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Time-dependent black hole horizons on spacetime solutions of Einstein’s equations with initial data. (English) Zbl 1161.83003
Plaue, M. (ed.) et al., Advances in Lorentzian geometry. Aachen: Shaker Verlag (ISBN 978-3-8322-7786-4/pbk). 51-61 (2008).
For non-static black holes, the author presents a method how to define a horizon, called a dynamical horizon. To this end he introduces the notion of a FOTH, a future outer trapped horizon. Methods applied cover: foliations of space-time into space-like hypersurfaces, which in a certain limit degenerate to a foliation into null hypersurfaces; the use of conformal Killing vectors; comparison between geometrically and physically motivated conditions. Finally, black hole uniqueness conditions are mentioned. For the entire collection see [Zbl 1152.53002].

83C05Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C57Black holes
53C50Lorentz manifolds, manifolds with indefinite metrics
83C75Space-time singularities, cosmic censorship, etc.