List of Figures

	Figure 1: Heuristic illustration of the hoop conjecture.
	Figure 2: This figure is based on Figure 1 of [208]. The vertical axis is time. The blue curve shows the singularity and the red curve the outermost marginally trapped surface. Note that the singularity forms at the poles (indicated by the blue arrow) before the outermost marginally trapped surface forms at the equator (indicated by the red arrow).
	Figure 3: This figure is the final frame of an animation of Type II critical behavior in Einstein–Yang–Mills collapse. Note the echoing in the near-critical solution. For the entire movie and related references see [78].
	Figure 4: Figure 1 from [66] is a schematic diagram of the singularity structure within a spherical charged black hole.
	Figure 5: The algorithm of [39] is used to generate a Mixmaster trajectory with more than 250 bounces. The trajectory is shown in the rescaled anisotropy plane with axes $β±∕\|Ω \|$ . The rescaling fixes (asymptotically) the location of the bounces.
	Figure 6: Behavior of the gravitational wave amplitude at a typical spatial point in a collapsing $U (1)$ symmetric cosmology. For details see [43, 37].