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Register a new userUniqueness of extremal isolated horizons and their identification with horizons of all type D black holes
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We systematically investigate axisymmetric extremal isolated horizons (EIHs) defined by vanishing surface gravity, corresponding to zero temperature. In the first part, using the Newman-Penrose and GHP formalism we derive the most general metric function for such EIHs in the Einstein-Maxwell theory, which complements the previous result of Lewandowski and Pawlowski. We prove that it depends on 5 independent parameters, namely deficit angles on the north and south poles of a spherical-like section of the horizon, its radius (area), and total electric and magnetic charges of the black hole. The deficit angles and both charges can be separately set to zero. In the second part of our paper, we identify this general axially symmetric solution for EIH with extremal horizons in exact electrovacuum Plebanski-Demianski spacetimes, using the convenient parametrization of this family by Griffiths and Podolsky. They represent all (double aligned) black holes of algebraic type D without a cosmological constant. Apart from a conicity, they depend on 6 physical parameters (mass, Kerr-like rotation, NUT parameter, acceleration, electric and magnetic charges) constrained by the extremality condition. We were able to determine their relation to the EIH geometrical parameters. This explicit identification of type D extremal black holes with a unique form of EIH includes several interesting subclasses, such as accelerating extremely charged Reissner-Nordstrom black hole (C-metric), extremal accelerating Kerr-Newman, accelerating Kerr-NUT, or non-accelerating Kerr-Newman-NUT black holes.
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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.)
Using the numerical method, we study dynamics of coalescing black holes on the Eguchi-Hanson base space. Effects of a difference in spacetime topology on the black hole dynamics is discussed. We analyze appearance and disappearance process of marginal surfaces. In our calculation, the area of a coverall black hole horizon at the creation time in the coalescing black holes solutions on Eguchi-Hanson space is larger than that in the five-dimensional Kastor-Traschen solutions. This fact suggests that the black hole production on the Eguchi-Hanson space is easier than that on the flat space.
We propose a simple method to prove non-smoothness of a black hole horizon. The existence of a $C^1$ extension across the horizon implies that there is no $C^{N + 2}$ extension across the horizon if some components of $N$-th covariant derivative of Riemann tensor diverge at the horizon in the coordinates of the $C^1$ extension. In particular, the divergence of a component of the Riemann tensor at the horizon directly indicates the presence of a curvature singularity. By using this method, we can confirm the existence of a curvature singularity for several cases where the scalar invariants constructed from the Riemann tensor, e.g., the Ricci scalar and the Kretschmann invariant, take finite values at the horizon. As a concrete example of the application, we show that the Kaluza-Klein black holes constructed by Myers have a curvature singularity at the horizon if the spacetime dimension is higher than five.
General Relativity predicts the existence of black-holes. Access to the complete space-time manifold is required to describe the black-hole. This feature necessitates that black-hole dynamics is specified by future or teleological boundary condition. Here we demonstrate that the statistical mechanical description of black-holes, the raison detre behind the existence of black-hole thermodynamics, requires teleological boundary condition. Within the fluid-gravity paradigm --- Einsteins equations when projected on space-time horizons resemble Navier-Stokes equation of a fluid --- we show that the specific heat and the coefficient of bulk viscosity of the horizon-fluid are negative only if the teleological boundary condition is taken into account. We argue that in a quantum theory of gravity, the future boundary condition plays a crucial role. We briefly discuss the possible implications of this at late stages of black-hole evaporation.
We introduce the concept of a geometric horizon, which is a surface distinguished by the vanishing of certain curvature invariants which characterize its special algebraic character. We motivate its use for the detection of the event horizon of a stationary black hole by providing a set of appropriate scalar polynomial curvature invariants that vanish on this surface. We extend this result by proving that a non-expanding horizon, which generalizes a Killing horizon, coincides with the geometric horizon. Finally, we consider the imploding spherically symmetric metrics and show that the geometric horizon identifies a unique quasi-local surface corresponding to the unique spherically symmetric marginally trapped tube, implying that the spherically symmetric dynamical black holes admit a geometric horizon. Based on these results, we propose a suite of conjectures concerning the application of geometric horizons to more general dynamical black hole scenarios.
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