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 non-zero 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 configuration 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 anti-quark pairs may not exist. By studying the corresponding dual gauge theory we confirm that the instability of the bound state of quark and anti-quark pair in the dual gauge theory.

Effects of a string cloud on the criticality and efficiency of AdS black holes as heat engines

“…We again remark that the qualitative behavior is similar to the RN-AdS black hole analyzed in [26]. For a discussion of the phase transitions based on the non-extended phase space, i.e., without the PdV working term, the reader is refereed to [37].…”

Effects of a cloud of strings on the extended phase space of Einstein–Gauss–Bonnet AdS black holes

“…At first Strominger and Vafa showed a connection between counting string states and the entropy of the black hole in [24] , later in [25] it was considered a model for a cloud of strings that would be the equivalent of a perfect fluids. Implications of that for a broad range of black holes have been studied by many authors [23][24][25][26][27][28][29][30][31][32], as we can see some earlier works performed these effects on gravitational theories like Schwarzschild solution in [50], higher derivative theories like Lovelock theory in [30,31,32] and modified gravity in [51] , and also by considering the effect of quintessence dark energy in [52,53]. Gauss Bonnet terms in higher derivative theories could be seen in the low-energy effective action of superstring theories.…”

AdS black holes with higher derivative corrections in presence of string cloud

“…We begin with black holes that has been obtained without the higher derivative coupling. Some result has already appeared in [12] and here we have a more elaborate analysis. If we drop the higher derivative terms, metric functions are [12]…”

“…= .408 (for details see [12]) there are certain range of temperature where three black hole solutions exist. Outside this range only one black hole solution exist.…”

“…Several works [11][12][13][14][15][16][17] have considered string clouds which amounts to considering external heavy quarks in the dual gauge theory. The Einstein theory with string clouds admits black hole solutions with three different radii and the thermodynamics of them has been discussed by one of us [12], which also showed a Hawking-Page like phase transition between two black hole solutions. Such three black hole solutions along with the phase transitions have been showed in [18,19] in the context of Einstein Gauss Bonnet (GB) theory in absence of the string clouds.…”