The to zero limit of spacetimes and its physical interpretation

We study the λ → 0 behaviour of Schwarzschild-de Sitter spacetime and show, according to Geroch's notion of spacetime limits, that it converges to the Schwarzschild spacetime. We use an embedding into AdS ₃ to illustrate and quantify this limiting behaviour. We use these quantitative observations to establish a hierarchy of validity between the Einstein-de Sitter equations and the Einstein equations (and therefore in a weak field limit also Newton's equations), analogous to the quantum-classical limit when taking h → 0.