Pieter Blue: On the stability of higher dimensions
Time: Tue 2019-11-26 11.00 - 12.00
Participating: Pieter Blue, University of Edinburgh
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. This talk will show that these spaces are stable as solutions of the Einstein equation when n is sufficiently large and, at least, when the internal space is a torus.
This requires taking the intersection of methods for quasilinear wave and Klein-Gordon equations. This stability result is a related to a conjecture of Penrose concerning the validity of string theory.