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

Asymptotic description of the formation of black holes from short-pulse data