Mathematics – Group Theory
Scientific paper
May 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978gregr...9..437c&link_type=abstract
General Relativity and Gravitation, vol. 9, May 1978, p. 437-450.
Mathematics
Group Theory
7
Black Holes (Astronomy), Group Theory, Relativity, Space-Time Functions, Invariance, Manifolds (Mathematics), Metric Space, Orthogonality, Topology
Scientific paper
The theory of stationary black holes is examined on the basis of relationships between isometry group invariance properties and causal connectivity. Attention is given to a connected time-oriented Lorentz-signature n-dimensional pseudo-Riemannian Hausdorff manifold, whose metric is at least c sq, on which there is a continuous p-transitive action of a connected continuous group of isometries. Results indicate that under conditions of the causality axiom, the domain of communications over any stationary domain has the form of a fiber bundle over a well-behaved base manifold, and that the corresponding globally defined horizons coincide with the relevant local isometry or Killing horizons when the domain of communication coincides with the stationary domain.
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