On maximal globally hyperbolic vacuum space-times

TL;DR

This paper proves the existence and uniqueness of maximal globally hyperbolic vacuum space-times derived from initial data in Sobolev spaces, advancing the mathematical understanding of Einstein's equations.

Contribution

It establishes the well-posedness of the vacuum Einstein equations for initial data in Sobolev spaces with minimal regularity assumptions.

Findings

Existence of maximal globally hyperbolic developments

Uniqueness of these developments

Applicability to initial data in Sobolev spaces

Abstract

We prove existence and uniqueness of maximal global hyperbolic developments of vacuum general relativistic initial data sets with initial data (g,K) in Sobolev spaces $H^s\oplus H^{s-1}$ with integer s > n/2 +1.