2019/07/31 by A. M. Gavrilik, A. V. Nazarenko
Physics and Astronomy · #Black Holes and Theoretical Physics #Black hole (networking) #Canonical ensemble #Cosmology and Gravitation Theories #Equivalence (formal languages) #Grand canonical ensemble #Gravitation #Monte Carlo method #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Statistical physics #Statistics #Theory of relativity #Time dilation #gr-qc #quant-ph
paper · pdf · doi:10.1142/s0217751x19502154
published in International Journal of Modern Physics A 34(32), 1950215 (World Scientific) · v2: 15 pages, 3 figures; refs., text and explanations added to match reviewers' suggestions, accepted for publication by Int. J. Mod. Phys. A
arxiv created 2019/11/12 · openalex publication_date 2019/11/20 · arxiv updated 2020/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the grand canonical ensemble of the static and extremal black holes, when the equivalence of the electric charge and mass of individual black hole is postulated. Assuming uniform distribution of black holes in space, we are finding the effective mass of test particle and mean time dilation at the admissible points of space, taking into account the gravitational action of surrounding black holes. Having specified the statistics that governs extremal black holes, we study its effect on those quantities. Here, the role of statistics is to assign a statistical weight to the configurations of certain fixed number of black holes. We borrow these weights from Bose–Einstein, Fermi–Dirac, classical and infinite statistics. Using mean field approximation, the aforementioned characteristics are calculated and visualized, which permits us to draw the conclusions on visible effect of each statistics.