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Extensions of spacetimes with Killing horizons. (English) Zbl 0782.53061

The authors prove that for a spacetime with a Killing horizon \(N\) [such that all orbits of a Killing vector field are diffeomorphic to \(\mathbb{R}\), and \(N\) admits a smooth cross section, \(\Sigma\), with each orbit intersecting \(\Sigma\) only once], an open neighbourhood of \(N\) can be extended so that \(N\) comprises a portion of bifurcate Killing horizon iff the surface gravity of \(N\) is constant and non-vanishing.

MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
83C57 Black holes
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