No P-V criticality for charged topological black holes in Horava-Lifshitz gravity

Searching for the unusual characteristics of HoA (TM) ava-Lifshitz gravity, we generalize our former research of charged topological black holes in HoA (TM) ava-Lifshitz gravity to the extended phase space. By treating cosmological constant as thermodynamic pressure, thermodynamic volume is derived as the conjugate quantity. P-V criticality is investigated by carrying out analytic analysis not only for the uncharged case but also for the charged case. All the topologies are considered. Unfortunately, no physical critical point has been found in all the cases. The results suggests again that the van der Waals like P-V criticality is not a universal phenomenon by providing one more example other than BTZ black holes. Our results also show that the existence of cosmological constant in the black hole metric is not sufficient for the existence of van der Waals like P-V criticality.