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Holographic entanglement entropy and Van der Waals transitions in Einstein-Maxwell-dilaton theory

Shou-Long Li and Hao Wei
Phys. Rev. D 99, 064002 – Published 5 March 2019
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  • INTRODUCTION
  • CHARGED DILATONIC AdS BLACK HOLES WITH…
  • EXTENDED THERMODYNAMICS
  • HEE
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    According to the gauge/gravity duality, the Van der Waals transition of charged AdS black holes in extended phase space is conjectured to be dual to a renormalization group flow on the space of field theories. So exploring the Van der Waals transition is potenitally valuable for studying holographic properties of charged black hole thermodynamics. There are different transition behaviors for charged dilatonic AdS black holes in Einstein-Maxwell-dilaton (EMD) theory with string-inspired potential with different dilaton coupling constants in diverse dimensions. In this work, we find a special class of charged dilatonic AdS black holes which have the standard Van der Waals transition. We study the extended thermodynamics of the special class of black holes, which, in the extremal limit, have near-horizon geometry conformal to AdS2×SD−2. We find that, for these black holes, both the pressure-volume transition in fixed charge ensemble and the inverse temperature-entropy transition in fixed pressure ensemble have the standard Van der Waals behaviors. We also find the holographic entanglement entropy undergoes the same transition behaviors for the same critical temperature in fixing the thermodynamic pressure ensemble.

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    • Received 26 September 2018

    DOI:https://doi.org/10.1103/PhysRevD.99.064002

    © 2019 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Gauge-gravity dualitiesGravity in dimensions other than fourQuantum aspects of black holes
    Gravitation, Cosmology & AstrophysicsParticles & Fields

    Authors & Affiliations

    Shou-Long Li1,2,* and Hao Wei1,†

    • 1School of Physics, Beijing Institute of Technology, Beijing 100081, China
    • 2Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin 300350, China

    • *sllee_phys@bit.edu.cn
    • †haowei@bit.edu.cn

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    Issue

    Vol. 99, Iss. 6 — 15 March 2019

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    Images

    • Figure 1
      Figure 1

      Qualitative relations between T and r0 for different values of N by fixing the charge parameter q and gauge coupling constant g. Left: 0<N<N⋆; middle: N=N⋆; right: N⋆<N≤NRN.

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    • Figure 2
      Figure 2

      Isotherms in P−v diagrams of charged dilatonic AdS black hole in diverse dimensions with N=N⋆. We set Q=1. Top left: D=4; top right: D=5; down left: D=6; down right: D=7. The blue, orange and green lines represent isotherms with T=1.5Tc, Tc, and 0.5Tc from top to bottom. The black points represent critical points.

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    • Figure 3
      Figure 3

      Isobars in T−v diagrams of charged dilatonic AdS black hole in diverse dimensions with N=N⋆. We set Q=1. Top left: D=4; top right: D=5; down left: D=6; down right: D=7. The blue, orange and green lines represent isobars with P=1.5Pc, Pc, and 0.5Pc from top to bottom. The black points represent critical points.

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    • Figure 4
      Figure 4

      Isobars in G−T diagrams of charged dilatonic AdS black hole in diverse dimensions with N=N⋆. We set Q=1. Top left: D=4; top right: D=5; down left: D=6; down right: D=7. The blue, orange and green lines represent isobars with P=1.2Pc, Pc, and 0.7Pc from top to bottom. The black points represent critical points.

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    • Figure 5
      Figure 5

      P−T phase diagrams for diverse dimensions. Top left: D=4; top right: D=5; down left: D=6; down right: D=7. The black points are critical points at the end of the coexistence lines.

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    • Figure 6
      Figure 6

      Iso-charges in T−1−S diagrams of charged dilatonic AdS black hole in diverse dimensions with N=N⋆. We set g=1. Top left: D=4; top right: D=5; down left: D=6; down right: D=7. The blue, orange and green lines represent isobars with Q=1.5Qc, Qc, and 0.5Qc from top to bottom. The black points represent critical points.

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    • Figure 7
      Figure 7

      Iso-charges in T−1−δS diagrams of charged dilatonic AdS black holes in diverse dimensions with N=N⋆. We set g=1. Top left: D=4; top right: D=5; down left: D=6; down right: D=7. The green, orange, and blue lines represent isobars with Q=1.5Qc, Qc, and 0.5Qc from top to bottom. The dash lines represent inverse critical temperatures.

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