Stationary Black Holes as Holographs

Abstract

Smooth spacetimes possessing a (global) one-parameter group of isometries and an associated Killing horizon in Einstein's theory of gravity are investigated. No assumption concerning the asymptotic structure is made, thereby, the selected spacetimes may be considered as generic distorted stationary black holes. First, spacetimes of arbitrary dimension, $n\ge 3$, with matter satisfying the dominant energy condition and allowing non-zero cosmological constant are investigated. In this part complete characterisation of the topology of the event horizon of ``distorted'' black holes is given. It is shown that the topology of the event horizon of ``distorted'' black holes is allowed to possess a much larger variety than that of the isolated black hole configurations. In the second part, 4-dimensional (non-degenerate) electrovac distorted black hole spacetimes are considered. It is shown that the spacetime geometry and the electromagnetic field are uniquely determined in the black hole region once the geometry of the bifurcation surface and one of the electromagnetic potentials are specified there. Conditions guaranteeing the same type of determinacy, in a neighbourhood of the event horizon, on the {\it domain of outer communication} side are also investigated. In particular, they are shown to be satisfied in the analytic case.

arXiv comment31 pages, LaTeX; typos corrected, new references added, to appear in CQG

References in corpus (32)

• Isolated and dynamical horizons and their applications
• Topological Black Holes in Anti-de Sitter Space
• Near-horizon symmetries of extremal black holes
• Relativistic Fluid Dynamics: Physics for Many Different Scales
• Entropy from Conformal Field Theory at Killing Horizons
• Thermodynamics of (3+1)-dimensional black holes with toroidal or higher genus horizons
• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• Mechanics of Rotating Isolated Horizons
• Geometry of Generic Isolated Horizons
• A generalization of Hawking's black hole topology theorem to higher dimensions
• Topological Censorship and Higher Genus Black Holes
• On the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon
• Horizon Entropy
• Analytic description of singularities in Gowdy spacetimes
• Fuchsian analysis of singularities in Gowdy spacetimes beyond analyticity
• A no-go theorem for polytropic spheres in Palatini f(R) gravity
• Near-Horizon Conformal Symmetry and Black Hole Entropy
• Global Extensions of Spacetimes Describing Asymptotic Final States of Black Holes
• Topology of Event Horizons and Topological Censorship
• Black Holes on Cylinders
• Dirty black holes: Symmetries at stationary non-static horizons
• Dirty black holes: Spacetime geometry and near-horizon symmetries
• A Cosmological Constant Limits the Size of Black Holes
• Quantum horizons and black hole entropy: Inclusion of distortion and rotation
• Distorted Black Holes with Charge
• On Further Generalization of the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon
• Black Holes in a Compactified Spacetime
• Interior of Distorted Black Holes
• On the existence of Killing vector fields
• Fuchsian methods and spacetime singularities
• Symmetries of spacetime and their relation to initial value problems
• Distortion of Schwarzschild-anti-de Sitter black holes to black strings

Cited by in corpus (19)

• Sachs' free data in real connection variables
• Null boundary terms for Lanczos-Lovelock gravity
• Local version of the no-hair theorem
• The Meissner Effect for axially symmetric charged black holes
• Stationary Black Holes as Holographs II
• The Petrov type D isolated null surfaces
• On the various aspects of electromagnetic potentials in spacetimes with symmetries
• Kerr-Newman black hole in the formalism of isolated horizons
• Covariant approach to the thermodynamic structure of a generic null surface
• The axial symmetry of Kerr without the rigidity theorem
• The Petrov type D equation on genus $>0$ sections of isolated horizons
• Killing spinor data on distorted black hole horizons and the uniqueness of stationary vacuum black holes
• Non-singular Kerr-NUT-de Sitter spacetimes
• Near Horizon Geometries and Black Hole Holograph
• Petrov type D equation on horizons of nontrivial bundle topology
• Space-time extensions II
• Isolated horizons of the Hopf bundle structure transversal to the null direction, the horizon equations and embeddability in NUT-like spacetimes
• Lightlike singular hypersurfaces in quadratic gravity
• A New Way of Proving Black Hole Rigidity