We present recent work with A. Ionescu on the stability of the simplest equilibrium in the Einstein-massive-scalar field system. This is one of the simplest model from general relativity that introduces a "matter-field" (where information propagates slower than the speed of light). One of the novel aspects is that we start with initial data which are rather general: the decay of the metric is slower than the "mass term" 1/r and consistent with the assumptions on the second fundamental form (i.e. time slices are not necessarily maximal or "almost radially symmetric"). Speaker(s): Benoit Pausader (Brown University)