  We define different notions of black holes, event horizons and Killing
horizons for a general time-oriented manifold $(M,g)$ extending previous
notions but without the assumption of asymptotical flatness. The notions of
'horizon' are always conformally invariant while the notions of 'black hole'
are genuinely geometric. Some connections between the different notions are
found. Finally, we put the definitions into the context of the weak cosmic
censorship conjecture.
