Affiliation:
1. Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine, UA–03143 Kyiv, Ukraine
Abstract
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.
Funder
The National Academy of Sciences of Ukraine
Publisher
World Scientific Pub Co Pte Lt
Subject
Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics