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arxiv: 1309.7591 · v3 · pith:3L2632EDnew · submitted 2013-09-29 · 🌀 gr-qc · math-ph· math.AP· math.DG· math.MP

On the Existence of a Maximal Cauchy Development for the Einstein Equations - a Dezornification

Jan Sbierski This is my paper
classification 🌀 gr-qc math-phmath.APmath.DGmath.MP
keywords developmentmaximalcauchyeinsteinequationsexistencegloballyhyperbolic
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In 1969, Choquet-Bruhat and Geroch established the existence of a unique maximal globally hyperbolic 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 this paper we present a proof that avoids the use of Zorn's lemma. In particular, we provide an explicit construction of this maximal globally hyperbolic development.

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    Introduces Lorentzian spaces as a weakening of Lorentzian length spaces and considers pointed Gromov-Hausdorff metrics, non-spacetime maximal examples, and canonical Cauchy development representatives.