Global solutions of the Einstein-Maxwell equations in higher dimensions

TL;DR

This paper extends the stability analysis of Einstein-Maxwell equations to higher dimensions, proving global existence and completeness of solutions close to Minkowski space, with detailed conformal structure and decay properties.

Contribution

It applies Lindblad-Rodnianski stability proof to higher dimensions and uses conformal methods to establish global stability and completeness results.

Findings

Stability proof applies for all dimensions n ≥ 3

Solutions are geodesically complete and have smooth conformal infinity

Gravitational fields decay at a rate of r^{-(n-1)/2}

Abstract

We consider the Einstein-Maxwell equations in space-dimension $n$. We point out that the Lindblad-Rodnianski stability proof applies to those equations whatever the space-dimension $n\ge 3$. In even space-time dimension $n+1\ge 6$ we use the standard conformal method on a Minkowski background to give a simple proof that the maximal globally hyperbolic development of initial data sets which are sufficiently close to the data for Minkowski space-time and which are Schwarzschildian outside of a compact set lead to geodesically complete space-times, with a complete Scri, with smooth conformal structure, and with the gravitational field approaching the Minkowski metric along null directions at least as fast as $r^{-(n-1)/2}$.