Maximal Globally Hyperbolic Development

A maximal globally hyperbolic development of initial data is a solution of the evolution equations containing the initial manifold as a Cauchy surface, into which every other globally hyperbolic development of the same data embeds compatibly. The abbreviation is MGHD. For smooth vacuum Einstein data it is considered up to an isometry preserving the initial embedding and time orientation. Maximality among globally hyperbolic developments does not exclude extensions that lose global hyperbolicity. Strong cosmic censorship asks whether such extensions are generically impossible at a specified metric regularity.