THE GLOBAL STABILITY OF THE KALUZA-KLEIN SPACETIME

Cécile Huneau (1) , Annalaura Stingo (1) , Zoe Wyatt (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 DPMMS - Department of Pure Mathematics and Mathematical Statistics

In this paper we show the classical global stability of the flat Kaluza-Klein spacetime, which corresponds to Minkowski spacetime in R 1+4 with one direction compactified on a circle. We consider small perturbations which are allowed to vary in all directions including the compact direction. These perturbations lead to the creation of massless modes and Klein-Gordon modes. On the analytic side, this leads to a PDE system coupling wave equations to an infinite sequence of Klein-Gordon equations with different masses. The techniques we use are based purely in physical space using the vectorfield method.

Domains: Analysis of PDEs [math.AP]

Cécile Huneau, Annalaura Stingo, Zoe Wyatt. THE GLOBAL STABILITY OF THE KALUZA-KLEIN SPACETIME. 2023. ⟨hal-04269692⟩