Tricritical point and solid/liquid/gas phase transition of higher dimensional AdS black hole in massive gravity

By considering the fifth order graviton term in massive gravity theory, we study the P – V critical behaviors of AdS black hole in d ≥ 7 dimensional space–time, and find the solid/liquid/gas phase transition with the “common” tricritical point, which does not exist in absence of higher graviton terms. Moreover, we also find the number of positive real roots of critical radius equation plays a key role in classifying different kinds of phase transitions. If there is only one positive root of equation, the first order Van der Waals-like phase transition emerges. For two roots, the system could experience a zero-order reentrant phase transition. Notably, for three roots, the solid/liquid/gas phase transition can occur. In addition, because the critical radius equation is a ( n − 2 )-order polynomial equation associated with the graviton terms, the critical phenomena of black holes in extended phase space depend crucially on the number n of the graviton terms in high dimensional massive gravity.