2016/05/31 by Gu-Qiang Li, Jie-Xiong Mo
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Canonical ensemble #Cosmology and Gravitation Theories #Curvature #Geometry #Grand canonical ensemble #Heat capacity #Mathematical physics #Mathematics #Monte Carlo method #Phase transition #Physics #Scalar curvature #Statistics #Thermodynamics #gr-qc
paper · pdf · doi:10.1103/physrevd.93.124021
published as Phys. Rev. D 93, 124021 (2016)
openalex publication_date 2016/06/08 · arxiv created 2016/06/11 · arxiv updated 2016/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
The phase transition of a four-dimensional charged AdS black hole solution in the R+f(R) gravity with constant curvature is investigated in the grand canonical ensemble, where we find novel characteristics quite different from that in the canonical ensemble. There exists no critical point for T\ensuremath-S curve while in former research critical point was found for both the T\ensuremath-S curve and T\ensuremath-r+ curve when the electric charge of f(R) black holes is kept fixed. Moreover, we derive the explicit expression for the specific heat, the analog of volume expansion coefficient and isothermal compressibility coefficient when the electric potential of f(R) AdS black hole is fixed. The specific heat C_\mathrm\ensuremathΦ encounters a divergence when 0<\mathrm\ensuremathΦ<b while there is no divergence for the case \mathrm\ensuremathΦ>b. This finding also differs from the result in the canonical ensemble, where there may be two, one or no divergence points for the specific heat CQ. To examine the phase structure newly found in the grand canonical ensemble, we appeal to the well-known thermodynamic geometry tools and derive the analytic expressions for both the Weinhold scalar curvature and Ruppeiner scalar curvature. It is shown that they diverge exactly where the specific heat C_\mathrm\ensuremathΦ diverges.