“…This condition is obviously violated for a spacelike slice in a homogeneous, spatially flat FLRW universe. 2 Interestingly, the problem of global non-linear stability for black holes has recently been solved for slow-rotating black holes in a de Sitter universe [16], 3 while the corresponding problem for asymptotically flat spacetimes remains one of the big challenges in the field of mathematical relativity, see [20,19,2,3,13,14] for recent progress on the linearised problem and [18] for the full non-linear problem under strong constraints. In this paper we will use the qualitative properties of how the Λ → 0 limit is approached to give a heuristic argument that the Einstein equations are a legitimate approximation to the fundamental Einstein-de Sitter equations, for calculations in the short-range regime.…”