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Global solutions of the Einstein-Maxwell equations in higher dimensions

Yvonne Choquet-Bruhat·Piotr T. Chrusciel·Julien Loizelet
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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 $r^{-(n-1)/2}$.

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Yvonne Choquet-Bruhat, Piotr T. Chrusciel, Julien Loizelet. 2006-11-01. Global solutions of the Einstein-Maxwell equations in higher dimensions. https://doi.org/10.1088/0264-9381%2F23%2F24%2F011

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