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Global stability of spacetimes with supersymmetric compactifications

Lars Andersson, Pieter Blue, Zoe Wyatt and Shing-Tung Yau

Vol. 16 (2023), No. 9, 2079–2107
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.

Keywords
Einstein equation, stability, initial-value problem, SUSY
Mathematical Subject Classification
Primary: 35L15, 35Q76, 53C25, 83E30
Milestones
Received: 30 November 2020
Revised: 25 February 2022
Accepted: 25 March 2022
Published: 11 November 2023
Authors
Lars Andersson
Albert Einstein Institute
Max–Planck Institute for Gravitational Physics
Potsdam
Germany
Pieter Blue
School of Mathematics
Maxwell Institute for Mathematical Sciences
University of Edinburgh
Edinburgh
United Kingdom
Zoe Wyatt
Department of Pure Mathematics & Mathematical Statistics
Faculty of Mathematics
University of Cambridge
Cambridge
United Kingdom
Shing-Tung Yau
Center of Mathematical Sciences and Applications
Harvard University
Cambridge, MA
United States
Yau Mathematical Sciences Center
Tsinghua University
Beijing
China

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