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We prove global existence for Einstein's equations with a charged scalarfield for initial conditions sufficiently close to the Minkowski spacetimewithout matter. The proof relies on generalized wave coordinates adapted to theoutgoing Schwarzschild light cones and the estimates for the masslessMaxwell-Klein-Gordon system, on the background of metrics asymptoticallyapproaching Schwarzschild at null infinity in such coordinates, by Kauffman.The generalized wave coordinates are obtained from a change of variables,introduced by Lindblad, to asymptotically Schwarzschild coordinates at nullinfinity. The main technical advances are that the change of coordinates makescritical components of the metric decay faster, making the quasilinear waveoperator closer to the flat wave operator, and that commuting with modified Liederivatives preserves the geometric null structure, improving the error terms.This improved decay of the metric is essential for proving our stabilityresult, and will likely be useful in other contexts as well.

Global stability of Minkowski space for the Einstein-Maxwell-Klein-Gordon system in generalized wave coordinates