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Macdonald, F. M.; Lingard, V. M.

doi:10.1007/978-1-4899-7270-5_18

Cited by 1 publication

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“…The critical exponents are the same as those in the Van der Waals system, modifying previous considerations that emerged from earlier studies [19][20][21][22] of the duality description. Intensive investigation in a broad variety of contexts [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] has led to the discovery of a variety of new thermodynamic phenomena for both AdS and de Sitter [38] black holes, including the existence of reentrant phase transitions in Born-Infeld [14] and rotating [39] black holes, the existence of a tricritical point in rotating black holes analogous to the triple point in water [39], a new type of thermodynamic criticality in the highercurvature case [40], and the notion of a holographic heat engine [37,41]. Indeed, the thermal radiation/large AdS black hole phase transition [1] can be understood as a solid/liquid phase transition from this perspective [34].…”

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confidence: 99%

Mass and thermodynamic volume in Lifshitz spacetimes

2015

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We examine the concept of black hole thermodynamic volume and its consistency with thermodynamic mass in spacetimes that are not asymptotically flat but instead have anisotropic Lifshitz scaling symmetry. We find that the generalized Smarr relation in anti de Sitter spaceextended to include a pressure-volume term -holds here as well, and that there exists a definition of thermodynamic mass and thermodynamic volume that satisfy both this relation and the 1 st law of thermodynamics. We compare the thermodynamic mass with other known quantities such as Arnowitt-Deser-Misner, Brown-York and Hollands-Ishibashi-Marolf masses. We also conjecture methods for obtaining a thermodynamic mass where there is ambiguity due to the cosmological constant lengthscale depending on the horizon radius lengthscale. I. BACKGROUNDGauge-gravity duality remains a subject of considerable interest, in large part because of the insights it yields into quantum gravity. Asymptotically anti de Sitter (AdS) spacetime admits a strongly coupled gauge theory description at its boundary via a holographic dictionary. It is straightforward to define thermodynamic equilibrium in this case, in turn giving rise to thermal radiation/large AdS black hole phase transitions [1].An interesting development in this subject that has been the subject of much current interest is the proposal that the mass of an AdS black hole can be understood as the enthalpy of spacetime [2]. This notion emerges from regarding the cosmological constant Λ as a thermodynamic variable [3] analogous to pressure in the first law [2,[4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], along with a notion of conjugate volume [2,12]. A complete analogy between 4-dimensional Reissner-Nordström AdS black holes and the Van der Waals liquid-gas system can be shown to hold [13]. The critical exponents are the same as those in the Van der Waals system, modifying previous considerations that emerged from earlier studies [19][20][21][22] of the duality description. Intensive investigation in a broad variety of contexts [23-37] has led to the discovery of a variety of new thermodynamic phenomena for both AdS and de Sitter [38] black holes, including the existence of reentrant phase transitions in Born-Infeld [14] and rotating [39] black holes, the existence of a tricritical point in rotating black holes analogous to the triple point in water [39], a new type of thermodynamic criticality in the highercurvature case [40], and the notion of a holographic heat engine [37, 41]. Indeed, the thermal radiation/large AdS black hole phase transition [1] can be understood as a solid/liquid phase transition from this perspective [34].Here we begin the first study of extended thermodynamics in the context of Lifshitz duality. Motivated by * Electronic address: wbrenna@uwaterloo.ca † Electronic address: rbmann@uwaterloo.ca ‡ Electronic address: miokpark@kias.re.kr the hope of obtaining a duality between condensed matter physics with quantum criticality, the anisotropic scaling properties of these systems im...

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