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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, what permits us to draw the conclusions on visible effect of each statistics.
We consider a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential and an U(1) electromagnetic field. Solving the coupled Einstein-Maxwell-scalar system we find exact hairy charged black hole
We develop a new perturbation method to study the dynamics of massive tensor fields on extremal and near-extremal static black hole spacetimes in arbitrary dimensions. On such backgrounds, one can classify the components of massive tensor fields into
We discuss a new perturbation method to study the dynamics of massive vector fields on (near-)extremal static black hole spacetimes. We start with, as our background, a rather generic class of warped product metrics, and classify the field variables
The spin angular momentum $S$ of an isolated Kerr black hole is bounded by the surface area $A$ of its apparent horizon: $8pi S le A$, with equality for extremal black holes. In this paper, we explore the extremality of individual and common apparent
We present a conformal isometry for static extremal black hole solutions in all four-dimensional Einstein-Maxwell-scalar theories with electromagnetic duality groups `of type $E_7$. This includes, but is not limited to, all supergravity theories with