The to zero limit of spacetimes and its physical interpretation

Abstract

We study the 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 AdS3 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 .