Advances in Theoretical and Mathematical Physics
Volume 19 (2015)
Pages: 747 – 760
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 the existence of a causal boundary for $(M,g)$. 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 state and compare different versions of the weak cosmic censorship conjecture with precise geometric assumptions.