While I have divided this topic into three subsections, there is considerable overlap. The primary questions can be formulated as the cosmic censorship conjecture. The weak cosmic censorship conjecture [209] requires a singularity formed from regular, asymptotically flat initial data to be hidden from an external observer by an event horizon. An excellent review of the meaning and status of weak cosmic censorship has been given by Wald [245]. Counter examples have been known for a long time but tend to be dismissed as unrealistic in some way. The strong form of the cosmic censorship conjecture [210] forbids timelike singularities, even within black holes.

2.1 Naked singularities and the hoop conjecture

2.1.1 Overview

2.1.2 Naked spindle singularities?

2.1.3 Recent results

2.1.4 Going further

2.2 Critical behavior in collapse

2.2.1 Gravitational collapse simulations

2.2.2 Critical solutions as an eigenvalue problem

2.2.3 Recent results

2.2.4 Going further

2.3 Nature of the singularity in charged or rotating black holes

2.3.1 Overview

2.3.2 Numerical studies

2.3.3 Going further

2.1.1 Overview

2.1.2 Naked spindle singularities?

2.1.3 Recent results

2.1.4 Going further

2.2 Critical behavior in collapse

2.2.1 Gravitational collapse simulations

2.2.2 Critical solutions as an eigenvalue problem

2.2.3 Recent results

2.2.4 Going further

2.3 Nature of the singularity in charged or rotating black holes

2.3.1 Overview

2.3.2 Numerical studies

2.3.3 Going further

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