Phase transition of AdS–Schwarzschild black hole and gauge theory dual in the presence of external string cloud

Abstract

We study the thermodynamics of AdS–Schwarzschild black hole in the presence of an external string cloud. We observe that, at any temperature, the black hole configuration is stable with nonzero entropy. We further notice that when the value of the curvature constant equals to one, if the string cloud density has less than a critical value, within a certain range of temperature three black holes configurations exist. One of these black holes is unstable and other two are stable. At a critical temperature, a transition between these two stable black holes takes place which leads us to conclude that the bound state of quark and antiquark pairs may not exist. By studying the corresponding dual gauge theory, we confirm the instability of the bound state of quark and antiquark pair in the dual gauge theory.