Existence of non-trivial, vacuum, asymptotically simple space-times

TL;DR

This paper constructs new non-trivial vacuum space-times with a complete null infinity by extending initial data across boundaries, utilizing gluing techniques, and achieving configurations that are Schwarzschild near infinity and horizons.

Contribution

It introduces novel extension results for initial data sets and demonstrates their application in creating vacuum space-times with specific asymptotic and horizon properties.

Findings

Existence of vacuum space-times with a complete Scri.

Initial data can be glued to Schwarzschild near infinity and horizons.

Extension results facilitate new constructions in general relativity.

Abstract

We construct non-trivial vacuum space-times with a global Scri. The construction proceeds by proving extension results across compact boundaries for initial data sets, adapting the gluing arguments of Corvino and Schoen. Another application of the extension results is existence of initial data which are exactly Schwarzschild both near infinity and near each of the connected component of the apparent horizon.