Remarks on evolution of space-times in 3+1 and 4+1 dimensions

TL;DR

This paper constructs a broad class of vacuum space-times in 4+1 dimensions from hyperboloidal initial data, which are complete, smooth, and extend through their horizons, with implications for 3+1 dimensions via dimensional reduction.

Contribution

It introduces a new method to generate large classes of vacuum space-times in higher dimensions without small perturbation assumptions.

Findings

Space-times are future geodesically complete.

They are smooth up to null infinity.

They extend through their Cauchy horizon.

Abstract

A large class of vacuum space-times is constructed in dimension 4+1 from hyperboloidal initial data sets which are not small perturbations of empty space data. These space-times are future geodesically complete, smooth up to their future null infinity, and extend as vacuum space-times through their Cauchy horizon. Dimensional reduction gives non-vacuum space-times with the same properties in 3+1 dimensions.