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Register a new userStatistics effects in extremal black holes ensemble
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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.
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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 solutions with the scalar field regular everywhere. We go to the zero temperature limit and we study the effect of the scalar field on the near horizon geometry of an extremal black hole. We find that except a critical value of the charge of the black hole there is also a critical value of the charge of the scalar field beyond of which the extremal black hole is destabilized. We study the thermodynamics of these solutions and we find that if the space is flat then at low temperature the Reissner-Nordstrom black hole is thermodynamically preferred, while if the space is AdS the hairy charged black hole is thermodynamically preferred at low temperature.
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 the tensor, vector, and scalar-type components. For the tensor-type components, which arise only in higher dimensions, the massive tensor field equation reduces to a single master equation, whereas the vector and scalar-type components remain coupled. We consider the near-horizon expansion of both the geometry and the field variables with respect to the near-horizon scaling parameter. By doing so, we reduce, at each order of the expansion, the equations of motion for the vector and scalar-type components to a set of five mutually decoupled wave equations with source terms consisting only of the lower-order variables. Thus, together with the tensor-type master equation, we obtain the set of mutually decoupled equations at each order of the expansion that govern all dynamical degrees of freedom of the massive tensor field on the extremal and near-extremal static black hole background.
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 into the vector(axial)- and scalar(polar)-type components. On this generic background, we show that for the vector-type components, the Proca equation reduces to a single master equation, whereas the scalar-type components remain to be coupled. Then, focusing on the case of (near-)extremal static black holes in four-dimensions, we consider the near-horizon expansion of both the background geometry and massive vector field by a scaling parameter $lambda$ with the leading-order geometry being the so called near-horizon geometry. We show that on the near-horizon geometry, thanks to its enhanced symmetry, the Proca equation for the scalar-type components also reduces to a set of two mutually decoupled homogeneous wave equations for two variables, plus a coupled equation through which the remaining variable is determined. Therefore, together with the vector-type master equation, we obtain the set of three decoupled master wave equations, which govern the three independent dynamical degrees of freedom of the massive vector field in four-dimensions. We further expand the geometry and massive vector field with respect to $lambda$ and show that at each order, the Proca equation for the scalar-type components can reduce to a set of decoupled inhomogeneous wave equations whose source terms consist only of the lower-order variables, plus one coupled equation that determins the remaining variable. Therefore, if one solves the master equations on the leading-order near-horizon geometry, then in principle one can successively solve the Proca equation at any order.
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 horizons for merging, rapidly spinning binary black holes. We consider simulations of merging black holes with equal masses $M$ and initial spin angular momenta aligned with the orbital angular momentum, including new simulations with spin magnitudes up to $S/M^2 = 0.994$. We measure the area and (using approximate Killing vectors) the spin on the individual and common apparent horizons, finding that the inequality $8pi S < A$ is satisfied in all cases but is very close to equality on the common apparent horizon at the instant it first appears. We also introduce a gauge-invariant lower bound on the extremality by computing the smallest value that Booth and Fairhursts extremality parameter can take for any scaling. Using this lower bound, we conclude that the common horizons are at least moderately close to extremal just after they appear. Finally, following Lovelace et al. (2008), we construct quasiequilibrium binary-black-hole initial data with overspun marginally trapped surfaces with $8pi S > A$ and for which our lower bound on their Booth-Fairhurst extremality exceeds unity. These superextremal surfaces are always surrounded by marginally outer trapped surfaces (i.e., by apparent horizons) with $8pi S<A$. The extremality lower bound on the enclosing apparent horizon is always less than unity but can exceed the value for an extremal Kerr black hole. (Abstract abbreviated.)
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 $mathcal{N}>2$ supersymmetry and all $mathcal{N}=2$ supergravity theories with symmetric scalar manifolds. The conformal isometry is valid for arbitrary electromagnetic charge configurations and relies crucially on the notion of Freudenthal duality.
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