Peculiar $P-V$ criticality of topological Ho\v{r}ava-Lifshitz black holes

TL;DR

This paper explores unique $P-V$ criticality in topological Hořava-Lifshitz black holes, revealing behaviors similar to van der Waals systems with novel features like a parameter-controlled criticality and an infinite number of critical points.

Contribution

It uncovers a new type of $P-V$ criticality in HL black holes, especially the uncharged case with a parameter-dependent behavior and a critical curve of multiple critical points.

Findings

Charged HL black holes exhibit van der Waals-like criticality.

Uncharged HL black holes show a peculiar $P-V$ criticality controlled by parameter $.

Existence of an infinite number of critical points forming a critical curve.

Abstract

We demonstrate the existence of $P-V$ criticality of the topological Ho\v{r}ava-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 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 $\epsilon$, but not the temperature $T$. When $\epsilon$ is larger than a critical value $\epsilon_c$, 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.