Abstract

We demonstrate the existence of P-V criticality of the topological Hořava-Lifshitz (HL) black holes with a spherical horizon (k=1) in the extended phase space. With the electric charge, we find that the critical behaviors of the HL black hole are nearly the same as those of a van der Waals (VdW) system. For the uncharged case, the HL black hole has a peculiar P-V criticality. The critical behavior is completely controlled by a parameter ε, but not the temperature T. When ε is larger than a critical value εc, no matter what the temperature is, there will be the first-order phase transition. Moreover, we find that there is an infinite number of critical points which form a “critical curve.” As far as we know, this is the first time to find this kind of peculiar P-V criticality.