Cosmological singularity theorems and black holes

Understand

An extension of Penrose's singularity theorem is proved for spacetimes where black holes are allowed to form from non-singular initial data.

• With standard assumptions about the spacetime, and assuming the existence of a trapped surface which lies outside of black hole horizons and is not completely surrounded by horizons, we show that the spacetime region outside (or on) the horizons must contain singularities.
• If the trapped surface is surrounded by horizons, we show that the horizons divide spacetime into causally disconnected pieces.
• Unlike the original Penrose's theorem, our theorems provide some information about the location of singularities.