Abstract
We reconsider the thermodynamics of anti-de Sitter black holes in the context of gauge-gravity duality. In this new setting, where both the cosmological constant Λ and the gravitational Newton's constant G are varied in the bulk, we rewrite the first law in a new form containing both Λ (associated with thermodynamic pressure) and the central charge C of the dual conformal field theory and their conjugate variables. We obtain a novel thermodynamic volume, in turn leading to a new understanding of the Van der Waals behavior of charged anti-de Sitter black holes in which phase changes are governed by the degrees of freedom in the conformal field theory. Compared to the "old" P-V criticality, this new criticality is "universal" (independent of the bulk pressure) and directly relates to the thermodynamics of the dual field theory and its central charge.
Highlights
Black holes and their thermodynamics have been of crucial importance in providing clues about the nature of quantum gravity
In this new setting, where both the cosmological constant Λ and the gravitational Newton’s constant G are varied in the bulk, we rewrite the first law in a new form containing both Λ and the central charge C of the dual conformal field theory and their conjugate variables
We obtain a novel thermodynamic volume, in turn leading to a new understanding of the Van der Waals behavior of charged anti–de Sitter black holes in which phase changes are governed by the degrees of freedom in the conformal field theory
Summary
∂M ∂P S;Q;J ð5Þ is the thermodynamic volume conjugate to P [9,10] In this framework, black hole thermodynamics is phenomenologically much richer than previously expected, with black holes exhibiting Van der Waals [7], reentrant [11], superfluid [12], and polymer-type phase transitions [13], along with triple points [14,15] and the universal scaling behavior of the Ruppeiner curvature [16]. Black hole thermodynamics is phenomenologically much richer than previously expected, with black holes exhibiting Van der Waals [7], reentrant [11], superfluid [12], and polymer-type phase transitions [13], along with triple points [14,15] and the universal scaling behavior of the Ruppeiner curvature [16] For these reasons, this subdiscipline has come to be called black hole chemistry [17]. Allowing both l and G to vary [27], from Eqs. (6) and (9) we obtain δðGMÞ κ 8π δA
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