Abstract
Basic relationships between the causal connectivity properties and the symmetry group invariance properties of space-time manifolds are discussed with a view to applications in the theory of stationary black holes. In particular the results given here provide a rigorous justification for the application of Israel's theorem [6] to static black holes as strictly defined; they also provide an essential step in the proof of the “no-hair” theorem for stationary-axisymmetric pure vacuum black holes as described by Carter [29] and extended by Robinson [10]. One of the main results is the demonstration that if the causality axiom holds, the domain of communications of any stationary domain has the form of a fiber bundle over a well-behaved base manifold and that if also the invariance group is orthogonally transitive and the stationary domain is simply connected, then the domain of communication coincides with the stationary domain, so that the correspondingglobally defined horizons coincide with the relevantlocal isometry or Killing horizons.
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This article is dedicated to Achille Papapetrou on the occasion of his retirement and forms a part of the Papapetrou Festschrift.
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Carter, B. Domains of stationary communications in space-time. Gen Relat Gravit 9, 437–450 (1978). https://doi.org/10.1007/BF00759844
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DOI: https://doi.org/10.1007/BF00759844