Global stability of spacetimes with supersymmetric compactifications

Abstract

This paper proves the stability, with respect to the evolution determined by the vacuum Einstein equations, of the Cartesian product of higher-dimensional Minkowski space with a compact, Ricci-flat Riemannian manifold that admits a spin structure and a nonzero parallel spinor. Such a product includes the example of Calabi–Yau and other special holonomy compactifications, which play a central role in supergravity and string theory. The stability result proved in this paper shows that Penrose’s instability argument [2003] does not apply to localised perturbations.