Cosmological singularity theorems and black holes

Abstract

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. We illustrate how they can be used to rule out some cosmological scenarios.

References added

References in corpus (1)

• Globally hyperbolic spacetimes can be defined as "causal" instead of "strongly causal"

Cited by in corpus (5)

• The 1965 Penrose singularity theorem
• On the initial singularity and extendibility of flat quasi-de Sitter spacetimes
• Newtonian Potential and Geodesic Completeness in Infinite Derivative Gravity
• Exotic Fluids Matching the Stress-Energy Tensor of Alcubierre Warp Drive Spacetimes
• Topology of Cosmological Black Holes