maxwell equal area law for black holes conformally coupled to scalar fields in 
spacetime
School of Physics, Nankai University, Tianjin, 300071, China
* e-mail: miaoyg@nankai.edu.cn
Received:
13
February
2017
Accepted:
8
June
2017
Published online:
16
June
2017
We investigate the 
criticality and the Maxwell equal area law for a five-dimensional spherically symmetric AdS black hole with a scalar hair in the absence of and in the presence of a Maxwell field, respectively. Especially in the charged case, we give the exact critical values. More importantly, we analyze the validity and invalidity of the Maxwell equal area law for the AdS hairy black hole in the scenarios without and with charges, respectively. Within the scope of validity of the Maxwell equal area law, we point out that there exists a representative van der Waals-type oscillation in the diagram. This oscillating part, which indicates the phase transition from a small black hole to a large one, can be replaced by an isobar. The small and large black holes have the same Gibbs free energy. We also give the distribution of the critical points in the parameter space both without and with charges, and we obtain for the uncharged case the fitting formula of the co-existence curve. Meanwhile, the latent heat is calculated, which gives the energy released or absorbed between the small and large black hole phases in the isothermal–isobaric procedure.
© The Author(s), 2017
