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.

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

References in corpus (5)

• Near-horizon symmetries of extremal black holes
• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• Analytic description of singularities in Gowdy spacetimes
• A no-go theorem for polytropic spheres in Palatini f(R) gravity
• Interior of Distorted Black Holes

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• On the various aspects of electromagnetic potentials in spacetimes with symmetries
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• 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