| Abstrakt: |
Let M be a time oriented Lorentzian manifold and a horizon. We will show that the differentiability order of the horizon can change only once along a generator, i.e. the following holds. If is a generator, thus, an inextendable past directed light-like geodesic on the horizon, where or then there exists a unique parameter and a positive integer such that the following is true. The horizon is exactly of class at , for every , moreover is only differentiable, but not of class at every point for which . Moreover, if is the endpoint of only one generator then for a suitable space-like submanifold the first cut point of R along γ is . Furthermore, all the points , for which , are non-injectivity points of R along Moreover, if is smooth at an interior point of γ, then is smooth at every point of γ. MSC 53C50 [ABSTRACT FROM AUTHOR] |
