Stationary Black Holes as Holographs

TL;DR

This paper investigates the geometry and topology of distorted stationary black holes in Einstein's gravity, revealing a broader variety of horizon topologies and establishing conditions for unique determination of spacetime and electromagnetic fields near black holes.

Contribution

It provides a comprehensive characterization of horizon topologies for distorted black holes and establishes uniqueness results for electrovac black hole spacetimes near the horizon.

Findings

Horizon topology of distorted black holes is more diverse than isolated ones.

Spacetime and electromagnetic fields are uniquely determined by data on the bifurcation surface.

Analyticity ensures conditions for determinacy in the domain of outer communication.

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, $n\geq 3$, 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.