Abstract:

There is a large class of Kaluza-Klein type spaces given by the Cartesian product of $1+n$ dimensional Minkowski space with a Ricci-flat Riemannian manifold, called the internal space. These are solutions of the Einstein equation. We will refer to these as SUSY spacetimes. These spaces are stable as solutions of the Einstein equation when $n$ is sufficiently large. The argument uses the intersection of methods for quasilinear wave and Klein-Gordon equations. This stability result is related to a conjecture of Penrose concerning the validity of string theory. I will outline some of the challenges in extending this to $n=3$.

This is joint work with Lars Andersson, Zoe Wyatt, and Shing-Tung Yau.

Organizers: Lars Andersson, Bowen Zhao