λ Phase Transition in Horava Gravity

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.