λ Phase Transition in Horava Gravity

Wei Xu

doi:10.1155/2018/2175818

Abstract

We present another example of superfluid black hole containing λ phase transition in Horava gravity. After studying the extended thermodynamics of general dimensional Horava-Lifshitz AdS black holes, it is found that only the one with spherical horizon in four and five dimensions has λ phase transition, which is a line of (continuous) second-order phase transitions and was famous in the discussion of superfluidity of liquid He4. The “superfluid” black hole phase and “normal” black hole phase are also distinguished. Particularly, six-dimensional Horava-Lifshitz AdS black holes exhibit infinitely many critical points in P-ν plane and the divergent points for specific heat, for which they only contain the “normal” black hole phase and the “superfluid” black hole phase disappears due to the physical temperature constraint; therefore there is no similar phase transition. In more than six dimensions, there is no P-ν critical behavior. After choosing the appropriate ordering field, we study the critical phenomena in different planes of thermodynamical phase space. We also calculate the critical exponents, which are the same as the van der Waals fluid.

Highlights

Black hole thermodynamics always provides valuable insight into quantum properties of gravity, and it has been studied extensively for quite a long time, especially for the quantum and microscopic interpretation of black hole temperature and entropy
Thermodynamics and phase transitions of AdS black holes have been of great interest since the Hawking-Page phase transition [3] between stable large black hole and thermal gas is explained as the confinement/deconfinement phase transition of gauge field [4] inspired by the AdS/CFT correspondence [5,6,7]
After identifying parameter ε as the ordering field instead of pressure and temperature, we study the critical phenomena in different planes of thermodynamical phase space

Summary

Introduction

Black hole thermodynamics always provides valuable insight into quantum properties of gravity, and it has been studied extensively for quite a long time, especially for the quantum and microscopic interpretation of black hole temperature and entropy (see [1, 2], for example). After treating the cosmological constant as a pressure with its conjugate quantity being the thermodynamic volume in thermodynamic phase space of charged AdS black holes [8,9,10,11,12,13,14], the small/large black hole phase transition is established in [15], which is exactly analogous to the liquid/gas phase transition of the van der Waals fluid This kind of black hole phase transitions has attracted much attention (see the recent review papers [16, 17]).

Extended Thermodynamics of Generalized HL Black Holes

P-T diagram in four dimensions

P-T diagram in six dimensions

Discussion