  In this thesis we present partial progress towards the dynamic formation of
black holes in the four-dimensional Einstein vacuum equations from
Christodoulou's short-pulse ansatz. We identify natural scaling in a putative
solution metric and use the technique of real blowup to propose a
desingularized manifold and an associated rescaled tangent bundle (which we
call the "short-pulse tangent bundle") on which the putative solution remains
regular. We prove the existence of a solution solving the vacuum Einstein
equations formally at each boundary face of the blown-up manifold and show that
for an open set of restricted short-pulse data, the formal solution exhibits
curvature blowup at a hypersurface in one of the boundary hypersurfaces of the
desingularized manifold.
  This thesis is intended to be partially expository. In particular, this
thesis presents an exposition of double-null gauges and the solution of the
characteristic initial value problem for the Einstein equations, as well as an
exposition of a new perspective of Christodoulou's monumental result on the
dynamic formation of trapped surfaces.
