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 3. In even spacetime dimension n + 1 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 spacetime and which are Schwarzschildian outside of a compact set lead to geodesically complete spacetimes, with a complete Scri, with a 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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