Studies of a general asymptotically flat black hole/hairy black hole transition model with methods familiar from holography

摘要

We study the asymptotically flat quasi-local black hole/hairy black holemodel with nonzero mass of the scalar filed. We disclose effects of the scalarmass on transitions in a grand canonical ensemble with condensation behaviorsof a parameter $\psi_{2}$ similar to approaches in holographic theories. Wefind that more negative scalar mass makes the phase transition easier tohappen. We also obtain an analytical relation$\psi_{2}\varpropto(T_{c}-T)^{1/2}$ around the critical phase transition pointsimplying a second order phase transition. Besides the parameter $\psi_{2}$, weshow that metric solutions can be used to disclose properties of transitions.At last, we point out that black hole/hairy black hole transitions in a box arestrikingly similar to holographic conductor/superconductor transitions.