Criticality of lower dimensional AdSd black holes

Aditya Dhumuntarao,Robert Mann

doi:10.1103/physrevd.104.064006

Aditya Dhumuntarao, Robert Mann

Open Access

https://doi.org/10.1103/physrevd.104.064006

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Abstract

In lower dimensions, charged AdS black holes in an extended phase space, where the cosmological constant is interpreted as the thermodynamic pressure, are typically absent of liquid/gas phase transitions. We investigate the criticality of lower dimensional charged, dilatonic, asymptotically AdS (CDAdS$_d$) black holes generated from consistent truncations of RNAdS$_{d+2}$ black objects. We demonstrate that CDAdS$_{d}$ black holes in $d<4$ can exhibit rich van der Waals behavior and confirm that the associated critical exponents match those expected from mean field theory.

Highlights

In recent years, black hole chemistry has substantially sharpened the connection between the thermodynamics of anti–de Sitter (AdS) black holes and ordinary fluid systems
We demonstrate that CDAdSd black holes in d < 4 can exhibit rich van der Waals behavior and confirm that the associated critical exponents match those expected from mean field theory
To set the stage for studying black hole chemistry in lower dimensions, we review some salient features of the Reissener-Nördstrom solution to Einstein-Maxwell-AdSd theory in the extended phase space

Summary

INTRODUCTION

Black hole chemistry has substantially sharpened the connection between the thermodynamics of anti–de Sitter (AdS) black holes and ordinary fluid systems. The program of black hole chemistry has completed this analogy by demonstrating that the equation of state for charged Reissner-Nördstrom AdSd (RN-AdSd) black holes shares identical critical behavior at the secondorder transition point and universal compressibility ratio in d 1⁄4 4 to a van der Waals fluid [14,15]. To set the stage for studying black hole chemistry in lower dimensions, we review some salient features of the Reissener-Nördstrom solution to Einstein-Maxwell-AdSd theory in the extended phase space. To demonstrate criticality of charged black holes, the natural starting point is to study the thermodynamics of Einstein-Maxwell-AdSd theory in d ≥ 4 This theory has been thoroughly analyzed in diverse dimensions with the on-shell regularized Euclidean action first calculated in [12,13].

Critical exponents

PRESSURE-VOLUME CRITICALITY IN LOWER DIMENSIONS

CDAdS2 black holes

CDAdS3 black holes

CONCLUSIONS