Jan Sbierski: A dezornification of the proof of the existence of a maximal Cauchy development for the Einstein equations

In 1969, Choquet-Bruhat and Geroch showed that there exists a unique maximal Cauchy development of given initial data for the Einstein equations. Their proof, however, has the unsatisfactory feature that it relies crucially on the axiom of choice in the form of Zorn's lemma. In particular, their proof ensures the existence of the maximal development without actually constructing it.

In this talk, we present a proof of the existence of a maximal Cauchy development which avoids the use of Zorn's lemma and, moreover, provides an explicit construction of the maximal development.