Global solutions of the Einstein-Maxwell equations in higher dimensions

Details Global solutions of the Einstein-Maxwell equations in higher dimensions Global solutions of the Einstein-Maxwell equations in higher dimensions

2006-08-24

arxiv.org/abs/gr-qc/0608108v2

Class.Quant.Grav. 23 (2006) 7383-7394

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

minor corrections

Scientific paper

10.1088/0264-9381/23/24/011

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 $r^{-(n-1)/2}$.

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