Global stability of spacetimes with supersymmetric compactifications

TL;DR

This paper proves the stability of certain high-dimensional spacetimes with supersymmetric compactifications, including Calabi-Yau manifolds, under Einstein vacuum evolution, challenging previous instability claims.

Contribution

It establishes the stability of Ricci-flat compactifications with special holonomy, providing a rigorous mathematical foundation for their role in supergravity and string theory.

Findings

Stability of product spacetimes with Ricci-flat compact manifolds.

Counterexample to Penrose's instability argument.

Reinforces the physical relevance of supersymmetric compactifications.

Abstract

This paper proves the stability, with respect to the evolution determined by the vacuum Einstein equations, of the Cartesian product of high-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 proved in this paper provides a counter example to an instability argument by Penrose.