2020/08/19 by Run Zhou, Yu-Xiao Liu, Shao-Wen Wei · 28 citations
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Canonical ensemble #Charged black hole #Cosmology and Gravitation Theories #Critical exponent #Curvature #Entropy (arrow of time) #Extremal black hole #Gauss–Bonnet theorem #Geometry #Grand canonical ensemble #Mathematical physics #Mathematics #Monte Carlo method #Phase transition #Physics #Quantum mechanics #Scalar (mathematics) #Scalar curvature #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.102.124015
published in Physical review. D/Physical review. D. 102(12) (American Physical Society) · 16 pages and 8 figures
arxiv created 2020/08/19 · openalex publication_date 2020/12/02 · arxiv updated 2020/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we study the small-large black hole phase transition and construct the Ruppeiner geometry for the five-dimensional charged Gauss-Bonnet-AdS black hole in the grand canonical ensemble. By making use of the equal area law, we obtain the analytical coexistence curve of the small and large black holes. Then the phase diagrams are examined. We also calculate the change of the thermodynamic volume during the small-large phase transition, which indicates that there exists a sudden change among the black hole microstructures. The corresponding normalized scalar curvature of the Ruppeiner geometry is also calculated. Combing with the empirical observation of scalar curvature, we find that for low electric potential, the attractive interaction dominates among the microstructures, while a high electric potential produces repulsive interactions. In the reduced parameter space, we observe that only attractive interaction is allowed when the coexistence region is excluded. The normalized scalar curvature also admits a critical exponent 2 and a universal constant \ensuremath-(1)/(8). In particular, the value of the normalized scalar curvature keeps the same along the coexistence small and large black hole curves. So in the grand canonical ensemble, the interaction can keep constant at the phase transition where the black hole microstructures change. These results disclose the intriguing microstructures for the charged AdS black hole in the Gauss-Bonnet gravity.